text:
Wikiversity:Vision/2010

}

Community goals
this section is for ways to make Wikiversity more useful for the Wikiversity community.

Usability goals
this section is for ways to improve the usability of Wikiversity by making changes to Wikiversity.

Merge School and Topic namespaces
Confusion about whether something is a school, a department, or a topic is still a problem a year later. How are people using the school namespace? How are people using the topic namespace? How are people deciding which namespace to use for what?

Some sampling:

 * There is School:Medicine and Topic:Medicine.
 * There is School:Computer science and Topic:Computer science
 * There is School:Accounting and Topic:Accounting
 * There is School:Biology and Topic:Biology
 * There is School:Chemistry and Topic:Chemistry
 * There is School:Physics and Topic:Physics
 * There is School:Astronomy and Topic:Astronomy
 * There is School:Geography and Topic:Geography
 * There is School:History and Topic:History
 * There is School:Law and Topic:Law
 * There is School:Business and Topic:Business

Most of the topic pages in the sampling redirect to the school pages. How are people using the topic namespace? The answer appears to be as redirects. How are people using the school namespace? The answer appears to be to list other schools, since topics redirect to schools. If every topic can eventually be turned into a school than there appears to be no community need for both a topic and a school namespace. The straightforward solution would be to merge topics into schools, however topics are more definitive for learners to understand. I propose that the school namespace be dropped and the topic namespace be used in its place. -- dark lama  15:01, 26 March 2010 (UTC)
 * see also Vision/2009/Namespace reform, Erkan Yilmaz uses the Chat (try) 15:07, 26 March 2010 (UTC)

Discussion
I'm not much a fan of the Topic: and School: namespaces myself - content in there seems to go cold. I wouldn't be unhappy with all the content from Topic: and School: going into the main space. -- Jtneill - Talk - c 18:35, 26 March 2010 (UTC)

I have a sample organizational scheme that we could discuss upon. Since Wikiversity is a university of open learning, I say we adopt a formal layout of all the schools, departments, and topics. Something along the lines of this:

My suggestion is to break the university down into 7 major colleges (or faculties):
 * 1) Agriculture
 * 2) Business Administration
 * 3) Engineering
 * 4) Environmental Design
 * 5) Humanities
 * 6) Science
 * 7) Social Sciences

A sample "college" might look something like this:

COLLEGE OF ENGINEERING
 * Aerospace Engineering Department
 * Chemical & Materials Engineering Department
 * Civil Engineering Department
 * Electrical & Computer Engineering Department
 * Engineering Technology Department
 * Industrial & Manufacturing Engineering Department
 * Mechanical Engineering Department

In addition, under each department can have subtopics.

By adopting this organization scheme, we then can start categorizing "classes" with an agreed acronym for each department. Take physics for example, we can agree to name it (PHY) and have all relevant courses and information numbered under that acronym (other acronyms can include something like CE=Civil Engineering, ECE = Electrical and Computer Engineering, etc..) Man4857 04:25, 3 December 2010 (UTC)

Outreach goals
this section is for ways to attract and get more people involved with Wikiversity through outreach efforts.
 * Has anyone tried asking our friends who can read/write or teach?

title: Wikiversity:Vision/2010


text:
User:Eml4500.f08.bottle.butler/HW 5

Principle of Virtual Work
We derive $$ k^{(e)}_{4X4}=T^{(e)^{T}}_{4X2}\hat{k}^{(e)}_{2X2}T^{(e)}_{2X4} $$ Recall the FD relationship with axial dof's $$q^{(e)}: \! $$ $$ \hat{k}^{(e)}_{2X4}q^{(e)}_{2X1}=p^{(e)}_{2X1} $$ $$ \Rightarrow equation (1) \hat{k}^{(e)}q^{(e)}-p^{(e)}= 0_{2X1}\! $$ Therefore: $$ \hat{W}_{2X1}\circ \underbrace{(\hat{k}^{(e)}q^{(e)}-p^{(e)})}_{2X1}=0_{1X1}$$ for all $$ \hat{W}_{2X1} \! $$

Recall that $$ q^{(e)}_{2X1}=T^{(e)}_{2X4}d^{(e)}_{4X1} $$ similarly, $$ \hat{w_{2X1}}=T^{(e)}_{2X4}w_{4X1}$$ where $$\hat{w}_{2X1}$$ is the virtual displacement corresponding to $$q^{(e)}_{2X1}$$ and $$w_{4X1} \!$$ is the virtual displacement in the global coordinate system corresponding to $$d^{(e)}_{4X1}$$

If we place equation $$ (3) \! $$ and $$ (4) \! $$ in equation $$ (2) \! $$ then we get $$ equation(5) = \! $$$$ (T^{(e)}w)\circ [\hat{k}^{(e)}(T^{(e)}d^{(e)})-P^{(e)}] =0 $$ for all $$ w_{4X1} \!$$

Recall: $$ equation (6) = \! $$$$ (AB)^{T}=B^{T}A^{T}\! $$  (see below for proof) and $$ equation (7) = \!$$ $$a\circ b=a^{T}b$$ Substituting equations $$ (6) \!$$ and $$ (7) \!$$ into $$ (5) \!$$ we get $$(T^{(e)}w)^{T}[\hat{k}^{(e)}(T^{(e)}d^{(e)})-P^{(e)}]=0_{1X1} $$ for all $$ w_{4X1} \! $$ $$ \Rightarrow w^{T}T^{(e)}[\hat{k}^{(e)}(T^{(e)}d^{(e)})-P^{(e)}]-0 $$ $$ \Rightarrow w\circ [\underbrace {(T^{(e)^{T}}\hat{k}^{(e)}T^{(e)})}_{k^{(e)}}d^{(e)}-\underbrace {(T^{(e)^{T}}P^{(e)})}_{f^{(e)}}]$$ for all $$ w_{4X1} \! $$  $$ \Rightarrow w\circ [k^{(e)}d^{(e)}-f^{(e)}]=0 $$ for all $$ w \! $$  therefore $$ k^{(e)}d^{(e)}=f^{(e)} \!$$

Continuous Case with PDE's
Motivational Model Problem: Elastic Bar with varying $$ A(x) \! $$ and $$ E(x) \! $$, subject to a varying axial load (distributed load), concentrated loading, and inertial forces (damping).

image $$ \sum{F_{x}}=0=-N(x,t)+N(x +dx, t)+f(x,t)dx-m(x)\ddot{u} \! $$ $$ equation (1) \! $$$$=\frac{\partial N}{\partial x}+h.o.t.+f(x,t)-m(x)\ddot{u}dx \! $$ neglecting the higher order terms, we recall the Taylor series expansion: $$f(x+dx)=f(x)+\frac{df(x)}{dx}+ \underbrace {\frac{1}{2}\frac{d^{2}f(x)}{dx^{2}}dx^{2}+\cdots}_{h.o.t.} $$

Equation $$ (1) \! $$ becomes $$ equation (2) = \! $$$$\frac{\partial N}{\partial x}+f=m\ddot{u}\! $$ the equation for the motion of the elastic bar $$ equation (3)= \! $$ $$ N(x,t)=A(x)\underbrace {\sigma (x)}_{E(x)\underbrace {\varepsilon (x,t)}_{\frac{\partial u (x,t)}{\partial x}}}$$ equation $$ (3) \! $$ into equation $$ (2) \! $$ yields: $$ \frac{\partial }{\partial x}[A(x)E(x)\frac{\partial u}{\partial x}]+f(x,t)=m(x)\underbrace {\ddot{u}}_{\frac{\partial ^{2}u}{\partial t^{2}}} $$ In order to solve this problem, we need 2 boundary conditions and 2 initial conditions.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: User:Eml4500.f08.bottle.butler/HW 5


text:
User:Eml4500.f08.team.guan/fixed108

 HW Redo: The derivation for the transverse displacement degrees of freedom is added. The figure of the elemental subject to axial and transverse degrees of freedom and forces is also added.

Transforming Local Degrees of Freedom
Goal: Want to find $$ \tilde{\mathbf{T}}^{(e)}$$ that frames fom the set of local (element) definions $$\boldsymbol{d}^{(e)}$$ to another set of local (element) defs $$\tilde{\boldsymbol{d}}^{(e)}$$ that $$ \tilde{\mathbf{T}}^{(e)}$$ is invertible.

$$\tilde{\boldsymbol{d}}^{(e)}= \tilde{\mathbf{T}}^{(e)}\boldsymbol{d}^{(e)}$$

This image shows that one can show displacements can be made in the x and y axis but the axises can also be aligned along the length of the beam. This causes the x~ axis displacement to be either tension or compression.

$$\tilde{\boldsymbol{d}}^{(e)}_{1}=\boldsymbol{q}^{(e)}_{1}$$ (comp of $$\tilde{\boldsymbol{d}}^{(e)}_{[1]} $$ along the $$\jmath $$ also known as $$\tilde{y}$$ axis

(1) $$ \tilde{\boldsymbol{d}}^{(e)}_{1}= \begin{bmatrix} l^{(e)} & m^{(e)} \end{bmatrix} \begin{Bmatrix} d_{1}^{(e)}\\ d_{2}^{(e)} \end{Bmatrix} $$

$$\tilde{\boldsymbol{d}^{(e)}_{2}=\boldsymbol{d}}^{(e)}_{[1]}\jmath$$

$$=-\sin \theta ^{e}d_{1}^{(e)}+ \cos \theta ^{e}d_{2}^{(e)}$$

(2) $$ \tilde{\boldsymbol{d}}^{(e)}_{2}= \begin{bmatrix} -m^{(e)} & l^{(e)} \end{bmatrix} \begin{Bmatrix} d_{1}^{(e)}\\ d_{2}^{(e)} \end{Bmatrix} $$

Put (1) and (2) together in matrix form

$$ \begin{Bmatrix} \tilde{d}_{1}^{(e)}\\ \tilde{d}_{2}^{(e)} \end{Bmatrix} = \begin{Bmatrix} l^{(e)} & m^{(e)}\\ -m^{(e)} & l^{(e)} \end{Bmatrix} \begin{Bmatrix} d_{1}^{(e)}\\ d_{2}^{(e)} \end{Bmatrix} $$

$$ R^{(e)}= \begin{Bmatrix} l^{(e)} & m^{(e)}\\ -m^{(e)} & l^{(e)} \end{Bmatrix} $$

$$ \begin{Bmatrix} \tilde{d}^{(e)}_{1}\\ \tilde{d}^{(e)}_{2}\\ \tilde{d}^{(e)}_{3}\\ \tilde{d}^{(e)}_{4} \end{Bmatrix} =\begin{bmatrix} \boldsymbol{R}^{(e)} & \boldsymbol{0}\\ \boldsymbol{0} & \boldsymbol{R}^{(e)} \end{bmatrix} \begin{Bmatrix} d^{(e)}_{1}\\ d^{(e)}_{2}\\ d^{(e)}_{3}\\ d^{(e)}_{4} \end{Bmatrix} $$

$$\boldsymbol{R}^{(e)}$$ is a 2x2 matrix $$\boldsymbol{0}^{(e)}$$ is a 2x2 0 matrix.

$$\tilde{\boldsymbol{f}}^{(e)} = K^{(e)}\begin{bmatrix} 1 & 0& -1 &0 \\ 0 &0  & 0 & 0\\ -1 &0  & 1 & 0\\ 0 & 0 & 0 &0 \end{bmatrix} \tilde{\boldsymbol{d}}^{(e)} $$

This means only the forces that act on the beam are the ones along beam. This means the force either acts a compression or tension.

Transverse forces do not stretch the springs.

title: User:Eml4500.f08.team.guan/fixed108


text: File:Axialtravdof.JPG

title: File:Axialtravdof.JPG


text:
User:Eml4500.f08.ateam.carr/HW5

Composite Materials
Composite materials consist of a strengthening fiber and matrix substrate. The addition of these fibers to a substrate is termed 'doping'. Due to the mixed material properties, composite materials often contain a varying elastic modulus. In other words, the Young's modulus is a function of position in the material.

Some examples of composite materials with this characteristic:

 * Carbon fiber
 * Fiber Glass

The Elastic Modulus is much higher in these materials in the fiber direction (longitudinal direction). However, perpendicular to the fibers (transverse direction) the Elastic Modulus is smaller as the fibers lose their strength in shear.

Free body diagram of a rigid body cross section

$$ \sum{F_x}=0=-N(x,t) + N(x+dx,t)+f(x,t)dx-m(x)\ddot{u}dx $$

$$ \sum{F_x}=0=\frac{\delta N}{\delta x}(x,t)dx+H.O.T.+f(x,t)dx-m(x)\ddot{u}dx $$

Cancel dx and neglect the higher order terms (H.O.T.)

(Eqn. 1): $$ \sum{F_x}=0=\frac{\delta N}{\delta x}(x,t)+f(x,t)-m(x)\ddot{u} $$

Recall Taylor Series Expansion:

$$f(x+dx)=f(x)+\frac{df(x)}{dx}dx+[\frac{d^2f(x)}{2dx^2}+...] $$

Where the content inside the brackets represent higher order terms.

(Eqn. 2):  $$\frac{\delta N}{\delta x}+ f =m\ddot{u} $$

Where Equation 2 represents the equation of motion(EOM) of the elastic bar.

$$ N(x,t)=A(x)\sigma(x,t) $$ where: $$ \sigma(x,t)=E(x)\epsilon (x,t)$$ and: $$ \epsilon (x,t)=\frac{\delta u}{\delta x }(x,t)$$ (Eqn. 3)

Substituting Eqn. 3 into Eqn. 2:

$$ \frac{\delta }{\delta x}(A(x)E(x)\frac{\delta u}{\delta x})+f(x,t)=m(x)\ddot{u} $$, where: $$ \ddot{u}=\frac{\delta ^2u}{\delta t^2}$$

Partial Differential Equation of Motion
In order to integrate differential equations of motion, boundary conditions are needed to evaluate the constants of integration. For the problem above, this translates to two initial conditions (due to the 2nd order nature of the equations).

Boundary Conditions:

$$u(0,t)=0=u(L,t)$$

$$u(0,t)=0$$

$$N(L,t)=F(t)$$

title: User:Eml4500.f08.ateam.carr/HW5


text:
User:Reynoldsd

My name is Danielle Reynolds and I am currently a third year student at UNC-Charlotte. I enjoy shopping, sleeping, and going out with my friends. I decided to become a teacher because I believe that it is one of the most important jobs in the world. I love kids and I believe that great teachers influence their studnts long after they have left their classrooms and would love to become a positive influence to my students.

title: User:Reynoldsd


text:
User:Jonesy22

 Project participation

 About me

 * Hi. I'm Jonesy from the Slovak Wikipedia. I will use this account mainly for small corrections if I notice errors, typos or vandalism during my research work.

  Jonesy22 Jonesy

title: User:Jonesy22


text: User talk:Jonesy22

title: User talk:Jonesy22


text: User talk:Jonesy22/Archives

title: User talk:Jonesy22/Archives


text:
User:DaniR

My name is Danielle Reynolds and I am currently a third year student at UNC-Charlotte. I enjoy shopping, sleeping, and going out with my friends. I decided to become a teacher because I believe that it is one of the most important jobs in the world. I love kids and I believe that great teachers influence their students long after they have left their classrooms and would love to become a positive influence to my students.

title: User:DaniR


title: User:Jonesy22/Icons


text:
User talk:Jenny O/Groups

Hey Jenny,

I agree with your opinion on groups of two. The dynamics of a couple or pair are completely different from a group of three or more. You only have to look at how difficult it is to make a decision in either. The process in a pair is relatively simple mostly. Add a third opinion and consensus can take forever. I think thats why group assignments are so difficult with three. Your page is great by the way!

Cheers Nikki

title: User talk:Jenny O/Groups


title: File:Disp1box3.JPG


text:
User:Eml4500.f08.team.foskey.ckf/teamHW5

Team "TEAM"

Homework 5 WIKI Report

EML4500 - Finite Element Analysis & Design

Summary of Lecture Notes - Oct. 20 through Oct 31

Oct. 20 (Meeting 24) - The Principle of Virtual Work

Oct. 22 (Meeting 25) - Exam 2 (No Lecture) ; Exam 2 solutions and grading standard ; Exam 2 grade distribution histogram

Oct. 24 - No Class (Homecoming)

Oct. 27 (Meeting 26) - The Principle of Virtual Work - Part II

Oct. 29 (Meeting 27) - The Principle of Virtual work - Part III

Oct. 31 (Meeting 28) - Introduction to Finite Element Analysis using Differential Equations

Additional Material

Space Truss Matrix Relationships

Composite Materials

Is the space truss statically indeterminate?

MATLAB Assignments

Debugging The Two Bar Truss MATLAB Code

The Six Bar Truss

The Three Bar Space Truss

All lecture note summaries are based upon the notes given in class by Dr. Vu-Quoc

Contributing Team Members

Cory Foskey Eml4500.f08.team.foskey.ckf 17:02, 5 November 2008 (UTC) Joseph Figuerrez Eml4500.f08.team.figuerrez 02:13, 6 November 2008 (UTC) Jin Yu Guan Eml4500.f08.team.guan 04:54, 7 November 2008 (UTC) James Dwyer Eml4500.f08.team.dwyer.jd 16:56, 7 November 2008 (UTC) Timothy BengtsonEml4500.f08.team.Bengtson 21:19, 7 November 2008 (UTC)


text:
User:Eml4500.f08.team.guan/fixed1013

 HW Redo: The eigenvectors and values were determined once again (correctly), more explanation and derivation was added to the math, and the eigenvectors were plotted and explained.

The originally submitted page was created in an incorrect namespace. This page represents the old page, with the things noted above. Due to the fact that this page and the original page were done in separate pages, no direct comparison is able to be made.

Eml4500.f08.team.foskey.ckf 00:46, 3 November 2008 (UTC)

Eigenvalues and Eigenvectors
Recall the eigenvalue problem of the global stiffness matrix:$$\displaystyle KV=\lambda V$$ Let $$\displaystyle $$ be the pure eigenvectors corresponding to 4 non zero eigenvalues. Zero Eigenvalues correspond to rigid body motion and zero stored elastic energy.

$$ \mathbf{k}\mathbf{u}\mathbf{i} = \mathbf{0}\mathbf{u}\mathbf{i} $$

The linear combination of $$ \left\{\mathbf{u}_{i}, i=1,...,4 \right\}$$ The equation which defines $$ \mathbf{w} $$ is $$ \sum_{i=1}^{4}{\alpha i\mathbf{u}_{i}}=:\mathbf{w} $$ w is also an eigenvector corresponding a zero eigenvalue. $$Kw=K(\sum_{i=1}^4{\alpha_i u_i})=\sum_{i=1}^4\alpha_i(Ku_i)=0=0w$$ w describes the linear combination of modal (eigenvectors) shapes. In the expression above, Ku_i equals zero and is a 6 by 1 matrix of zeros.

title: User:Eml4500.f08.team.guan/fixed1013


title: File:Eigenvectorplot1.JPG


text:
User:Eofeapr

Hello to all. It is my ambition to help develop the section on Christian Studies. Although I am a student and not an educator in Christian Studies my aim is to contribute sound and factual content for use by all who visit the section. I would encourage any who have a degree of any kind in Theology with concentration in Christianity to please help.

The other side of me is invested in Audio and Video. If you care to share your knowledge, ask questions, get someone's opinion I'd love to hear from you.

JRG

title: User:Eofeapr


text:
User:Kwj2772/monobook.js

/*Global javascript*/ mw.loader.load('https://meta.wikimedia.org/w/index.php?title=User:Kwj2772/remote.js&action=raw&ctype=text/javascript');

title: User:Kwj2772/monobook.js


text: File:Varyingtruss.jpg

title: File:Varyingtruss.jpg


text: Template:Signature

title: Template:Signature


text:
Help:Wikiquette

Good wikiquette is a bit like having polite table manners, but more importantly contributes to effective communication, efficiency, and the development of high quality content. Good wikiquette includes:
 * 1) Signing comments with your signature.
 * 2) Providing edit summaries when you make changes, particular for edits which aren't marked as minor changes.
 * 3) Avoiding the use of ALL CAPITALS (which is generally understood to mean that you are shouting), unless you really are wanting to SHOUT!!!

title: Help:Wikiquette


text:
Category:Wikiversity tips

ar:تصنيف:نصائح ويكي الجامعة

title: Category:Wikiversity tips


text:
User:Eml4500.f08.team.guan/fixed1015

 HW Redo: The free body diagrams of the elements were added. Further explanation of the math and equations were provided.

Justifying the Global Stiffness Matrix
The assembly of the elemental stiffness matrices, k(e) into a global striffness matrix, K, can be justified by reviewing the two bar truss problem.

If we look back at the Two bar truss problem, and recall the element force-displacement relation $$ k^{(e)}d^{(e)} = f^{(e)}$$, we can use the Euler Cut Principle to give the equilibrium of the node relationship.

Then, if the free body diagrams of elements 1 and 2 are considered, and the global degrees of freedom for global node 2 are compared to the degrees of freedom for elements 1 and 2, the equilibrium of the node can be confirmed. Below are the free body diagrams of element 1, element 2, and the global node number 2. It is simple to see that the forces are the global node 2 in the elemental diagrams are directed in the opposite directions of the forces in the free body diagram of global node 2. This is the convention used in statics.

Looking at the equilbrium of node 2, the addition of k values is because the forces in the x and y direction sum up to equal zero. Using a statics approach and calculating the forces in each direction gives:

$$ \Sigma F_x = 0= -f^{(1)}_3 - f^{(2)}_1=0$$     (1) $$ \Sigma F_y = 0= P-f^{(1)}_4 - f^{(2)}_2=0$$     (2)

This next step is to involve the force displacement relationship. Replacing f with kd will get the middle of the 6 by 6 global stiffness matrix. Thus, statics and equilibrium evaluation of global node 2 has verified the middle of the global stiffness matrix.

title: User:Eml4500.f08.team.guan/fixed1015


title: File:Feafbd1.JPG


title: File:Feafbd2.JPG


title: File:Feafbd3.JPG


text:
User:Eml4500.f08.team.guan/fixed1017

 HW Redo: Further explanation for the math is added. The third motivation for the PVW is added. Initial derivation of the PVW is added.

Equilibrium of Node 2:
Now, the sum of the forces in the x and the y directions are put into equation form in the following equations. Then, using the force displacement relationship, this forces in the equation are replaced with the product of the stiffness and the corresponding displacement degree of freedom.

 * Eq (1):

$$f_3^{(1)}+f_1^{(2)}=0 \quad (1)$$

 * Eq (2):

$$f_4^{(1)}+f_2^{(2)}=\underline{P}\quad (2)$$

 * From p 8-3:

$$d_3=d_3^{(1)}=d_1^{(2)}$$ $$d_4=d_4^{(1)}=d_4^{(2)}$$

Assembly Rows 3 & 4 From Eq (1) & (2) into:
Recall that the global stiffness matrix has the following values. Replacing the forces in equation one with the product of the stiffness and displacement degrees of freedom results in the following new equation one. Thus, this new equation one is consequently the third row of the global stiffnes matrix on 9.1. Also see 8.4 for the global force displacement relationship. The new equation two is similarly derived.

$$\mathbf{K}= \begin{bmatrix} k_{11}^{(1)} & k_{12}^{(1)} & k_{13}^{(1)} & k_{14}^{(1)} & 0 & 0\\k_{21}^{(1)} & k_{22}^{(1)} & k_{23}^{(1)} & k_{24}^{(1)} & 0 & 0\\k_{31}^{(1)} & k_{32}^{(1)} & (k_{33}^{(1)}+k_{11}^{(2)}) & (k_{34}^{(1)}+k_{12}^{(2)}) & k_{13}^{(2)} & k_{14}^{(2)}\\k_{41}^{(1)} & k_{42}^{(1)} & (k_{43}^{(1)}+k_{21}^{(2)}) & (k_{44}^{(1)}+k_{22}^{(2)}) & k_{23}^{(2)} & k_{24}^{(2)}\\0 & 0 & k_{31}^{(2)} & k_{32}^{(2)} & k_{33}^{(2)} & k_{34}^{(2)}\\0 & 0 & k_{41}^{(2)} & k_{42}^{(2)} & k_{43}^{(2)} & k_{44}^{(2)}\end{bmatrix}$$

$$\left [ k_{31}^{(1)}*d_1+k_{32}^{(1)}*d_2+k_{33}^{(1)}*d_3+k_{34}^{(1)}*d_4 \right ]+\left [ k_{11}^{(2)}*d_3+k_{12}^{(2)}*d_4+k_{13}^{(2)}*d_5+k_{14}^{(2)}*d_6 \right ]=0\quad (1)$$

$$\left [ k_{41}^{(1)}*d_1+k_{42}^{(1)}*d_2+k_{43}^{(1)}*d_3+k_{44}^{(1)}*d_4 \right ]+\left [ k_{21}^{(2)}*d_3+k_{22}^{(2)}*d_4+k_{23}^{(2)}*d_5+k_{24}^{(2)}*d_6 \right ]=\underline{P}\quad (2)$$

Now, an expression can be written to describe the assembly of a general (an arbitrary number of elements) global stiffness matrix using general elemental stiffness matrices. Assembly of $$\underline{k^{(e)}}$$, e = 1, ....., nel (number of elements), into global stiffness matrix K is as follows. It is necessary to denote a symbol other than $$\sum$$ to allow the below assembly expression to be possible and true. This is because the global stiffness matrix and the elemental stiffness matrices are of different dimensions where the dimensions of the global stiffness matrix can be millions by millions. Thus, simple matrix addition cannot be utilized here and another symbol other than $$\sum$$ must be used. Let "A" be this designated assembly operator.

Principle of Virtual Work (PVW)
There are three motivations for applying the principle of virtual work. 1) (p 10-1): Elimination of rows corresponding boundary conditions to obtain $$\underline{K}$$.

$$\underline{K} = \begin{bmatrix}K_{33} & K_{34}\\ K_{43} & K_{44}\\ \end{bmatrix}$$

2)(p 12-1): Element Force-Displacement Relationship described by axial forces and displacements and the transformation matrix T.

$$ \mathbf{\underset{2 \times 1}q^{(e)}}=\mathbf{\underset{2 \times 4}T^{(e)}}\mathbf{\underset{4 \times 1}d^{(e)}} $$

This leads to the following relationship:

$$	\underbrace{\begin{pmatrix}

q^{(e)}_1 \\

q^{(e)}_2 \end{pmatrix}}_{\underset{2 \times 1}q^{(e)}} = \underbrace{\begin{bmatrix}

l^{(e)} & m^{(e)} & 0 & 0 \\

0 & 0 & l^{(e)} & m^{(e)} \\ \end{bmatrix}}_{\underset{2 \times 4}T^{(e)}}\underbrace{\begin{pmatrix}

d^{(e)}_1 \\ d^{(e)}_2 \\ d^{(e)}_3 \\ d^{(e)}_4 \end{pmatrix}}_{\underset{4 \times 1}d^{(e)}}$$

$$\mathbf k^{e} = \mathbf {T^{(e)^T} \hat k^{(e)} T^{(e)}}$$ 3) Deriving the finite element method for partial differential equations (PDEs). Let's begin by stating the force displacement relationship for a bar of a spring. $$\displaystyle Kd=F, Kd-F=0...(3)$$ $$\displaystyle w(Kd-F)=0$$ for all w $$\displaystyle ...(4)$$ Equation four is the "weak form" which is the principle of virtual work. The proof is as follows. a) The fact that equation 3 implies equation 4 is trivial. One can just plug in equation 3 into 4 and get zero. b) However equation 4 implying equation 3is not trivial since equation 4 is valid for all w. You can select any arbitrary value say w=1 then equation 4 becomes 1(Kd-F)=0. Therefore, equation 3 is obtained.

title: User:Eml4500.f08.team.guan/fixed1017


text:
User:Sandy~enwikiversity/Week 5 Prejudice

Prejudice
A negative attitude, or feeling, towards a person purely because they are a member of a certain group.
 * Discrimination – unequal (positive or negative) treatment bases on group membership e.g. woman in particular roles
 * Stereotypes – beliefs that associate groups with certain traits e.g. indigenous alcoholism
 * Subtypes – categories for people who don’t fit in to a general stereotype e.g. woman in the fire brigade

Categorisation – a natural human tendency to group object

Social Categorisation – sorting people in to groups based on their common characteristics e.g. men.

Cognitive Miser – to think in simple ways e.g. we sort people into categories to predict behaviour

Prejudice and intergroup Relations

 * Outgroup members (them) – belonging to another group
 * Ingroup members – (us) – the group I belong to
 * Out-group homogeneity bias – the assumption that the outgroup members have more in common than ingroups e.g. they all look the same
 * Eyewitnesses are more accurate when identifying people in their own racial group and angry outgroup members are easier to identify than angry ingroup members

Common Prejudices and Targets
Racial prejudice (racism) Gender prejudice (sexism) Overweight anti-fat attitudes begin as early as preschool The overweight stigma is that it is socially unappealing Both men and woman are intolerant of homosexuality in their own gender through perhaps the possible fear of a homosexual making advance on them or they may fear they’ll have a positive response to advances
 * Most prejudices come are the result of external characteristics such as the colour of the skin
 * Gender and race are the most common groups
 * Other common groups are Arabs (since September 11, 2001), overweight people and homosexuals (homophobia)
 * Stigma by association – discrimination towards those associated with the stigmatised person
 * Most people claim they are not prejudice but their behaviour can differ from the attitudes they express

Racism
Prejudice attitudes toward a particular group. It is much more subtle today than in the past.

Aversive Racism Holding egalitarian values (everyone is equal) and negative feelings at the same time. Believing in racial equality and equal opportunity while feeling uncomfortable around and trying to avoid minorities where possible.

Discrimination
The unequal treatment of different people purely because of the groups or categories they belong to.

A B C of Intergroup Relationships
People are increasingly aware of what is socially acceptable (social identity theory)
 * Affective (emotional) component – prejudice
 * Behavioural component – discrimination (action taken not giving)
 * Cognitive component – stereotyping (putting people in groups)

Why Prejudice Exists

 * Our tendency to hold stereotypes and prejudices may be inborn. We learn the content of stereotypes through socialisation
 * We seem to automatically know stereotypes and have to consciously work to override them
 * We have ingroup favouritism and give preferential treatment to our own group members
 * Ingroup favouritism still occurs even if the group is randomly selected
 * Rationalisation for oppression – a powerful group retains its power through the use of stereotypes and prejudices
 * Prejudice and self-esteem – it can be self-affirming and if other groups are inferior ours must be superior. We also like to compete.
 * Culture increases the importance of stereotypes and helps us to deal with our social world
 * Stereotypes allow us to take mental shortcuts. “The law of least effort”(Allport)

Us Versus Them: Groups in Competition
Discontinuity Effect Reduce intergroup competitiveness
 * Groups are more competitive than individuals and are motivated by greed or fear.
 * Realistic conflict theory – competing for a lack of resources leads to intergroup hostility
 * Create subordinate goals where the groups need to solve a problem or work together
 * Get the groups to look at the long-term effect of their action
 * By making the group member identifiable

Inner Processes
 * Although most stereotypes are negative they can also positive e.g. all Ethiopians are good long distance runners
 * The negative stereotypes last longer and it takes more exceptions to dispel a bad stereotype
 * Stereotypes can be formed on features that aren’t the norm and stand out (salience)
 * Scapegoat theory blames problems on the outgroup which in turn contributes and confirms the negative views
 * Self-serving bias – when things go right we attribute it to ourselves but when things wrong we blame another cause such as others or our environment
 * We behave aggressively to outgroups when things are going tough
 * Conflict and stress bring out stereotypes
 * To confirm our biases we use our existing stereotypes

Overcoming Stereotypes and Reducing Prejudice

 * We need to consciously override our prejudices and stereotypes
 * We have internal (morally wrong) and external (not socially acceptable) motivations to our prejudices and stereotypes
 * If we are accused of prejudice we tend to overcompensate or discriminate in reverse to prove the opposite
 * If we have frequent contact with a person or group this may reduce our prejudice

Impact of Prejudice of Targets
Self-fulfilling Prophecy
 * Our prediction may influence our behaviour which in turn may prove our prediction
 * Some target begin to behave the way they are stereotyped to behave

Self-defeating Prophecy
 * Our prediction may influence our behaviour which in turn may make the prediction not come true

Contact Hypothesis There needs to be equal status The social norms need to favour the equality The contact must be sustained The groups need to cooperate The groups need to be perceived as similar
 * Direct contact reduces prejudice, but:

Blue Eye Brown Eye Study - Reflections
It was very interseting to see how profoundly some of the participants in this experiment were affected by the prejudical way in which they were treated even though they new it was an experiment.

It was not surprising to me that the two older gentlement left the experiment within the first 5 to 10 minutes. I suspect most men of their generation would expect to be spoken to in a respectful way, particularly by a woman and may also be used to holding positions with authrity. I know my father in his 70s would not tolerate it at all.

Seeing resistance at first followed by conformity and than total submission by most of the blue-eyed group was obvious in the way their manner, including body language, changed.

Seeing the brown eyed group adapt to their control over the blue eyed group was very interesting. A lot of these people had been on the 'receiving end' for all or most all of their lives but although they new what it truly felt like to be disciminated against they were happy (not in all cases) to inflict the same prejudical victimisation. A very valuable lesson in what it must feel like to be the victim of discrimination and prejudice for no apparent reason other than there's something about you that is different. In this case eye colour.


title: File:P9110052.JPG


text:
User:Eml4500.f08.group/HW5

 Warning: Must link to archived version of each part before the deadline; see below and Team Carbon as an example. Eml4500.f08 15:49, 9 November 2008 (UTC)

=Homework 5=

 * Lecture Notes (current version) (archived version)
 * MATLAB Code (current version) (archived version)
 * HW5 Contributors (current version) (archived version)

title: User:Eml4500.f08.group/HW5


text:
User:Eml4500.f08.group/HW5/Lecture Notes

=Lecture Notes=

Lecture 24: 10/20/08
Justification of eliminating rows 1, 2, 5, 6 to obtain the K2x2 in the two bar truss system: FD relation: K6x6d6x6=F6x1 $$Kd-F=0$$ Eq (1) Where 0 is a 6x1 matrix Principle of Virtual Work(PVW): $$W\cdot (Kd-F)=0$$ Eq(2) where W is the the weighting matrix (6x1)

$$Eq(1)\Leftrightarrow Eq(2)$$

Proof:

A) $$(1)\Rightarrow (2)$$ :Trivial

B) Want to show $$(2)\Rightarrow (1)$$

$$(2)\Rightarrow W\cdot (Kd-F)=0$$  for all W

$$W_{1} = 1: \mathbf{W}^{T}_{1x6} = \begin{bmatrix} 1 & 0 & 0 & 0 & 0 & 0 \end{bmatrix}_{1x6}$$

$$\mathbf{W} * (\mathbf{kd - F}) = 1 * [\sum_{j=1}^{6}{K_{1j}d_{j}} - F_{1}] + 0*[\sum_{j=1}^{6}{K_{2j}d_{j}} - F_{2}] +  0*[\sum_{j=1}^{6}{K_{3j}d_{j}} - F_{3}] +  0*[\sum_{j=1}^{6}{K_{4j}d_{j}} - F_{4}] +  0*[\sum_{j=1}^{6}{K_{5j}d_{j}} - F_{5}] +  0*[\sum_{j=1}^{6}{K_{6j}d_{j}} - F_{6}] = 0 $$

(1) $$\Rightarrow \sum_{j=1}^{6}{K_{1j}d_{j}} = F_{1}$$

$$W_{2} = 1: \mathbf{W}^{T}_{1x6} = \begin{bmatrix} 0 & 1 & 0 & 0 & 0 & 0 \end{bmatrix}_{1x6}$$

$$\mathbf{W} * (\mathbf{kd - F}) = 0*[\sum_{j=1}^{6}{K_{1j}d_{j}} - F_{1}] + 1*[\sum_{j=1}^{6}{K_{2j}d_{j}} - F_{2}] +  ... + 0*[\sum_{j=1}^{6}{K_{6j}d_{j}} - F_{6}] = 0 $$

(2) $$\Rightarrow \sum_{j=1}^{6}{K_{2j}d_{j}} = F_{2}$$

 * {| class="toccolours collapsible collapsed" width="60%" style="text-align:left"

!HW Weak Form, from team group 0 & 0 & 1 & 0 & 0 & 0 \end{bmatrix}_{1x6}$$
 * $$W_{3} = 1: \mathbf{W}^{T}_{1x6} = \begin{bmatrix}
 * $$W_{3} = 1: \mathbf{W}^{T}_{1x6} = \begin{bmatrix}

$$\mathbf{W} * (\mathbf{kd - F}) = 0*[\sum_{j=1}^{6}{K_{1j}d_{j}} - F_{1}] + ... + 1*[\sum_{j=1}^{6}{K_{3j}d_{j}} - F_{3}] +  ... + 0*[\sum_{j=1}^{6}{K_{6j}d_{j}} - F_{6}] = 0 $$

(3) $$\Rightarrow \sum_{j=1}^{6}{K_{3j}d_{j}} = F_{3}$$

$$W_{4} = 1: \mathbf{W}^{T}_{1x6} = \begin{bmatrix} 0 & 0 & 0 & 1 & 0 & 0 \end{bmatrix}_{1x6}$$

$$\mathbf{W} * (\mathbf{kd - F}) = 0*[\sum_{j=1}^{6}{K_{1j}d_{j}} - F_{1}] + ... + 1*[\sum_{j=1}^{6}{K_{4j}d_{j}} - F_{4}] +  ... + 0*[\sum_{j=1}^{6}{K_{6j}d_{j}} - F_{6}] = 0 $$

(4) $$\Rightarrow \sum_{j=1}^{6}{K_{4j}d_{j}} = F_{4}$$

$$W_{3} = 1: \mathbf{W}^{T}_{1x6} = \begin{bmatrix} 0 & 0 & 0 & 0 & 1 & 0 \end{bmatrix}_{1x6}$$

$$\mathbf{W} * (\mathbf{kd - F}) = 0*[\sum_{j=1}^{6}{K_{1j}d_{j}} - F_{1}] + ... + 1*[\sum_{j=1}^{6}{K_{5j}d_{j}} - F_{5}] + 0*[\sum_{j=1}^{6}{K_{6j}d_{j}} - F_{6}] = 0 $$

(5) $$\Rightarrow \sum_{j=1}^{6}{K_{5j}d_{j}} = F_{5}$$

$$W_{3} = 1: \mathbf{W}^{T}_{1x6} = \begin{bmatrix} 0 & 0 & 0 & 0 & 0 & 1 \end{bmatrix}_{1x6}$$

$$\mathbf{W} * (\mathbf{kd - F}) = 0*[\sum_{j=1}^{6}{K_{1j}d_{j}} - F_{1}] + ... + 1*[\sum_{j=1}^{6}{K_{6j}d_{j}} - F_{6}] = 0 $$

(6) $$\Rightarrow \sum_{j=1}^{6}{K_{6j}d_{j}} = F_{6}$$

contribution by carbon.w
 * }

Principle of Virtual Work: Accounting for Boundary Conditions

From the 2 bar truss example: d1=d2=d5=d6=0)

Weighting Coefficients must be "kinematically admissible"(can't violate the boundary conditions)

Weightind coefficients = virtual displacement (W1=W2=W5=W6=0

$$W\cdot (Kd-F)$$ Where $$K=\begin{bmatrix}

k_{33} &k_{34} \\ k_{43}& k_{44} \end{bmatrix}$$ $$d=\begin{Bmatrix} d_{3}\\ d_{4}

\end{Bmatrix}$$ $$F=\begin{Bmatrix} f_{3}\\ f_{4}

\end{Bmatrix}$$

 * {| class="toccolours collapsible collapsed" width="60%" style="text-align:left"

!HW Force-Distance Relationship from Weak Form, from team group W_{3}\\ W_{4} \end{Bmatrix}*(\mathbf{\bar{K}\bar{d} - \bar{F}}) = 0$$
 * $$\begin{Bmatrix}
 * $$\begin{Bmatrix}

Multiply both sides by $$\mathbf{\bar{W}}^{-1}$$:

$$\begin{Bmatrix} W_{3}\\ W_{4} \end{Bmatrix} * \begin{Bmatrix} W_{3}\\ W_{4} \end{Bmatrix}^{-1}*(\mathbf{\bar{K}\bar{d} - \bar{F}}) = 0 * \begin{Bmatrix} W_{3}\\ W_{4} \end{Bmatrix}^{-1}$$

$$\Rightarrow 1 * (\mathbf{\bar{K}\bar{d} - \bar{F}}) = 0$$

(4) $$\Rightarrow \mathbf{\bar{K}\bar{d} = \bar{F}}$$

contribution by carbon.w
 * }

Lecture 26: 10/27/08
Continued from Lecture 24:

Back to PVW:

Example: $$\displaystyle grade = \alpha_o (HW grade) + \sum_{i=1}^{3} \alpha_i$$

Motivation:

 * 1) Elimination of rows (p 10-1, 23-2)
 * 2) Deriving $$\displaystyle \mathbf{{k^{(e)}_{4x4}} = {T^{(e)T}_{4x2}} \hat{k^{(e)}_{2x2}} {T^{(e)}_{2x4}}}$$ (p 14-3, 23-3)

Recall Force Dispacement (FD) relationship with axial degrees of freedom, $$\displaystyle \mathbf{q^{(e)}}$$

$$\displaystyle => \mathbf{ \hat{k^{(e)}_{2x2}} q^{(e)} = p^{(e)}}$$

$$\displaystyle => \mathbf{ \hat{k^{(e)}} q^{(e)} - p^{(e)} = 0_{2x1}}$$ Eq. (1)

PVW: $$\displaystyle => \mathbf{ \hat{w} (\hat{k^{(e)}_{2x2}} q^{(e)} - p^{(e)}) = 0_{1x}}$$ for all $$\displaystyle \mathbf{\hat{w_{2x1}}}$$ Eq. (2)

We showed (1) <=> (2) on p 24-1

Recall: $$\displaystyle \mathbf{{q^{(e)}_{2x1}} = T^{(e)}_{2x4} d^{(e)}_{4x1}}$$, Eq. (3), where $$\displaystyle \mathbf$$ is the real displacement

Similarly: $$\displaystyle \mathbf{ \hat{w_{2x1}} = T^{(e)}_{2x4} w_{4x1}}$$, Eq. (4). where $$\displaystyle \mathbf{ \hat{w}}$$ is the virtual displacement

Lecture 27: 10/29/08
$$\boldsymbol{\hat {w}_{2x1}} = $$ virtual axial displacement, corresponding to $$\boldsymbol q_{2x1}^{(e)}$$

$$\boldsymbol{\hat {w}_{4x1}} = $$ virtual displacement in the global coordinate system, corresponding to the real displacement in the global coordinate system $$\boldsymbol d_{2x1}^{(e)}$$

Replacing equations (3) and (4) into (2) yields:

$$\boldsymbol {(T^{(e)}w)}[\boldsymbol {\hat k^{(e)}}(\boldsymbol {T^{(e)}d^{(e)})-p^{(e)}]}=0, $$ for all $$\boldsymbol{\hat {w}_{4x1}}$$

Recall that $$\boldsymbol{(A_{pxq}B_{qx1})^T} = \boldsymbol {B^TA^T}$$.

Also, Recall that $$\boldsymbol{a_{nx1}b_{nx1}} = \boldsymbol{a_{1xn}^Tb_{nx1}}$$.

Now, apply equation (7) and (6) into equation (5):

$$\boldsymbol {(T^{(e)}w)^T}[\boldsymbol {\hat k^{(e)}}(\boldsymbol {T^{(e)}d^{(e)})-p^{(e)}]}=0, $$ for all $$\boldsymbol{\hat {w}_{4x1}}$$

$$=>\boldsymbol{w^TT^{(e)}}[\boldsymbol {\hat k^{(e)}}(\boldsymbol {T^{(e)}d^{(e)})-p^{(e)}]}=0$$

$$=>\boldsymbol w [\boldsymbol{( T^{(e)}\hat k^{(e)}T^{(e)})d^{(e)} - (T^{(e)}p^{(e)})}]=0$$, for all vitrual displacements, $$\boldsymbol w_{4x1}$$

$$=>\boldsymbol w [\boldsymbol{k^{(e)}d^{(e)}-f^{(e)}}]=0$$

So far, we have been dealing with the discrete (i.e. not continuous) case for matrices.

Now, let's look at the continuous case (PDE's):

Motivational model problem: An elastic bar with carying cross-section A(x), E(x), subjected to non-uniform (i.e. varying) axial loads (distributed) + a concentric (point) load + inertia forces (dynamic).

 * Note: Axial and concentric loads can be time dependant.

Lecture 28: 10/31/08
To date, our discussions have been limited to using the Finite Element Method for discrete cases, i.e. a finite number of elements. Now we turn our attention to using partial differential equations (PDEs) with the Finite Element Method. As always, we start by drawing a free body diagram. For this example, we will use the structure shown in the figure below.

In order to use PDEs, we must draw the free body diagram of a differential element. This element is shown above, highlighted in red, with the FBD drawn below.

$$\sum{F_y}=0$$ $$\sum{F_x)}=-N(x,t) + N(x+dx,t)+f(x,t)*dx-m(x)*a*dx$$ We use a Taylor series expansion to further evaluate $$\sum{F_x)}$$ Recall Taylor Series Expansion $$f(x+dx)=f(x)+\frac{df(x)}{dx}*dx+\frac{1}{2}\frac{d^2f(x)}{dx^2}*dx^2+ ...$$ where everything from $$\frac{1}{2}\frac{d^2f(x)}{dx^2}*dx^2$$ and above is considered a higher order term (H.O.T.) Applying this expansion to $$\sum{F_x}$$ results in the following equation. $$\sum{F_x}=0=\frac{\partial N(x,t)}{\partial x}*dx + H.O.T.+ f(x,t)*dx -m*a*dx$$ noting that we are neglecing the higher order terms and that the dx variable drops out in the remaining terms, we are left with the following. $$\sum{F_x}=0=\frac{\partial N(x,t)}{\partial x}+ f(x,t) -m*a$$ Equation (1) This equation then becomes $$\frac{\partial N}{\partial x}+f=m*a$$  Equation (2) recall that $$\N(x,t)=A(x)*\sigma (x)$$ where $$\sigma (x)=E(x)*\varepsilon (x,t)$$ and $$\varepsilon (x,t)=\frac{\partial (x,t)}{\partial x}$$ Thus: $$N(x,t)=A(x)*E(x)*\frac{\partial (x,t)}{\partial x}$$ Equation (3) Plugging Equation (3) into Equation (2) yields: $$\frac{\partial }{\partial x}[A(x)*E(x)*\frac{\partial (x,t)}{\partial x}]+f(x,t)=m(x)*a$$ This is called the Partial Differntial Equation of Motion (PDE of motion) In order to solve this equation, we need 4 boundary conditions, 2 position based boundary condiditions and 2 time based boundary conditions. This is because we have 2nd order derivative with respect to x and a 2nd order derivative with respect to time (acceleration) in the PDE of motion.

To help determine these boundary conditions, please consider the two figures below. Since both ends are fixed, the two x boundary conditions can be found by observing: $$\displaystyle u(0,t)=u(L,t)=0$$ Both t boundary conditions can be found by knowing the initial displacement and the initial velocity.

As above, both t based boundary conditions are taken to be the inital velocity and the initial displacement while the x bounday condidtions can be obtained as follows: $$\displaystyle u(0,t)=0$$ $$u(L,t)=\frac{\partial u(L,t)}{\partial x}=\frac{F(t)}{A(L)*E(L)}$$

 * {| class="toccolours collapsible collapsed" width="60%" style="text-align:left"

!HW Global Force-Distance Relationship from Weak Form, from team group
 * $$\mathbf{W}_{2x1}*(\mathbf{\bar{k}^{(e)}\bar{q}^{(e)} - \bar{p}^{(e)}}) = 0_{1x1}$$
 * $$\mathbf{W}_{2x1}*(\mathbf{\bar{k}^{(e)}\bar{q}^{(e)} - \bar{p}^{(e)}}) = 0_{1x1}$$

Multiply both sides by $$\mathbf{W}^{-1}$$:

$$\mathbf{W}_{2x1} * \mathbf{W}_{2x1}^{-1}*(\mathbf{\bar{k}^{(e)}\bar{q}^{(e)} - \bar{p}^{(e)}}) = 0 * \mathbf{W}_{2x1}^{-1}$$

$$\Rightarrow 1 * (\mathbf{\bar{k}^{(e)}\bar{q}^{(e)} - \bar{p}^{(e)}}) = 0$$

(4) $$\Rightarrow \mathbf{\bar{k}^{(e)}\bar{q}^{(e)} = \bar{p}^{(e)}}$$

contribution by carbon.w
 * }

 * {| class="toccolours collapsible collapsed" width="60%" style="text-align:left"

!HW Ad-hoc Proof of Transpose Property, from team group
 * Prove: $$(\mathbf{AB})^{T} = \mathbf{B}^{T}\mathbf{A}^{T}$$
 * Prove: $$(\mathbf{AB})^{T} = \mathbf{B}^{T}\mathbf{A}^{T}$$

Use the example matrices $$\mathbf{A}_{2x3} = \begin{bmatrix} 1 & 2 & 3\\ 4 & 5 & 6 \end{bmatrix}_{2x3}$$ and $$\mathbf{B}_{3x3} = \begin{bmatrix} 7 & 8 & 9\\ 1 & 2 & 3\\ 4 & 5 & 6 \end{bmatrix}_{3x3}$$

$$(\mathbf{AB})^{T} = \begin{bmatrix} 1 & 2 & 3\\ 4 & 5 & 6 \end{bmatrix} * \begin{bmatrix} 7 & 8 & 9\\ 1 & 2 & 3\\ 4 & 5 & 6 \end{bmatrix} = \begin{bmatrix} 21 & 27 & 33\\ 57 & 72 & 87 \end{bmatrix}^{T} = \begin{bmatrix} 87 & 72 & 57\\ 33 & 27 & 21 \end{bmatrix}$$

$$\mathbf{B}^{T}\mathbf{A}^{T} = \begin{bmatrix} 1 & 2 & 3\\ 4 & 5 & 6 \end{bmatrix}^{T} * \begin{bmatrix} 7 & 8 & 9\\ 1 & 2 & 3\\ 4 & 5 & 6 \end{bmatrix}^{T} = \begin{bmatrix} 6 & 5 & 4\\ 3 & 2 & 1 \end{bmatrix} * \begin{bmatrix} 6 & 5 & 4\\ 3 & 2 & 1\\ 9 & 8 & 7 \end{bmatrix} = \begin{bmatrix} 87 & 72 & 57\\ 33 & 27 & 21 \end{bmatrix}$$

contribution by carbon.w
 * }

 * {| class="toccolours collapsible collapsed" width="60%" style="text-align:left"

!HW Local Force-Distance Relationship from Weak Form, from team group
 * $$\mathbf{W}*(\mathbf{k^{(e)}d^{(e)} - f^{(e)}}) = 0_{1x1}$$
 * $$\mathbf{W}*(\mathbf{k^{(e)}d^{(e)} - f^{(e)}}) = 0_{1x1}$$

Multiply both sides by $$\mathbf{W}^{-1}$$:

$$\mathbf{W} * \mathbf{W}^{-1}*(\mathbf{k^{(e)}d^{(e)} - f^{(e)}}) = 0 * \mathbf{W}^{-1}$$

$$\Rightarrow 1 * (\mathbf{k^{(e)}d^{(e)} - f^{(e)}}) = 0$$

(4) $$\Rightarrow \mathbf{k^{(e)}d^{(e)} = f^{(e)}}$$

contribution by carbon.w
 * }

Lecture 29: 11/3/08

 * {| class="toccolours collapsible collapsed" width="60%" style="text-align:left"

!HW Literature on Composite Materials, from team group
 * In the article "The effect of interphase on residual thermal stresses. 1. Single fiber composite materials" from the journal "Mechanics of Composite Materials", the authors Kushnevsky, Wacher, Chate, and Bledzki treat the composite material as a region with variable Young's Modulus. They make this conclusion as "a direct consequence of the changes in the microstructure of the matrix near the fiber surface".
 * In the article "The effect of interphase on residual thermal stresses. 1. Single fiber composite materials" from the journal "Mechanics of Composite Materials", the authors Kushnevsky, Wacher, Chate, and Bledzki treat the composite material as a region with variable Young's Modulus. They make this conclusion as "a direct consequence of the changes in the microstructure of the matrix near the fiber surface".

Source: http://www.springerlink.com/content/v3735152h75775mu/

contribution by carbon.w
 * }

 * {| class="toccolours collapsible collapsed" width="60%" style="text-align:left"

!Contribution History of Calculus Notations, from team group
 * Calculus has two primary systems of notations developed by Leibniz and Newton (however Leibniz's notation is the most popular notation used today). Newton used dots over the variables as such.
 * Calculus has two primary systems of notations developed by Leibniz and Newton (however Leibniz's notation is the most popular notation used today). Newton used dots over the variables as such.

Newton first derivative of x:       $$\dot{x}$$

While Leibniz used a "d" in the numerator and denominator to symbolize "derivative". Leibniz also developed the integral symbol commonly used today.

Leibniz first derivative of x with respect to time:     $$\frac{dx}{dt}$$

contribution by carbon.w =E-mail Homework=
 * }

$$\begin{Bmatrix} f^{(e)}_1\\ f^{(e)}_2\\ f^{(e)}_3\\ f^{(e)}_4 \end{Bmatrix}=$$$$*\begin{Bmatrix} d^{(e)}_1\\ d^{(e)}_2\\ d^{(e)}_3\\ d^{(e)}_4 \end{Bmatrix}$$ $$l_s=cos(\theta)$$ $$m_s=sin(\theta)$$

transformation matrix T (2x6) to transform the 6 element dofs in global xyz coordinates to the 2 axial dofs
$$\underline{k}^{(e)} = k^{(e)} \begin{bmatrix} (l^{(e)})^2   & l^{(e)}m^{(e)} & l^{(e)}n^{(e)} &-(l^{(e)})^2    &-l^{(e)}m^{(e)} &-l^{(e)}n^{(e)} \\ l^{(e)}m^{(e)} & (m^{(e)})^2   & m^{(e)}n^{(e)} &-l^{(e)}m^{(e)} &-(m^{(e)})^2    &-m^{(e)}n^{(e)} \\ l^{(e)}n^{(e)} & m^{(e)}n^{(e)} & (n^{(e)})^2   &-l^{(e)}n^{(e)} &-m^{(e)}n^{(e)} &-(n^{(e)})^2    \\ -(l^{(e)})^2   &-l^{(e)}m^{(e)} &-l^{(e)}n^{(e)} & (l^{(e)})^2    & l^{(e)}m^{(e)} & l^{(e)}n^{(e)} \\ -l^{(e)}m^{(e)} &-(m^{(e)})^2   &-m^{(e)}n^{(e)} & l^{(e)}m^{(e)} & (m^{(e)})^2    & m^{(e)}n^{(e)} \\ -l^{(e)}n^{(e)} &-m^{(e)}n^{(e)} &-(n^{(e)})^2   & l^{(e)}n^{(e)} & m^{(e)}n^{(e)} & (n^{(e)})^2    \\ \end{bmatrix} $$


text:
User:Eml4500.f08.group/HW5/Matlab

=Constant Element Properties=

Below is the code for analysis and plotting of the 6-Bar truss with equivalent elements.

Additional Fuctions
The book's code divides up the work load on the FEA analysis among a a number of functions. The three functions called upon in the above code are shown below.

Results
The Results obtained were identical to the results in the book.

K =

85355       35355       -50000            0            0            0            0            0       -35355       -35355        35355        35355            0            0            0            0            0            0       -35355       -35355       -50000            0        85355       -35355            0            0            0            0       -35355        35355            0            0       -35355  1.0202e+005            0            0            0       -66667        35355       -35355 0           0            0            0        71554       -35777            0            0       -71554        35777            0            0            0            0       -35777        17889            0            0        35777       -17889            0            0            0            0            0            0        71554        35777       -71554       -35777            0            0            0       -66667            0            0        35777        84555       -35777       -17889       -35355       -35355       -35355        35355       -71554        35777       -71554       -35777  2.1382e+005            0 -35355      -35355        35355       -35355        35777       -17889       -35777       -17889            0  1.0649e+005

R (Loading N)=

0           0        10000        17321            0            0            0            0            0            0

d (displacement)=

d1          0 d2          0 d3    0.21311 d4    0.24998 d5          0 d6          0 d7          0 d8          0 d9 -0.0060971 d10  0.012242

reactions (N) =

F1     -10873 F2    -217.27 F5     874.27 F6    -437.13 F7    -1.7279 F8     -16666

results = Stress (MPA)  Axial Forces (N) 5.3276e-005      10.655        10655 -4.6334e-006    -0.92669      -926.69 -4.8873e-006    -0.97746      -977.46 -8.3326e-005     -16.665       -16665 1.5363e-006     0.30727       307.27 -9.659e-009  -0.0019318      -1.9318

=Variable Element Properties=

Below is the code for analysis and plotting of the 6-Bar truss with varying elements properties.

Results
The Variation of the element properties has a minor effect on the displace and reactions, but it isn't very noticeable. This is because Elements 2 and 4, which are working the most against the applied load were in one case left unchanged, and in the other changed to a slightly lower E of 180 GPa instead of 200 GPa.

K =

76391       38891       -37500            0            0            0            0            0       -38891       -38891        38891        38891            0            0            0            0            0            0       -38891       -38891       -37500            0        69320       -31820            0            0            0            0       -31820        31820            0            0       -31820        98486            0            0            0       -66667        31820       -31820            0            0            0            0        71554       -35777            0            0       -71554        35777            0            0            0            0       -35777        17889            0            0        35777       -17889            0            0            0            0            0            0        89443        44721       -89443       -44721            0            0            0       -66667            0            0        44721        89027       -44721       -22361       -38891       -38891       -31820        31820       -71554        35777       -89443       -44721  2.3171e+005        16015 -38891      -38891        31820       -31820        35777       -17889       -44721       -22361        16015  1.1096e+005

R (Loading in N) =

0           0        10000        17321            0            0            0            0            0            0

d (displacement) =

d1          0 d2          0 d3    0.26485 d4    0.26083 d5          0 d6          0 d7          0 d8          0 d9 0.00063864 d10 -0.001246

reactions (N) =

F1    -9908.3 F2     23.619 F5    -90.274 F6     45.137 F7    -1.4008 F8     -17389

results = Stress (MPA)  Axial Forces (N) 6.6213e-005      9.9319       9931.9 5.347e-007    0.096245       96.245 5.0465e-007     0.10093       100.93 -8.6943e-005     -17.389       -17389 -1.5183e-007   -0.033402      -33.402 -6.2645e-009  -0.0015661      -1.5661

=3D Trusses=

Additional Fuctions
The book's code divides up the work load on the FEA analysis among a a number of functions. The three functions called upon in the above code are shown below.

Results
This three bar truss is statically indeterminate. See other three bar trusses

conn =

1    4     2     4     3     4

lmm =

1    2     3    10    11    12     4     5     6    10    11    12     7     8     9    10    11    12

d =

d1     0 d2     0 d3     0 d4     0 d5     0 d6     0 d7     0 d8     0 d9     0 d10   -0.18705 d11   -2.592 d12   -0.3858

reactions (N) =

F1     6666.7 F2      13333 F3     -13889 F4    -6666.7 F5     6666.7 F6    -9259.3 F7          0 F8          0 F9      23148

results = Stress (MPA)  Axial Forces (N) 0.00050936      101.87        20375   0.00033036       66.072        13214   -0.0001929       -38.58       -23148

Plots

title: User:Eml4500.f08.group/HW5/Matlab


text:
User:Eml4500.f08.group/HW5/Contributors

=Homework 5 Contributors=

Jeff Wright Eml4500.f08.group.w 04:56, 2 November 2008 (UTC)

Brian Taylor Eml4500.f08.group.taylor 22:21, 4 November 2008 (UTC)

Aaron Clausen Eas4200c.f08.carbon.clausen 00:57, 7 November 2008 (UTC)

Julia Setlak Eml4500.f08.group.setlak 15:15, 7 November 2008 (UTC)

Melisa Gaar Eml4500.f08.group.gaar 15:34, 7 November 2008 (UTC)

Tom Cady Eml4500.f08.group.cady 18:31, 7 November 2008 (UTC)

title: User:Eml4500.f08.group/HW5/Contributors


text: File:Proposition Type A.png

title: File:Proposition Type A.png


text: File:Proposition Type E.png

title: File:Proposition Type E.png


text: File:Proposition Type IO.png

title: File:Proposition Type IO.png


text:
User:Sandy~enwikiversity/Week 10 Relationships

Week 10 - Relationships
Relationships stem from our desire for affiliation and a clear need to belong

Our Need to Belong
Evolution – there are more resources available to us when we form groups. Survival is much more difficult when we are alone We seek balanced relationships Solitary is used as an one of the strongest and extreme forms of punishment

Marriage

 * People who marry (and stay married) live longer and healthier lives. Having said this, the marriage needs to be a happy one.

Reinforcement Theory
We associate an attractive person with reward
 * Behaviours reinforced are usually repeated
 * We attract those we see as rewarding to us
 * The reinforcement affect model is based on the principles of classical conditioning

Reciprocity

 * We like those who like us
 * Mimicking another increases the chance of them liking us
 * We prefer relationship that are psychologically balanced
 * We like most people the most if they initially dislike us then later like us

Interpersonal Attraction

 * Like a magnetic force field
 * Ingratiation (giving compliments) is one of the techniques of attraction
 * To show ingratiation we give compliments
 * Similarity attracts – over time similar people end up together. E.g. race, class
 * In the short term opposites attract but hey stay together less than people who are similar (matching hypothesis)
 * There are risks in joining a new group so people look for similarity
 * People become more similar over time and couples that stay together tend to have worked out their differences through compromise

The gain/loss hypothesis Playing hard to get makes you more attractive

Social Exchange Theory
We are motivated to increase benefits while decreasing the cost in relationships The benefits or rewards might be love and companionship while the costs might be effort and compromise.
 * Comparison level for alternatives – rewards elsewhere, is there something better?
 * Social comparison
 * Sunk Investment – what we have put in to the relationship can’t be recovered and can hold us in the relationship i.e. children

Equity Theory

 * Input to output balance for both parties is desirable
 * You can only take more from a relationship if you put in more
 * We prefer relationships that are psychologically balance
 * We are motivated to restore balance in relationships
 * commitment to a relationship is weaker when there are many high-quality alternative partners available

Propinquity

 * Exposure to the same people or psychological proximity e.g. same neighbourhood or tribe
 * Mere exposure of effect – familiar things become more attractive
 * Overexposure can reduce liking
 * Availability and expectation of continued interaction are desirable

'Familiarity and exposure

 * Social allergy effect – annoying habits become more annoying over time
 * Familiarity and repeated exposure can either make bad things worse or encourage liking

Attractiveness

 * Mostly we prefer attractive over un-attractive
 * Attractiveness represents superiority over other traits
 * Attractive children are more popular
 * Babies respond more positively to attractive faces
 * For men clothing represents wealth an status and this represents attractiveness

Beauty

 * We agree on what is beautiful but not necessarily why
 * Evolutionary psychology – beauty in woman represents, health, youth and fertility
 * Symmetry is attractive
 * Average or typical faces are considered more attractive than ‘different’ faces
 * Although there are some cultural and historical differences we generally agree on what is thought to be beautiful

Rejection & Social Exclusion

 * We are psychologically programmed to try to connect and belong
 * It is bad for our to not belong and effects our inner states like self-esteem
 * When a person develops ‘’rejection sensitivity’’ they expect rejection and become hypersensitive to possible rejection|
 * The extent of the effect of the rejection depends on the value of the relationship and the rejection signal
 * Comparison level for alternatives; is there something better?
 * Social comparison
 * Our initial reaction is one of emotional numbness

Love Relationships
There are two types of love: Important for the start of a relationship but not good for long term commitment as it based on a temporary state important for successful marriages
 * Passionate – intense feelings of longing, desire and excitement
 * Companionate – mutual understanding and affection for those we share our lives with

‘’’Sternberg’s Triangular Model of Love’’’
 * Passion – ‘’motivational’’ – physiological arousal
 * Intimacy – ‘’emotional’’ – closeness, understanding and support
 * Commitment – ‘’cognitive’’ – long term conscious decision and defining it as love

Attachment Styles

 * Secure attachment– trust in self and other to continue to provide love and support
 * Preoccupied attachment – don’t avoid close relationships but do experience high anxiety and more negative attitudes towards themselves
 * Dismissing avoidant – keep relationships at a distance which keeps anxieties low. More reliant on self than others
 * Fearful avoidant – high anxiety and high avoidance, low self opinion

Avoidant Attachment Styles
 * have a need to belong but inner conflict
 * want contact but fear closeness
 * same amount of social contact as others
 * may have several partners none of which are close

Ending Relationships
There are four stages once the relationship has started to fail:

1. Loyalty – stay and wait for an improvement 2. Neglect – let the deterioration happen 3. Voice behaviour – try and work it out/improve things 4. Exit behaviour – the end of the relationship

../Week 11 Groups/


text:
User:Sandy~enwikiversity/Week 11 Groups

Week 11 – Groups and Leadership
We adapt to the group normative behaviour

What is a group?
Other characteristics other than people together are:
 * At least two people
 * When you are not alone
 * Operating as a collective
 * Perceived similarities
 * Shared goals e.g. people at a bus stop
 * Shared identity
 * Some sort of interdependence
 * Behaviour compatible with your goals
 * Outgroup – not wanting to be part of a particular group or understanding our group in relation to other groups as a frame of reference

A social group can’t just exist in a static form. It needs group dynamics to keep it alive with new people joining the group and others leaving.

Belonging to a group has many advantages but also takes responsibility to reap the rewards like conformity etc.

Groups are essential to culture starting with family/kinship and tribes.

The advantages for animals to belong to groups are:
 * There is safety in numbers
 * A collective brain
 * More eyes to see danger
 * Collectively bringing down a large animal and sharing the spoils

The advantages of human groups are:
 * The ability to specialise i.e. grow food, build houses
 * Be an expert – we rely on education to develop experts
 * Economic exchange

Social Facilitation (make easy)
 * Improved performance, e.g. rowing together
 * Social inhibition, e.g. someone looking over your shoulder while you are working
 * When we become aroused we perform better unless it is a difficult job

The Hawthorn Effect

 * More effective workers in factories experiment being watched increased productivity with a ‘somebody upstairs care syndrome’

Social Loafing
 * We often slack off when working in groups and make less of an effort.
 * Reward for effort isn’t as strong when given to a group; it is defused
 * The more cohesive the group is the less loafing there is

Prototypical Member - The person who is a typical member. The average person as opposed to the stereotype (exaggerated)

../Week 12 Prosocial/

title: User:Sandy~enwikiversity/Week 11 Groups


text:
User:Sandy~enwikiversity/Week 12 Prosocial

Prosocial Behaviour vs Altruism
Prosocial Behaviour

Altruism – focusing on the well-being of others Altruism does exist but there still may be some underlying self interest at heart Who helps whom?

Not everybody helps or helps others equally Social influence is used to get people to behave in a certain way

What is prosocial behaviour?

 * Actions that are intended to help or benefit another individual or group
 * We usually expect to reap some sort of benefit from the collectivity of helping over time

Philanthropy – businesses putting together a foundation to give to charities etc. i.e. Bill Gates gives away 5% of the profit to health research etc.

Motivations and reasons to be prosocial

Self interest – e.g. we may donate blood for the purpose of our own long term benefit such as medical research that might save us one day

Notion of Similarity - Relate to the situation – e.g. we might give blood because someone in our family needed a transfusion in the past

Reciprocity – Obligation to return in kind what another has done for us

Direct Reciprocity – Helping someone who may help you later

Indirect Reciprocity – Helping someone so someone else may help you later

Fairness Equity – you desire what you put in

Equality – everybody gets the same amount

Over benefiting - People who feel they are over benefiting are more prone to suicide i.e. taking/being a burden on society and are not in a position to give back

Underbenefiting – People who perceive than are giving more than they are receiving. As a result they may experience anger and frustration that what they are giving is not being recognised or rewarded.

Learning Theory

Milgrim’s study of obedience Teacher teaching the learner through administering what they think are real electric shocks for the incorrect answers to questions. The supposedly real electric shocks increase with intensity as the experiment progresses. The learner is a confederate who is instructed to react to electric shocks in an increasingly distressed manner as the experiment progresses. The pressure of perceived authority persuades the teacher to proceed with the shocks against the learners protests.

Evolutionary perspective – form an evolutionary perspective goals are a motive to be prosocial

Egoism – Helps others to be of more value to society

Volunteering – can have an altruistic or have varied rewards depending on the motivation such as:
 * increased self understanding, perhaps to relieve distress
 * career enhancement through the development of skills
 * social – developing networks and social contacts
 * protective

Tutorial – The Australian Zeitgeist
Zeitgeist – spirit of the time

Social Capital

 * collective positive networks
 * large amount of positive goodwill that can be drawn upon in times of crisis
 * reasonable amounts of social interaction
 * needs ongoing reinforcement and facilitation

Social Disengagement

 * individual or couples focus
 * less community participation
 * less family support

Changing times:

 * Egalitarian – believing in the equality of all people – a dream gone sour
 * IT revolution
 * Industrial revolution
 * Increase in instances of depression because we haven’t adapted
 * Changes are to fast for our comfort
 * Globalisation

How are we dealing with these changes in society?

We aren’t; it’s all to much. We are avoiding the ‘big picture’ stuff and focusing on the things we can control i.e. backyards, renovations (another symptom of disengagement)

Other factors of disengagement

 * increasing intolerance
 * less compassion
 * we focus on ourselves – not outside our own back yard
 * value materialism, wealth and prosperity
 * we are disengaging on a political as well as social level
 * personal salvation
 * a kind of reductionism
 * abdication of personal responsibility

../Week 13 Environmental/


text:
User:MandaG/Tutorial and lecture 5

Prejudice

 * Prejudice: A negative feeling toward an individual based soley on his or her membership in a particular group.
 * Racism: An example of prejudice aimed towards members of a certain race.[[Image:AfricanAmericans2.jpg|200px|right|thumb|some prejudices are tackled by courageous leaders]]
 * Aversive Racism: Simultaneously holding egalitarian values and negative feelings. This means that a person believes that all are created equal, should be treated the same and should get the same. I guess its kind of like cognitive disonance internally.

Who experiences Prejudice?
Given the definition of prejudice I'm sure that anybody can be a victim of prejudice and that a large part of who is effected is based around culture. Groups who have been or are effected by prejudice include: African Americans, led to the civil rights movement in the 60's led by Martin Luther King Jr. subsequently assasinated. The prejudice was so severe that until Rosa Park http://au.youtube.com/watch?v=ab-mbg1SLjw made a stand (or in her case a sit...) african americans could not even have a seat on the bus if there was a white person standing. The prejudice was so deep in some people they joined a group called the Ku Klux Klan (KKK)a radical group of white supremeists who also persecuted catholics and Jewish people by lynching and terrorising them. People who are overweight are prejudiced against and I think a large part of that is due to our new hollywood culture where to be overweight is treated as if its the end of the world, hell normal sized people are criticised for being overweight. Religious groups are also victims of prejudice, usually due to be associated with a very small minority of extremeists. Homosexuals are also prejudiced against and have been for a long time. Though the prejudice on the surface appears to have lowered, I think they still suffer basic rights afforded to the rest of us. One of the main ones often debated in the church and the legislative assembly as well as parliament is whether or not they should be allowed to get married. Seriously??? Why not, the rest of us can and a lot of people say marriage is just a piece of paper anyway (not that I'm down on marriage at all...mines been planned since I was 14), as far as I'm aware though more than happy to be corrected, couples straight or homosexual have the same rights under de facto law (that is couples that have been together for over 2 years meeting a certain criteria) so what difference to outsiders would it make if homosexual couples get married or not? One of the questions in the leccture was whether if we had the cognitive resources would we still have stereotypes and prejudices. I think this is a question that will never be answered because we do have this cognitive miser that right or wrong creates shortcuts and stereotype for us to be able to be more effective in our day to day functioning. However in saying this, I think just knowing everyone is a unique individual is not enough to eliminate the problem, we should all know that already. I think it is the experience we have with people that will lead to a decrease (or increase) in our own personal preudices and stereotypes.

Why Does Prejudice Exist

 * Ingroup favoritism- Simply put you favour group more than another. I think this happens all the time and is only natural. Of course you are going to like people you associate with more, or that you talk to or have more in common with more. The problem arises when you develop a prejudice. I like my softball team more than some others because I am in that team, but that does not mean I dislike the others. You don't have to like everyone equally but you should not be prejudiced over differences! This becomes particularly problematic when looking at say neo-nazi's or extremeists (probably not so much in sport).
 * Rationalisation for Opression- Powerful groups get and maintain power through stereotypes and prejudices (and if that fails a few assasinations). An example of this can be seen in a number of political and violence fuelled conflicts. In Japan it used to be anything that was not fully Japanese including people was trashed, Hitler used his prejudices for an ethnic "cleansing" as was the conflict in Serbia Croatia and Rwanda. SLAVERY!!!!

Hope is not lost!
Prejudice, stereotyping and discrimination can be devastating so I feel it is really important that we try to minimise as much as possible the occurence of such things. One idea on how to do this is the contact hypothesis. To start with we must be aware of any prejudice beliefs held. Once we are aware we as individuals can conciously make an effort to override such attitudes. We must not be cognitively lazy as implicit attitudes can be indicative of behaviour when faced with what we are prejudiced against. The notes talk about 2 reasons one might be motivated to change their attitude, first up is that internally they feel they are morally wrong and the other is that they fear it will garner societal diasaproval. While it is of course better to have internal motivations I think I would be ok with reducing prejudice attitudes and behaviours for whatever reason.
 * The contact hypothesis- Under favourable conditions, regular contact between group members of different groups reduce prejudice. It is important that the conditions are favourable as otherwise it may reinforce the negative attitude that was first held. The critisicms of the contact hypothesis state that there are a number of necessary conditions for this theory to work such as: Equal social status and percieved similarity. However, I think it would depend on the motivations and situation for overcoming the prejudice in the first place. The reason for this is because maybe you decide to have contact with the poor and hungary by working at a soup kitchen. Your previous prejudice is that all the homeless are that way through lack of trying to get a job and are basically leeches on hard working taxpayers. After a few weeks at the kitchen you realise that most of these people are trying desperatly to find employment and get out of their present situation. You, a succesful private practise $200 an hour psychologist have nothing in common with them and are certainly well above them in socioeconomic status still change your attitude towards them.

title: User:MandaG/Tutorial and lecture 5


text:
User:Sandy~enwikiversity/Week 13 Environmental

What is Environmental Psychology?
anthropology architecture urban planning politics, and sociology
 * The study of the interaction between people and their environment
 * Applied psychology
 * Affects of the environment on human psychology
 * How humans affect the environment
 * Our interface with the world
 * Our impacts on the environment effect our future well-being and our capacity to survive
 * It is related to

There are two types of investigation to be focused on:
 * The relationship between the artificial environment and people
 * The relationship between the natural environment and people

Environmental Psychology is also known as, or closely related to:
 * environmental social sciences
 * architectural psychology
 * Socio-architecture
 * ecological psychology
 * ecopsychology
 * behavioural geography
 * environment behaviour studies
 * person- environment studies
 * environmental sociology
 * social ecology
 * environmental design research

Negative Environmental influences

 * human spatial behaviour
 * environmental stressors
 * environmental risks
 * environmental design
 * complex relations – physical, mental and emotional adjustments to it

Human Spatial Behaviour: Density and Crowding
Density – ratio of the number of people to space

Crowding – this is subjective, it’s up to you whether you feel crowded or not. You can feel crowded out in the desert but with someone ‘in your face’ crowding you. Crowding itself is stressful because it gives us a feeling of being out of control. Having a sense of control prevents us from feeling crowded. Control over your physical space for example engaging in a book or reading a news paper on a train puts up a wall.

Environmental Stressors Environmental conditions that interfere with us functioning include:
 * crowding
 * daily stress and life events
 * noise – the most common stressor
 * temperature, and
 * Environmental disasters

Environmental Risks

We are not objective with what we see as a threat, for example we overemphasise the risk of a shark attack and underemphasise the risk of road accidents. We don’t look at the percentages of the risk occurring.

Environmental Design
We shape our buildings and environment - our buildings and environment shape us

 * Assessing and planning – predicting human behaviour for artificial design. Everything that is artificial that we create is designed.
 * Architectural psychology – psychologists who can design things to influence human behavious
 * Permaculture – represents concepts for maximising coherence between the environment anf human nature
 * Wayfinding – the study of how people find their way

Natural Environment To animals Nature scenes Adventure therapy Exercising outdoors It lowers our blood pressure and exposure Sunlight alters our mood and sense of well-being
 * We have a preference for natural over built environments. We have a need to engage with our natural environment. The most common human activity is gardening.
 * We have a positive physical and psychological reaction to nature:
 * Mental imagery and sound of our natural environment affects us psychologically.
 * Our infinity with nature is in-ground in our genotype.
 * We value windows very highly and rooms with natural light.
 * We are attracted to homes with views of nature
 * We have photos and art work of nature in our homes, at work and as computer screen savers
 * We are likely to choose a painting of nature over an abstract painting
 * 90% of all children’s stories have animals as the main character
 * Hospital patients with a window in their room or a picture of recover quicker
 * Patients that are exposed to animals tend recover better

Nature Deficit Disorder (Richard Louv) – suggests children are spending less time outdoors which is resulting in behavioural problems like ADHD

Deborah Winter is quoted as saying “...environmental problems are caused primarily by human behaviours, feelings and attitudes. We can’t solve these problems without psychology’s help and we really need psychologist to go work on them.”

Environmental Paradigms
The fundamental issue is we are stuck in ego and anthropocentric; we need to be ecocentric and work with the environment respecting the environment as an equal. Morally humans are no more important than any other part of the environment.
 * Egocentric – self focused
 * Anthropocentric – the common good for everybody. Maximum benefit for human beings.
 * Ecocentric – Equal with nature and the rest of the species

Best Solution?
These changes are only possible if the efforts of psychological strategy and public policy (on energy use, pollution, solid waste, environmental justice, natural resource management and population) are combined. Attitude and Behaviour
 * Slow growth – to slow down the rapid rate of development. This is inevitable for environment protection
 * Faster transition to sustainability – If the best technology available was implemented we’d be fifteen times more efficient
 * Technology model – switching to smart technology means we don’t have to do much to compromise

Attitude wise we know what’s required but we don’t match this with our behaviour. A combination of reward and punishment would preserve pro-environment attitudes although people tend to respond to punishment such as fines for littering. Use of persuasion and social influence will increased desired environmental behaviour.

Environmental Impact
I = P x A x T A function of population x consumption x effect of technologies
 * I – Impact on the environment
 * P - Population
 * A – Affluence (consumption per person)
 * T – Technologies (the environmental effect of technologies that support the level of affluence

Permaculture – permanent culture Permaculture is about the design of systems using natural principles in order to minimise human effort and maximise returns in a sustainable way. Environment and community design.

Psychology and the future
More psychologists working for environmental management agencies, planning authorities and government bodies providing advice on:
 * The measurement and assessment of community attitudes and values
 * The effectiveness of the various communication and behaviour change strategies
 * The planning and design of sustainable human settings as well as natural environment based services


text: User talk:Eas4200c.f08.aeris.mcrae

title: User talk:Eas4200c.f08.aeris.mcrae


text: User talk:EML4500.f08.A-team.kirley

title: User talk:EML4500.f08.A-team.kirley


text:
User:MandaG/Turorial 1 Week 2

The first tutorial was not bad as far as first tuorials go. I found the icebreakers to be a lot of fun particularly given some of the poor ones that are out there. I appreciated that instead of saying a verb that starts with the same letter of our name (Oh yes those in my psych 101 tute last year know what tht was like!) we got to learn things about others and were at times a little out of our comfort zone. Getting into groups on eye colour or number of sibblings seemed simple enough, it started to get interesting when we had to group according to religion and politics, as far as I knew they were public taboo topics! My particular tute though was very open about ourselves and we all had a bit of a giggle. The one that I found most interesting was when asked to line up according to whether we believed actions to be largely a result of situational cicumstances or a result of the individual. I found myself standing alone at the individual end while the others were largely fencesitters with a few strongly on the situational end. I have yet to think of a good reason as to why that may be... .

title: User:MandaG/Turorial 1 Week 2


text:
Standard error (statistics)

The standard error (SE), in statistics, is a measure of spread for a sample of data. Mathematically, the SE is the standard deviation divided by the square root of the sample size.

Standard error vs. standard deviation
The standard error is commonly confused with the standard deviation.

For a simple explanation of the difference, see What is the difference between standard deviation and standard error?

For a more indepth explanation, perhaps Standard deviations and standard errors.

title: Standard error (statistics)


text: Help:Table of contents

title: Help:Table of contents


text:
Faculty of Law

Welcome to the Faculty of Law. Here you will courses related to the study of law in general.

Courses Available: Introduction to Law 101

new courser: Discovery Privileges

SUBJECT: DISCOVERY PRIVILEGES UNDER FEDERAL RULES OF CIVIL PROCEDURE--Tonyd 19:44, 13 January 2010 (UTC)

Rule 26(b)(1), Fed. R. Civ. P., provides that discovery may be had regarding any matter not privileged. Rule 26(b)(5) requires that the party asserting a privilege must make the claim expressly and describe the nature of the documents, communications or things not produced or disclosed in a manner that without revealing information itself privileged or protected, will enable other parties to assess the applicability of the privilege or protection. Withholding materials without providing the information required by Rule 26(b)(5) subjects the attorney to sanctions under Rule 37(b)(2) and may be viewed as a waiver of the privilege or protection.

The privileges were once sought to be codified in Rules 501-510, of the Federal Rules of Evidence (FRE), but Congress declined to adopt them. See Advisory Committee Notes to 1974 enactment. While these privileges were not adopted, Rule 501, as adopted, Pub. L. 93-595, '1, states:

Except as otherwise required by the Constitution of the United States or provided by Act of Congress or in rules prescribed by the Supreme Court pursuant to statutory authority, the privilege of a witness, person, government, State or political subdivision thereof shall be governed by the principles of the common law as they may be interpreted by the courts of the United States in the light of reason and experience. However, in civil actions and proceedings, with respect to an element of a claim or defense as to which State law supplies the rule of decision, the privilege of a witness, person, government, State or political subdivision thereof shall be determined in accordance with State law.

Federal courts therefore have the flexibility to adopt new common law privileges, on a case by case basis, pursuant to Rule 501, FRE. Jaffee v. Redmond, 116 S.Ct. 1923 (1996) (adopting psychotherapist-patient privilege in Federal civil cases); see, University of Pa. v. EEOC, 493 U.S. 182, 189, 110 S.Ct. 577, 582 (1990) (declining to adopt a privilege for peer review in an employment discrimination context). The privileges available are set forth below. Obviously, some are more useful than others in the context of Federal employment matters.

1. Required reports privileged by statute, e.g.,:

a. 5 U.S.C. '552a (Privacy Act, covering systems of 		records kept by the Federal government and accessible 		by a personal identifier, but many exemptions).

b. 5 U.S.C. '7362 and 42 U.S.C. '290dd-3 		(confidentiality of medical records concerning 		alcoholism, alcohol abuse and treatment).

c. 13 U.S.C. '9 (prohibiting disclosure of census 		information.

d. 26 U.S.C. '6103 (income tax returns)

e. 42 U.S.C. '2000e-5(b), -5(e) and -8(e) (prohibiting 		disclosure of charges, investigations conciliation 		efforts and statistical reports of individual 		companies).

f. 42 U.S.C. '2240 (reports of incidents at nuclear 		facility licensees inadmissible in certain actions).

g. 42 U.S.C. '3610(d)(1) (prohibiting disclosure of 		conciliation efforts, but not the agreement, unless 		confidentiality is specified in the agreement).

h. 45 U.S.C. '33, 41 (similar reports of accidents by 		railroads).

2. Attorney-client privilege. See Upjohn Co., et al. v. United States, et al., 449 U.S. 383, 101 S.Ct. 677 (1981)(discussing privilege in the corporate context); CFTC v. Weintraub, 471 U.S. 343, 105 S.Ct. 343 (1985) (discussing who can waive the privilege); U.S. v. Zolin, 491 U.S. 562, 109 S.Ct. 2619, 2626 (1989); In Re Grand Jury Proceedings, 43 F.3d 966, 970 (5th Cir. 1994); McKenzie v. McCormick, 27 F.3d 1415, 1420 (9th Cir. 1994). This privilege may exist between two Federal agencies. Thill Securities Corp. v. New York Stock Exchange, 57 FRD 133 (E.D. Wis. 1972). However, the confidentiality of communications covered by a privilege must be jealously guarded by the holder of the privilege lest it be waived. In Re Sealed Case, 877 F.2d 976, 980 (D.C. Cir. 1989). See, Gray v. Bicknell, 86 F.3d 1472, 1483-84 (8th Cir. 1995), for discussion of approaches to waiver of attorney client privilege. A party may overcome the privilege when it can demonstrate that the crime/fraud exception applies. In Re: Sealed Case, __F.3d__ (D.C. Cir. March 4, 19977, No. 96-3085). That exception applies where: 1) the client made or received an otherwise privileged communication with the intent to further an unlawful or fraudulent act and 2) the client must have carried out the crime or fraud. Ibid.

3. Joint Defense Privilege (multiparty litigation). This privilege is an extension of the attorney-client privilege. The doctrine provides that communications between and among persons and their respective legal counsel, who share a common interest in presenting or defending a claim, are protected from disclosure. The party asserting this privilege must establish all of the elements of the attorney-client privilege and the additional requirement that the communication in question was made in the course of a common effort and to further a common interest. In Re Grand Jury Subpoenas, 89-3 and 89-4, 902 F.2d 244 (4th Cir. 1990); United States v. Schwimmer, 892 F.2d 237 (2d Cir. 1989), cert. denied, 502 U.S. 810 (1990); United States v. Lopez, 777 F.2d 543 (10th Cir. 1985) (waiver of privilege); United States v. McPartlin, 595 F.2d 1321 (7th Cir.), cert. denied, 444 U.S. 833 (1979) (whether legal interests must be identical or only compatible); Continental Oil Co. v. United States, 330 F.2d 347 (9th Cir. 1964).

4. Deliberative process privilege (intergovernmental opinions and recommendations submitted in the performance of decisional or policymaking functions). Freeman v. Seligson, 405 F.2d 1326 (D.C. Cir. 1968); Davis v. Braswell Motor Freight Lines, Inc., 363 F.2d 600 (5th Cir. 1966); Carl Zeiss Stiftung v. V.E.B. Carl Zeiss, Jena, 40 FRD 318 (D.D.C. 1966); aff'd per curiam sub nom. V.E. B. Carl Zeiss, Jena v. Clark, 384 F.2d 979 (D.C. Cir. 1966), cert. denied, 389 U.S. 952 (1967); Machin v. Zuchert, 316 F.2d 336 (D.C. Cir.), cert denied, 375 U.S. 896 (1963); Kaiser Aluminum & Chemical Corp. v. United States, 157 F.Supp. 939 (Ct.Cl. 1958); see, Ackerly v. Ley, 420 F.2d 1336 (D.C. Cir. 1969). (consistent with fifth exemption of Freedom of Information Act, 5 U.S.C. '552(b)(5)). This privilege must be invoked by the head of the agency. See, Thill, supra. The bank examiner qualified privilege is also included within the deliberative process privilege. In Re: Supoena Served Upon the Comptroller of the Currency and the Secretary of the Bd. of Governors of the Federal Reserve System, __F.2d __(D.C. Cir. 1992).

5. Executive Privilege (Presidential communications). United States v. Nixon, 418 U.S. 708, 94 S.Ct. 3090 (1974); In Re: Sealed Case, __F.3d__(D.C. Cir. June 17, 1997, No. 96-3124)(detailing explanation and history of Presidential Communications privilege and distinguishing it from deliberative process privilege). 6. Jenks Act, 18 U.S.C. '3500. Usually, in criminal cases, statements or reports in possession of U.S. made by a Government witness shall not be subject to a subpoena, discovery or inspection until the witness has testified on direct examination at trial. However, some agencies utilize the procedures of the Jenks Act in civil matters before an ALJ. See, e.g., 7 C.F.R. '1.141(g)(1)(iii). What is covered by the Jenks Act and its purpose are discussed in such cases as: Norisberg Corp. v. United States Dept. of Agriculture, 47 F.3d 1224 (D.C. Cir. 1995), cert. denied, 116 S.Ct. 474; Blackfoot Livestock Com'n v. USDA, 810 F.2d 916 (9th Cir. 1987); United States v. Carrasco, 537 F.2d 372 (9th Cir. 1981); United States v. Prieto, 505 F.2d 8 (5th Cir. 1974).

7. Identity of informer, civil cases. Dole v. Local 1942, IBEW, 870 F.2d 368 (7th Cir. 1989) (good discussion); Wirtz v. Continental Finance and Loan Co., 326 F.2d 561 (5th Cir. 1964); Wirtz v. B.A.C. Steel Products, Inc., 312 F.2d 14 (4th Cir. 1962); Mitchell v. Roma, 265 F.2d 633 (3d. Cir. 1959). But note, only the identity of the informer is privileged, not the communication itself, unless disclosure would operate to disclose the informer's identity. Brock v. On Shore Quality Control Specialists, Inc., 811 F.2d 282 (5th Cir. 1987); Wirtz v. Robinson & Stephens, Inc., 368 F.2d 114 (5th Cir. 1966); see, Roviaro v. United States, 353 U.S. 53, 77 S.Ct. 623 (1957).

8. Work-product privilege. Hickman v. Taylor, 329 U.S. 495 67 S.Ct. 385 (1947); Rule 26(b)(3), Fed. R. Civ. P.; Upjohn Co., et al. v. United States, et al., 449 U.S. 383, 101 S.Ct. 677 (1981). Applied to federal attorneys. See, NLRB v. Sears, Roebuck & Co., 412 U.S. 191, 154, 95 S.Ct. 1504, 1518 (1975), citing Kaiser Aluminum & Chemical Corp v. United States, 157 F.Supp 939, 946-947 (Ct.Cl. 1958).

9. Self-critical analysis privilege. A qualified privilege tha allows businesses to candidly assess their compliance with regulatory and legal requirements without creating evidence that may be used against them by their opponents in future litigation. Reichhold Chemicals, Inc. v. Textron, Inc., __F. Supp. __(N.D. Fla. 1994), 1994 WL 532165; Bredice v. Doctor's Hospital, Inc., 50 FRD 249 (D.D.C. 1970), aff'd without op., 479 F.2d 920 (D.C. Cir. 1973); Banks v. Lockheed-Georgia Co., 53 FRD 283 (N.D. Ga. 1971); In Re Crazy Eddie Securities Litigation, 792 F. Supp. 197 (E.D. N.Y. 1992); Keyes v. Lenoir Rhyne College, 552 F.2d 579 (4th Cir.), cert. denied, 434 U.S. 904 (1977); Lloyd v. Cessna Aircraft Co., 74 FRD 555 (E.D. Tenn 1977). But see policy considerations discussed in University of Pa. supra, militating against use of the self-critical analysis privilege in the EEO context.

10. Secrets of state and military secrets. United States v. Reynolds, 345 U.S. 1, 73 S.Ct. 528 (1953); Carl Zeiss, supra.

11. Trade secrets. Cases on trade secrets are: E.I. Du Pont de Nemours v. Masland, 244 U.S. 100, 37 S.Ct. 575 (1917); Tavoulareas v. The Washington Post Co., 724 F.2d 1010, 1017-1019 (D.C. Cir. 1984); Paul v. Sinnott, 217 F.Supp. 84 (W.D. Pa. 1963). See also 18 U.S.C. '1905 (prohibiting disclosure of trade secrets by government officials).

12. Grand jury privilege. United States v. Proctor & Gamble Co., 356 U.S. 677, 78 S.Ct. 983 (1958); see, Douglas Oil Co. of California v. Petrol Stops Northwest, 441 U.S. 211 (1979).

13. Psychotherapist-patient privilege. Counseling sessions between licensed psychiatrist or psychologist and patient and counseling sessions between licensed clinical social worker and patient. Recently adopted in Jaffee v. Redmond, 116 S.Ct. 1923 (1996).

14. Husband-wife privilege. SEC v. Levin, __F.3d__ (D.C. 	Cir. May 2, 1997, No. 96-5286).

15. Communications to clergy (priest-penitent) privilege.

16. Political vote privilege.

17. Doctor-patient privilege.

18. Researcher's or scholar's privilege. A qualified privilege principally to protect the interest of the researcher in not having the results of his or her research disclosed prematurely. Deitchman v. E.R. Squibb & Sons, Inc, 740 F.2d 556, 560-561 (7th Cir. 1984); Dow Chemical Co. v. Allen, 672 F.2d 1262, 1274-1276 (7th Cir. 1982); but see, In Re American Tobacco Co., 880 F.2d 1520 (2d Cir. 1989); Burka v. U.S. Dpet. of Health and Human Services, 87 F.3d 508 (D.C. Cir. 1996); Smith v. Dow Chemical Co., 173 F.R.D. 54, 57 (W.D.N.Y. 1997); Wilkinson v. FBI, 111 F.R.D. 42 (C.D. Cal. 1986).

A privilege log must be issued by the party claiming privilege, by specifically identifying each document or communication to be protected and the typoe of privilege or protection being asserted. See, e.g., Burns v. Imagine Films Entertainment, Inc., 164 F.R.D. 589, 594 (W.D.N.Y. 1996).

title: Faculty of Law


text:
User:MandaG/Tutorial 2 Week 3

My gosh this was a fun tutorial! We started by talking about types and levels of communication then moved onto what I found a very amusing game.

Levels of Communication

Shallow: Deeper: THOUGHTS AND OPINIONS- Unique to the individual, shows a degree of comfort "I think Rudd is an idiot for the tax on alchopops!" Deepest: FREUDIAN SLIP- Expression from the unconcious, eg. "A Freudian slip is like saying one thing, but meaning your mother."
 * GREETING- Script/establish contact. It means more NOT to communicate a greeting than to do so.
 * SMALL TALK- "Hey about this weather. "did you see them Knicks last night" etc
 * SHARING OF INFORMATION- Possibly unique, heading to deeper territory- eg. "How are the kids?"
 * EMOTIONAL- Shows a connection to the comunicatee (usually) eg. "Why doesn't he love me!?!?!?!"

Channels Of communication Facial Expressions, smiles, frowns, eyebrow movement. Body Language, closed off or open Tone of voice, you can usually tell by the tone of someones voice the meaning behind what they are trying to convey. My mother (as I expect all mothers are) is an expert at that one. Sign Language, for the hearing impaired communication through signs with the fingers. Like spoken words the language can vary between cultures and follows its own rules with grammer.
 * 1) Non-verbal: We tend to track the eye's and the mouth when watching someone speak.
 * 1) Verbal: The spoken and written word

The Games The first game we played was invasion of personal space. The reason I enjoyed this game so much was somewhat at the expense of my poor partner. You see since I was little I've always played contact sports or had my space invaded by one of my brothers so I'm very comfortable with people being closer than expected. My poor partner was not, as soon as I got close to him (and he swears it wasn't personal), he began to fidget and step back all the while giggling nervously. When we added eye contact to the equation it was all just too much and the poor fellow actually had to distance himself from the situation (again promising it wasn't personal). I found it interesting how nearly every person during the exercise was uncomfortable and gigglin or at least smiling.

The next game was the minefield. One partner was blindfolded and the other had to guide them through the maze safely. As some people left our group turned into a trio and I was impressed by how easily my two partners were able to guide me. I was then partnered with James and had to guide him while moving the object in the minefield around to force the leaders to change instructions to their partners quickly. This was a lot of fun and I managed to get James through safely and box in my old partner for giggling so much in the previous game...cruel yes but fun.

title: User:MandaG/Tutorial 2 Week 3


text: User talk:Rlbarnha

title: User talk:Rlbarnha


text: User talk:Altrotte

title: User talk:Altrotte


text: User talk:Gmurrell

title: User talk:Gmurrell


text: User talk:Acoberly

title: User talk:Acoberly


text: User talk:AshleyStacy

title: User talk:AshleyStacy


text: User talk:Wjones54

title: User talk:Wjones54


text: User talk:Iglika kazanaklieva

title: User talk:Iglika kazanaklieva


text:
User:Eas4200c.f08.blue.a/Lecture 27

Continuing from the equation of equilibrium in terms of $$\bar{\sigma}$$

The goal is to find $$\frac{\partial \sigma_{yx}}{\partial y}+\frac{\partial \sigma_{zx}}{\partial z}=0$$ (equation 3.14 in textbook) Lets use indicial notation $$\frac{\partial \sigma_{21}}{\partial x_{2}}+\frac{\partial \sigma_{31}}{\partial x_{3}}=0$$

Recall from section 2.4 that

$$\frac{\partial \sigma_{xx}}{\partial x}+\frac{\partial \tau_{yx}}{\partial y}+\frac{\partial \tau_{zx}}{\partial z}=0$$ (equation 2.21 in textbook)

It follows, using the indicial notation that the three equilibrium equations become

$$\frac{\partial \sigma_{11}}{\partial x_{1}}+\frac{\partial \tau_{21}}{\partial x_{2}}+\frac{\partial \tau_{31}}{\partial x_{3}}=0$$ (equation 2.21 in textbook)

$$\frac{\partial \tau_{12}}{\partial x_{1}}+\frac{\partial \sigma_{22}}{\partial x_{2}}+\frac{\partial \tau_{32}}{\partial x_{3}}=0$$ (equation 2.22 in textbook)

$$\frac{\partial \tau_{13}}{\partial x_{1}}+\frac{\partial \tau_{23}}{\partial x_{2}}+\frac{\partial \sigma_{33}}{\partial x_{3}}=0$$ (equation 2.23 in textbook)

Therefore the summation notation of the equilibrium equations is as follows

$$\sum_{i=1}^{3}{\frac{\partial \sigma_{ij}}{\partial x_{i}}}=0$$ for $$j=1,2,3$$

title: User:Eas4200c.f08.blue.a/Lecture 27