text:
Elasticity/Rotating rectangular beam

Example : Rotating Rectangular Beam
The body force potential is given by
 * $$\text{(52)}\qquad

V = -\cfrac{\rho\dot{\theta}^2}{2} \left(x_1^2 + x_2^2\right) $$ Hence,
 * $$ \text{(53)}\qquad

\nabla^2{V} = V_{,11} + V_{,22} = -\cfrac{\rho\dot{\theta}^2}{2} \left(2 + 2\right) $$ or,
 * $$ \text{(54)}\qquad

\nabla^2{V} = -2\rho\dot{\theta}^2 $$ The compatibility condition (in terms of stress) is
 * $$ \text{(55)} \qquad

\nabla^4{\varphi} + \left(2 - \cfrac{1}{\alpha}\right) \nabla^2{V} = 0 $$ Plug $$V$$ in to get
 * $$ \text{(56)} \qquad

\nabla^4{\varphi} - \left(2-\cfrac{1}{\alpha}\right) 2\rho\dot{\theta}^2 = 0 $$ Since $$V$$ is even in $$x_1$$ and $$x_2$$ and BCs are homogeneous, assume
 * $$ \text{(57)} \qquad

\varphi = A x_1^4 + B x_1^2 x_2^2 + C x_2^4 + D x_1^2 + E x_2^2 $$ Hence,
 * $$\begin{align}

\text{(58)}\qquad \sigma_{11} & = \varphi_{,22} + V = 2 B x_1^2 + 12 C x_2^2 + 2 E     -\cfrac{\rho\dot{\theta}^2}{2} \left(x_1^2 + x_2^2\right)\\ \text{(59)}\qquad\sigma_{22} & = \varphi_{,11} + V = 12 A x_1^2 + 2 B x_2^2 + 2 D      -\cfrac{\rho\dot{\theta}^2}{2} \left(x_1^2 + x_2^2\right)\\ \text{(60)}\qquad\sigma_{12} & = -\varphi_{,12} = - 4 B x_1 x_2 \end{align}$$ The traction BCs are
 * $$\begin{align}

\text{(61)} \qquad \text{at}~ x_1 = \pm a & &  t_1 = t_2 = 0 \Rightarrow \sigma_{11} = \sigma_{12} = 0 \\ \text{(62)} \qquad \text{at}~ x_2 = \pm b & & t_1 = t_2 = 0 \Rightarrow \sigma_{12} = \sigma_{22} = 0 \end{align}$$ Apply BCs at $$x_2 = \pm b$$.
 * $$\begin{align}

\text{(63}) \qquad \sigma_{22} = 0 & = 12 A x_1^2 + 2 B b^2 + 2 D      -\cfrac{\rho\dot{\theta}^2}{2} \left(x_1^2 + b^2\right)\\ \text{(64}) \qquad \sigma_{12} = 0 & = - 4 B b x_1 \end{align}$$ Therefore,
 * $$\begin{align}

\text{(65)} \qquad B & = 0 \\ \text{(66)} \qquad A & = \cfrac{\rho\dot{\theta}^2}{24} \\ \text{(67)} \qquad D & = \cfrac{\rho\dot{\theta}^2b^2}{4} \end{align}$$ We then have,
 * $$ \text{(68)} \qquad

\varphi = \cfrac{\rho\dot{\theta}^2}{24} x_1^4 + C x_2^4 + \cfrac{\rho\dot{\theta}^2b^2}{4} x_1^2 + E x_2^2 $$ Plug into compatibility equation
 * $$ \text{(69)} \qquad

\varphi_{,1111} + 2\varphi_{,1122} + \varphi_{,2222} - \left(2-\cfrac{1}{\alpha}\right) 2\rho\dot{\theta}^2 = 0 $$ to get
 * $$ \text{(70)} \qquad

24 \left(\cfrac{\rho\dot{\theta}^2}{24} + C\right) - \left(2-\cfrac{1}{\alpha}\right) 2\rho\dot{\theta}^2 = 0 $$ or,
 * $$\begin{align}

C & = \left(2-\cfrac{1}{\alpha}\right) \cfrac{\rho\dot{\theta}^2}{12} - \cfrac{\rho\dot{\theta}^2}{24} \\ & = \left(3-\cfrac{2}{\alpha}\right) \cfrac{\rho\dot{\theta}^2}{24} \qquad \text{(71)} \end{align}$$ Apply BCs at $$x_1 = \pm a$$.
 * $$\begin{align}

\text{(72)} \qquad \sigma_{11} = 0 & = 2 B a^2 + 12 C x_2^2 + 2 E     -\cfrac{\rho\dot{\theta}^2}{2} \left(a^2 + x_2^2\right)\\ & = \left(3-\cfrac{2}{\alpha}\right) \cfrac{\rho\dot{\theta}^2}{2} x_2^2 + 2 E -\cfrac{\rho\dot{\theta}^2}{2} \left(a^2 + x_2^2\right) \qquad \text{(73)} \end{align}$$ Strong BCs imply that
 * $$ \text{(74)} \qquad

\left(3-\cfrac{2}{\alpha}\right) \cfrac{\rho\dot{\theta}^2}{2} -\cfrac{\rho\dot{\theta}^2}{2} = 0 $$ which cannot be true. So weak BCs on $$\sigma_{11}$$ need to be applied at $$x_1 = \pm a$$.
 * $$\begin{align}

\text{(75)} \qquad \text{at}~ x_1 = \pm a & & \int_{-b}^{b} \sigma_{11} dx_2 = 0 \end{align}$$ Hence,
 * $$\text{(76)} \qquad

\left(3-\cfrac{2}{\alpha}\right) \cfrac{\rho\dot{\theta}^2}{2}\cfrac{2b^3}{3} + 4 Eb -\cfrac{\rho\dot{\theta}^2}{2} \left(2a^2b + \cfrac{2b^3}{3}\right)=0 $$ or,
 * $$\text{(77)} \qquad

\left(2-\cfrac{2}{\alpha}\right)\cfrac{\rho\dot{\theta}^2b^2}{3} + 4 E -\rho\dot{\theta}^2a^2 = 0 $$ Hence,
 * $$\text{(78)} \qquad

E = \cfrac{\rho\dot{\theta}^2}{4}\left[a^2- \left(2-\cfrac{2}{\alpha}\right)\cfrac{b^2}{3} \right] $$ The stress field is, therefore,
 * $$\begin{align}

\text{(79}) \qquad \sigma_{11} & = \left(3-\cfrac{2}{\alpha}\right) \cfrac{\rho\dot{\theta}^2}{2} x_2^2 + \cfrac{\rho\dot{\theta}^2}{2}\left[a^2- \left(2-\cfrac{2}{\alpha}\right)\cfrac{b^2}{3} \right] -\cfrac{\rho\dot{\theta}^2}{2} \left(x_1^2 + x_2^2\right)\\ \text{(80}) \qquad \sigma_{22} & = \cfrac{\rho\dot{\theta}^2}{2} x_1^2 + \cfrac{\rho\dot{\theta}^2b^2}{2} -\cfrac{\rho\dot{\theta}^2}{2} \left(x_1^2 + x_2^2\right) \\ \qquad \sigma_{12} & = 0 \end{align}$$ or,
 * $$\begin{align}

\text{(81)} \qquad \sigma_{11} & = \cfrac{\rho\dot{\theta}^2}{2}\left[\left(a^2 - x_1^2\right)+ 2\left(1-\cfrac{1}{\alpha}\right)\left(x_2^2-\cfrac{b^2}{3}\right)\right] \\   \text{(82)} \qquad \sigma_{22} & = \cfrac{\rho\dot{\theta}^2}{2}\left(b^2 - x_2^2\right) \\   \sigma_{12} & = 0 \end{align}$$ The displacements can be found in the standard manner.

title: Elasticity/Rotating rectangular beam


text:
Elasticity/Spinning disk

Problem 1:
A thin disk of radius $$a$$ is spinning about its axis with a constant angular velocity $$\dot{\theta}$$. Find the stress field in the disk using an Airy stress function and a body force potential.

Solution:
The acceleration of a point ($$r,\theta$$) on the disk is
 * $$ \text{(1)} \qquad

a_r = -\dot{\theta}^2 r ~; a_{\theta} = 0 $$ The body force field is
 * $$ \text{(2)} \qquad

f_r = \rho\dot{\theta}^2 r ~; f_{\theta} = 0 $$ Since there is no rotational acceleration, the body force can be derived from a potential $$V$$. The relations between the stresses, the Airy stress function and the body force potential are
 * $$\begin{align}

\text{(3)} \qquad \sigma_{rr} & = \frac{1}{r}\frac{\partial \varphi}{\partial r} + \frac{1}{r^2}\frac{\partial^2 \varphi}{\partial \theta^2} + V  \\ \text{(4)} \qquad \sigma_{\theta\theta} & = \frac{\partial^2 \varphi}{\partial r^2} + V \\ \text{(5)} \qquad \sigma_{r\theta} & = -\frac{\partial }{\partial r}     \left(\frac{1}{r}\frac{\partial \varphi }{\partial \theta} \right) \end{align}$$ where
 * $$ \text{(6)} \qquad

f_r = -\frac{\partial V }{\partial r} ~;~ f_{\theta} = -\frac{1}{r}\frac{\partial V}{\partial \theta} $$ From equations (2) and (6), we have,
 * $$\begin{align}

\text{(7)} \qquad \rho\dot{\theta}^2 r & = -\frac{\partial V}{\partial r} \\ \text{(8)} \qquad 0 & = -\frac{1}{r}\frac{\partial V}{\partial \theta} \end{align}$$ Integrating equation (7), we have
 * $$\text{(9)} \qquad

V = -\rho\dot{\theta}^2 \frac{r^2}{2} + h(\theta) $$ Substituting equation (9) into equation (8), we get
 * $$\text{(10)} \qquad

\frac{dh(\theta)}{d\theta} = 0 \Rightarrow h(\theta) = C $$ This constant can be set to zero without loss of generality. Therefore,
 * $$\text{(11)} \qquad

V = -\rho\dot{\theta}^2 \frac{r^2}{2} $$ The spinning disk problem is a plane stress problem. Hence the compatibility condition is
 * $$\text{(12)} \qquad

\nabla^4{\varphi} + \left(2-\frac{1}{\alpha}\right)\nabla^2{V} = 0 \Rightarrow \nabla^4{\varphi} + (1-\nu)\nabla^2{V} = 0 $$ where
 * $$\begin{align}

\text{(13)} \qquad \nabla^2{} & = \frac{\partial^2 }{\partial r^2} + \frac{1}{r}\frac{\partial  }{\partial r} + \frac{1}{r^2}\frac{\partial^2 }{\partial \theta} \\ \text{(14)} \qquad \nabla^4{} & = \nabla^2{[\nabla^2{}]} \end{align}$$ Now, from equations (11) and (13)
 * $$\text{(15)} \qquad

\nabla^2{V} = -\rho\dot{\theta}^2[1 + 1 + 0] = -2\rho\dot{\theta}^2 $$ Therefore, equation (12) becomes
 * $$\text{(16)} \qquad

\nabla^4{\varphi} = 2 \rho\dot{\theta}^2(1-\nu) $$ Since the problem is axisymmetric, there can be no shear stresses, i.e. $$\sigma_{r\theta} = 0$$ and no dependence on $$\theta$$. From Michell's solution, the appropriate terms of the Airy stress function are
 * $$\text{(17)} \qquad

r^2 ~; r^2\ln(r) ~; \ln(r) $$ Axisymmetry also requires that $$u_{\theta}$$, the displacement in the $$\theta$$ direction must be zero. However, if we look at Mitchell's solution, we see that $$u_{\theta}$$ is non-zero if the term $$r^2\ln(r)$$ is used in the Airy stress function. Hence, we reject this term and are left with
 * $$\text{(18)} \qquad

\varphi = C_1r^2 + C_2 \ln(r) $$ If we plug this stress function into equation (16) we see that $$\nabla^4{\varphi} = 0$$. Therefore, equation (18) represents a homogeneous solution of equation (16). The $$\varphi$$ that is a general solution of equation (16) is obtained by adding a particular solution of the equation.

One such particular solution is the stress function $$\varphi = C_0 r^4$$ since the biharmonic equation must evaluate to a constant. Plugging this into equation (16) we have
 * $$\text{(19)} \qquad

\nabla^4{\varphi} = 64 C_0 = 2 \rho\dot{\theta}^2(1-\nu) $$ or,
 * $$\text{(20)} \qquad

C_0 = \frac{\rho\dot{\theta}^2(1-\nu)}{32} $$ Therefore, the general solution is
 * $$\text{(21)} \qquad

\varphi = \frac{\rho\dot{\theta}^2(1-\nu)}{32}r^4 + C_1r^2 + C_2 \ln(r) $$ The corresponding stresses are (from equations (3, 4, 5)),
 * $$\begin{align}

\text{(22)} \qquad \sigma_{rr} & = -\frac{(3+\nu)\dot{\theta}^2\rho r^2}{8} + 2 C_1 + \frac{C_2}{r^2} \\ \text{(23)} \qquad \sigma_{\theta\theta} & = -\frac{(1+3\nu)\dot{\theta}^2\rho r^2}{8} + 2 C_1 - \frac{C_2}{r^2} \\ \text{(24)} \qquad \sigma_{r\theta} & = 0 \end{align}$$ At $$r = 0$$, the stresses must be finite. Hence, $$C_2 = 0$$. At $$r = a$$, $$\sigma_{rr} = \sigma_{r\theta} = 0$$. Evaluating $$\sigma_{rr}$$ at $$ r = a$$ we get
 * $$\text{(25)} \qquad

C_1 = \frac{(3+\nu)\rho\dot{\theta}^2 a^2}{16} $$ Substituting back into equations (22) and (23), we get
 * $$\text{(26)} \qquad

\sigma_{rr} = \frac{\rho\dot{\theta}^2}{8}(3+\nu)(a^2-r^2) $$
 * $$\text{(27)} \qquad

\sigma_{\theta\theta} = \frac{\rho\dot{\theta}^2}{8}\left[ (3+\nu)a^2 - (1+3\nu)r^2\right] $$
 * $$\text{(28)} \qquad

\sigma_{r\theta} = 0 $$

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

title: Elasticity/Spinning disk


text: File:Elastic spinning disk.png

title: File:Elastic spinning disk.png


text:
Characteristics of developing economies

Developing nations are those with low, lower middle, or middle incomes relative to other countries. Common characteristics of developing countries are low levels of living characterized by low income, inequality, poor health and inadequate education.Also they are countries with low Human Development Index

Low levels of living are not only in relation to their counterparts in rich nations, but also in relation to the small elite class within their own countries. These low levels of living are manifested quantitatively and qualitatively in the following
 * a general sense of malaise and hopelessness.
 * a low gdp (gross domestic product)

Many people in developing nations fight a constant battle against malnutrition, disease and ill health. In least developed countries life expectancy in 1998 averaged only 48 years, 68 years among developing countries and 75 in developed countries.

In the 1990's in Asia and Africa, over 60% of the population barely met minimum caloric requirements needed to maintain adequate health.

Malnutrition, waterborne disease, and aids also afflict these countries while low literacy levels require significant school development.

Activities

 * 1) Consider: if you could create your own country, what would it be like? What would you call it? What are the rules?

title: Characteristics of developing economies


text:
User:AlistairReece

Background
I am an army brat, which means my father was a soldier and I grew up in a military environment and moved regularly from place to place, I lived mainly in the UK and Germany when I was a child. Eventually we settled in the Outer Hebrides on an island called Benbecula.

I studied in Birmingham, although the college was validated by the University of Wales, and I have 2:1 degree in theology, in particular I enjoyed studying hermeneutics.

I enjoy learning languages and can speak at differing levels the following

 * Czech - quite good but awful grammar
 * French - reasonable, have forgotten loads but it is coming back as my parents live near Limoges and their friends are all French
 * German - similar to my French, but I would love to brush it up again.
 * Slavic languages - I can read Cyrillic and can work out the meaning of most things I read in several Slavic languages.
 * I have a working knowledge of American English.

Position and Roles
I am a Business Analyst for a software company that builds hosting platforms for academic publishers, focusing on the Science, Technology and Medical markets.

I work in the support and enhancement side of the company, and am responsible for gathering and documenting requirements for bugs, client functionality requests and platform enhancements.

Goals
My work goals are as follows:

 * 1) Learn as much about technical writing as possible
 * 2) Become as good a technical writer as I can be
 * 3) Progress through the technical writing department assuming more responsibility and being productive

My life goals are

 * 1) To buy at least 50 acres of land somewhere and become self-sufficient - I wrote this in 2007, I now have 1.6 acres and a vegetable garden which provides most of the daily vegetables my wife and I need.
 * 2) To finally write the novel in my head - still rattling around...
 * 3) To die old, fat and happy

Interests
I love reading, I can't imagine life without books. My favourite author is Umberto Eco, although I recently read the Harry Potter books and was pleasantly surprised.

I also enjoy music, I like bands such as the Smiths, Fleetwood Mac, Madness, Starflyer 59, Morex Optimo, as well as enjoying both classical music and opera, but I can't stand jazz and techno.

My other hobbies are cooking, which I am good at, football and photography.

title: User:AlistairReece


text:
BCP/Anthemis nobilis

Anthemis nobilis

title: BCP/Anthemis nobilis


text:
BCP/Anthemis nobilis/Logs

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title: BCP/Anthemis nobilis/Logs


text:
BCP/Belamcanda chinensis

Belamcanda chinensis

title: BCP/Belamcanda chinensis


text:
BCP/Belamcanda chinensis/Logs

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title: BCP/Belamcanda chinensis/Logs


text:
BCP/Buddleja davidii

Buddleja davidii

title: BCP/Buddleja davidii


text:
BCP/Buddleja davidii/Logs

2007 Logs

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title: BCP/Buddleja davidii/Logs


text:
BCP/Clematis virginiana/Logs

This page contains recent bloom logs for the plant Clematis virginiana (Virgin's Bower).

Recent Logs

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=====Archived Logs===== (If there are more than 5 signatures under the recent logs heading, move the oldest logs to under this heading (generally leave the 3 most recent).
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title: BCP/Clematis virginiana/Logs


text:
BCP/Plantago lanceolata/Logs

2007 Logs

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2009 Logs

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title: BCP/Plantago lanceolata/Logs


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BCP/Vernonia noveboracensis/Logs

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title: BCP/Vernonia noveboracensis/Logs


text:
BCP/Lythrum salicaria/Logs

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title: BCP/Lythrum salicaria/Logs


text:
Bloom Clock/Keys/Southeastern Pennsylvania/August/White Flowers/DPL

This page is used to help create a graphical list.

 category=White flowered plants category=BCP/SEPA/8 order=descending ordermethod=lastedit


text:
Bloom Clock/Keys/Southeastern Pennsylvania/August/White Flowers

The plants pictured below have been recorded as blooming during the month of August in Southeastern Pennsylvania.

last updated 09:02, 18 October 2007 (UTC) with 62 plants


text:
User talk:Adexofall

Hello Adexofall, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. When leaving comments for others to read, remember to sign and date; it helps everyone keep track of who is writing messages. The signature icon in the edit window makes it simple. To help you get started:
 * Take a guided tour and learn how to edit;
 * Explore our learning projects;
 * Browse our portals, schools, and research pages; and
 * Read and help develop our community policies.

Also, don't forget to experiment with the links to your left. Be bold, and see you around Wikiversity! --JWSchmidt 14:01, 3 August 2007 (UTC)

title: User talk:Adexofall


text:
User talk:AlistairReece

Hello AlistairReece, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. When leaving comments for others to read, remember to sign and date; it helps everyone keep track of who is writing messages. The signature icon in the edit window makes it simple. To help you get started:
 * Take a guided tour and learn how to edit;
 * Explore our learning projects;
 * Browse our portals, schools, and research pages; and
 * Read and help develop our community policies.

Also, don't forget to experiment with the links to your left. Be bold, and see you around Wikiversity! --JWSchmidt 14:12, 3 August 2007 (UTC)

Pages
Hi there! Could you check out the page Pavel Swarz and see if it needs some updating? One user requested it to be deleted, but I was under the impression that it was needed for another project, so I declined the deletion request. If it needs removal, do let me know. --HappyCamper 03:19, 15 August 2007 (UTC)

Morning - sure, go ahead and delete it. Sorry, I started it for the personas section of the Technical Writing course and did it wrong, oops. AlistairReece 05:33, 15 August 2007 (UTC)

 * Oh, no problem at all. OK, I'll go ahead then. Thanks for your note! --HappyCamper 16:21, 15 August 2007 (UTC)

Only really started learning more about wiki a few weeks ago. Thanks for your help. AlistairReece 06:15, 16 August 2007 (UTC)

copyright information for images
Image:Fredpic.jpg needs copyright information. Please indicate the source of the image and if the image is in the public domain or available under a copyleft license. --JWSchmidt 15:45, 21 August 2007 (UTC)

The source of the picture was TWFred himself. AlistairReece 07:10, 22 August 2007 (UTC)

 * Please add that source information to the image's page. Also, take a look at copyright information and decide of a license for the image. If you want to place it in the public domain, just add to the image's page. If you want people to attribute the image to you when they copy/re-use it, then you can license it under the GFDL or another copyleft license. Please do not turn pages in the "Image:" namespace into redirect pages. You are creating a source of needless confusion for other editors. --JWSchmidt 14:24, 22 August 2007 (UTC)

Will do - we were using the images to show how to make re-directs using wiki markup as part of the technical writing course. AlistairReece 05:40, 23 August 2007 (UTC)

Thanks for the heads up by the way. AlistairReece 06:35, 23 August 2007 (UTC)

Redirects and page names
Hi Alistair. I wasn't quite sure who was in charge of this course! There some slightly strange things going on as regards page titles and redirects - perhaps we should talk about it? The page titles definitely aren't best practice, and I don't know why your students are redirecting images to pages. I've tried to make some alternative suggestions about page titles, and I'll undo the image redirects. Can you tell me what you want to do with the images? And I'll try and sort out that template for you - perhaps I accidentally did something. McCormack 10:06, 23 August 2007 (UTC)

Replying to your 2nd message: I'm trying to help you guys out here - can you look at my questions above? Thanks! McCormack 10:20, 23 August 2007 (UTC)

I actually just asked you about it. To clarify, the students are doing the re-directs as part of the course. If it is a problem for wikiveristy, then we can remove the re-directs after our next class, which is tonight. Does that work for you? With reagrd to the "in charge" thing, TWFred is teaching the course, I am the main editor of the wikiversity site but it is a collaborative effort from the entire class AlistairReece 10:22, 23 August 2007 (UTC)

 * If you redirect the images, the images cannot be used or viewed any more. There's no purpose I can see behind uploading an image, and then rendering it both non-viewable and non-usable! The normal way to use an image is to follow the instructions I added to the technical writing page. Can you explain to me why you want to use the redirects? Perhaps there's a better way to achieve the same goal? McCormack 10:29, 23 August 2007 (UTC)

The purpose of the exercise was to create a thumbnail picture and a re-direct to a studetn page. We did this mainly to show what can be done with wiki. Personally speaking I would rather click on a picture than be given a list of names. The use of the picture is to solely exist as a re-direct. AlistairReece 11:03, 23 August 2007 (UTC)

Imagemaps
There is a little trick you can use to solve this problem, it is called "imagemap". Try clicking on various parts of this image: There is an instruction manual page about image maps at this wiki. If you need help with this, let me know. --JWSchmidt 13:57, 23 August 2007 (UTC)

I looked at that as an option, but decided that the re-direct thing was quicker. On our internal wiki we use a re-direct off pictures as a naivigation aid. We decided to use it in the tech writing course just as a feature of wiki - which is new to most of the class. As I said earlier we were planning on removing the re-directs this evening, perhaps we should have noted this somewhere - spent the afternoon dealing with people wondering why their exercise was working one minute and then not the next. Anyway, learning plenty in the process. Thanks for your help again so far - and your patience! AlistairReece 14:29, 23 August 2007 (UTC)

Redirects
I am curious - I've noticed that a lot of the images for the technical writing group have redirects to other pages - what is supposed to be the intended effect? It's very rare to see these redirects on other wikis, so I'm wondering that there might be something I could do that could be better to help out. Thoughts? --HappyCamper 15:39, 23 August 2007 (UTC)
 * OK, I see that I'm a bit late to the party after reading the sections above. Let me get back to you if I find another alternative. --HappyCamper 15:45, 23 August 2007 (UTC)

question about Wing Lee - What is the signifiance of this page in Wikiversity?
Hello, could you have a look at Talk:Wing Lee, since you were the creator of that page. Thanks, Erkan Yilmaz ( my talk page, wiki blog ) 14:56, 7 October 2007 (UTC)
 * Thank you for the exaplanation.
 * I just see, that there are also these pages about Wing Lee:
 * Technical writing Persona Wing Lee
 * Technical writing persona Wing Lee
 * Can these be deleted then ? Perhaps also somewhere on the Lee page could be written that it is an invented figure and has no similarity with a living person ? Erkan Yilmaz ( my talk page, wiki blog ) 06:21, 8 October 2007 (UTC)

Perhaps it is better to delete the first page you mentioned. I will put a disclaimer on the others. Cheers. AlistairReece 12:04, 9 October 2007 (UTC)
 * Hello AlistairReece, well we would need only 1 page I guess, so please you decide which one should live for the next 100 years? :-) Erkan Yilmaz ( my talk page, wiki blog ) 17:12, 9 October 2007 (UTC)

Ok: feel free to delete Wing Lee and Technical writing Persona Wing Lee. Thanks for pointing out the duplication. AlistairReece 07:48, 10 October 2007 (UTC)
 * done, Erkan Yilmaz ( my talk page, wiki blog ) 15:56, 10 October 2007 (UTC)

Image copyright problems

 * The following images are affected. Please provide a source and license template for each one. Thanks. – Mike.lifeguard | @en.wb 23:29, 13 February 2008 (UTC)

 * 2007-08-09 15:20, AlistairReece: Algrab.jpg: untagged! ; 1 (1)
 * 2007-08-17 06:28, AlistairReece: 3 04.gif: untagged! ; 1 (1)
 * 2007-08-17 06:29, AlistairReece: 3 03.gif: untagged! ; 1 (1)
 * 2007-08-21 10:51, AlistairReece: IMG 1595.jpg: untagged! ; 0 (0)
 * 2007-08-21 10:53, AlistairReece: Alistair.jpg: untagged! ; 0 (0)

title: User talk:AlistairReece


text:
User talk:Kumaarps

Hello Kumaarps, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. When leaving comments for others to read, remember to sign and date; it helps everyone keep track of who is writing messages. The signature icon in the edit window makes it simple. To help you get started:
 * Take a guided tour and learn how to edit;
 * Explore our learning projects;
 * Browse our portals, schools, and research pages; and
 * Read and help develop our community policies.

Also, don't forget to experiment with the links to your left. Be bold, and see you around Wikiversity! --JWSchmidt 14:17, 3 August 2007 (UTC)

protecting pages from editing
You can use Template:Protect. See also Page protection templates. --JWSchmidt 02:48, 4 August 2007 (UTC)

hi
hi kumar. i am a BCA student. i am just looking for the BCA section to complete.anyways it is a very good attempt.that will be very helpful.

title: User talk:Kumaarps


text: File:SaveDev-C++.jpg

title: File:SaveDev-C++.jpg


text:
Installing and using Dev-C++

This little article will teach you how to install the latest version of Dev-C++ and how to write a C program in it. This way, you will know how to write C programs, compile, and find the executable.

Dev-C++ is not actually a compiler, but an IDE. The link below is an installation of Dev-C++ which is prepackaged with MinGW. MinGW is the GCC compiler but made for usability in Windows.

Downloading
Click on this

Installing
Hit all the next buttons before install Dev-cpp.

Using Dev-C++
By default Dev-C++ is installed to C:\Dev-Cpp.

Go there and open up the .exe called devcpp.

It should look something like this.

Creating a Project
To write a program, you have to make the source code files. To do this you create a project.

To create a project you go to File > New > Project.

A dialog will come up asking you what kind of project you would like to make, what you would like to name it, and if you want to compile in C++ or C. There are many project templates for different types of programs. Select the Console Application template and the language you want to compile in is C. Then name the project something. It would be recommended that when you save this project, that you should save it to it's own folder. You should probably make a folder under C:\Dev-Cpp called Projects and then make a folder this project. The reason being wherever you save this project it'll create multiple files and could get cluttered very fast if you do not make a folder.

Compiling and Executing
Compiling and executing a program is very simple. You can hit F9 to compile and execute or click the button.

If all goes well then a console should come up and display "Press any key to continue..."

The Interface
There are many features, and the Dev-C++ is pretty easy to understand. There are two important windows that you should know to get you started.

The first is where you actually edit the source code for your programs. It has syntax highlighting and formatting making it easier to read.

The second would be the navigating of your projects and your source code files. This is so you can see how your projects are organized.

title: Installing and using Dev-C++


text:
BCP/Persicaria maculosa/Logs

This page contains recent bloom logs for the plant Persicaria maculosa (Lady's Thumb).

Recent Logs

 * --Luai lashire 18:31, 22 September 2007 (UTC)
 * --SB_Johnny | talk 14:12, 1 October 2007 (UTC)
 * --Luai lashire 20:45, 17 October 2007 (UTC)
 * --SB_Johnny | talk 13:08, 24 October 2007 (UTC)
 * --SB_Johnny | talk 10:01, 2 November 2007 (UTC)
 * --SB_Johnny | talk 07:32, 19 June 2008 (UTC)
 * --SB_Johnny | talk 10:22, 14 July 2008 (UTC)

=====Archived Logs===== (If there are more than 5 signatures under the recent logs heading, move the oldest logs to under this heading (generally leave the 3 most recent).

 * --SB_Johnny | talk 12:11, 4 July 2007 (UTC)
 * --SB_Johnny | PA! 17:03, 3 August 2007 (UTC)
 * --SB_Johnny | PA! 10:18, 12 August 2007 (UTC)
 * --Luai lashire 18:43, 25 August 2007 (UTC)
 * --SB_Johnny | talk 10:38, 1 September 2007 (UTC)
 * --Luai lashire 21:55, 1 September 2007 (UTC)
 * --Luai lashire 21:52, 5 September 2007 (UTC)
 * --Luai lashire 14:13, 9 September 2007 (UTC)

title: BCP/Persicaria maculosa/Logs


text:
Storing and processing imprecise data

Purpose
This is an original Computer Science research program to create standards, algorithms and open source library software for storing data with varying levels of precision and granularity.

For example, in an application containing family history, some information is, of necessity, anecdotal. A picture may be known to include "one of the Jones twins, but I can't remember if it's Bobby or James". The date of the photograph may be known (July 4th, say) but the year may only be approximate.

A Plan

 * 1) Decide what we should be able to store
 * 2) Create test cases, including performance requirements for a minimal set of features as release 0.1
 * 3) Implement release 0.1
 * 4) Evaluate the release 0.1 including refining overall goals
 * 5) Repeat steps 2-4 for subsequent releases until overall goals have been met

Participants

 * User:Dmclean (principal investigator)

Please add your name here if you are interested in participating as a co-investigator or reviewer.

Categories of data

 * Dates and date ranges

title: Storing and processing imprecise data


text:
Science Journalism/Characteristics

Back to Topic:Science journalism or Introduction to Science Journalism

How would you rank these?

 * Newsworthiness
 * Novelty
 * Mass appeal
 * Human interest
 * Highlighting/protecting the public interest
 * Investigative
 * Audience fit
 * Good writing/a story well told
 * Context setting (sounds in radio, etc)
 * Structure
 * Science ok
 * Expert quotes (Who and what)
 * Balance or diversity
 * Voice – close fit or distinctive
 * Good translation
 * Fit with publication agenda
 * Avoiding cliché
 * Illustration
 * Does the piece fit together as a whole?

Additional considerations

 * The pitch
 * Contacts
 * Delivery
 * Turnover
 * Legwork and working within budget

title: Science Journalism/Characteristics


text:
Science Journalism/Activities/Organisations

Back to Topic:Science journalism or Introduction to Science Journalism

You will find links to national science writing organisations in the pages of the World Federation of Science Journalists. Look on the left hand menu and you will see a link to Member Associations. Science writing associations often welcome broadcasters and other media professionals as well. Many of the associations that have the word 'writer' in the title, such as the Association of British Science Writers, were often formed in the 1940s when broadcasting was a relatively new medium. Associations that were formed later, such as the European Union of Science Journalists' Associations, often use the word 'journalist' instead.


text:
Electric Circuit Analysis/Simple Resistive Circuits/Answers

 * 1) 600 V, 180,000W.
 * 2) 0.04A, more commonly written 40mA.
 * 3) 134.164V, 0.447A.
 * 4) No. There is not enough information. The only thing that is given is the voltage. With two equations there can only be two unknowns, one unknown is great, but we have three.
 * 5) How did you do?


text:
User talk:Jose~enwikiversity

hi As I just created the account I dont know the exact proceedure to follow. Help me to learn. Well what is this

Jose

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Jose. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Jose~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:35, 17 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 06:12, 19 April 2015 (UTC)

title: User talk:Jose~enwikiversity


text:
Talk:Across the Wikiverse

Phase me! CQ 18:19, 3 August 2007 (UTC)

Production center in New Orleans area
I've relocated to the New Orleans area. I've found some new friends down here that are developing community centers in Metairie and New Orleans. I'm their new "computer guy" and they are open to new ideas. The centers will have music gear (even drums!) and extensive computing power. We may even be able to put a version of the Sandbox Server online from here (we'll see). If anyone out there is in or near NOLA and wants to help out (in the non-abstract realm), please contact me immediately! CQ 18:31, 3 August 2007 (UTC)

 * After a year and two month's of trying to establish a working base in New orleans, run into much difficulty but made some inroads. There are several artists, musicians, clergy folks, business people, drunks and bartenders (I don't limit my associations much) who are receptive to the idea of creating a base like the one I have in mind. It's just that the "land-lordy" type people have one thing to say:

 * "Show Me the Money!"

 * A center is still plausible at 1242 St.Roch in New Orleans, if the storm didn't damage it. I'm still not sure how much lattitude and creative freedom there would be unless I was the one securing the actual capital (which I'm not good at). Currently, I'm evacuated to Shreveport due to Gustav and quite up in the air. I shall now consider proposals to relocate to another part of the planet. I hear a rumor that SBJohnny may have an alternative place. Hmmm. Something to think (and pray) about. Hmmmm. • CQ 16:40, 3 September 2008 (UTC)

Needs greater clarity, focus, and copyediting
Hmmm sounds like my life. Thanks for the cleanup tag, Jtneill.

Clarity: The whole idea of the Across the Wikiverse WCR show is to help build community.

Focus: The production of open-content media captured from the real world.

Participation is Everything!, after all. The logistics involved in the Across the Wikiverse experiment are difficult. I'm not well-established out here in the "real world". (no car, no equipment, very little cash, no particular place to dwell, etc.) I'm currently in New Jersey, but heading back to New Orleans tomorrow. I was in Central Park today, in fact. Well I gotta run as soon as I copyedit a little.

Next time, if you want to phase me, do it here on the talk page, please. But thanks for your interest in Quality! • CQ 04:34, 12 June 2008 (UTC)

Update
I am now back at my sister's farm in Kentucky. The situations in New Orleans and Memphis are still favorable for establishing urban production centers and cyber-cafe facilities there. I'm connecting with similar ideas all over the world, so this is just a matter of time and confluence. The centers can be urban, suburban or rural.

The needs:
 * 1) Realty: storefronts, garages, kitchen tables...
 * 2) Network: servers, software and bandwidth...
 * 3) Production: talent, equipment, enthusiasm...
 * 4) Wiki: participation, ideas, promotion in the wikiverse

I'm working with OpenKollab members and Espians who understand this concept clearly. CQ 16:11, 22 August 2009 (UTC)

Build 20150325
Been working on the Internet version of this since 2001:
 * It is now up to us to displace the complacent attitudes in this region by radical actions based on some advanced concepts that we've discovered. A few people in the area understand these concepts and see how we intend to apply them. CQ Build 20010725

I've since my last edit spent a couple of years in Chicago, USA and still waiting for reality to make it to Wikiversity. See Chicago Acoustic Underground for some ideas of how the program's music will evolve. We're connecting with many other places, too.

I know this is taking too long, but this program and practicum are still on queue as soon as ONE PERSON agrees that the show is real. But what does Wikiversity or ANY web community have to do with the real world? Consider this:

 * "Perhaps the Distributed Autonomous Organization itself should be held liable for its own actions. But then we encounter an ever bigger problem in terms of law enforcement. It is virtually impossible to recover damages or to obtain an injunction unless these measures have been specifically encoded into the contract/constitution of the organization." Retrofuturism

The conversation moves the groove from Moore's law through Peter Diamandis and on through the blockchain to new possibilities like Ethereum ... and we are taking it further... CQ (discuss • contribs) 00:52, 25 March 2015 (UTC)

Build 20160123
SYZYGY17 - LibrePlanet.org - Google Doc • CQ (discuss • contribs) 18:37, 9 February 2016 (UTC)

title: Talk:Across the Wikiverse


text:
Talk:Lecture Digital Logic Gates

I am going to put in some LaTeX to illustrate the symbols that are talked about.

--Bgorges 18:20, 3 August 2007 (UTC)

2 preposed page moves for EE111 Class
I'm really thinking we should move the page to the page Number system to "EE 111 Digital Electronics/Lecture 1, Introduction to Binary, Octal and Hexadecimal Mathematics" and the page Lecture 2, Digital Logic to "EE 111 Digital Electronics/Lecture 2, Digital Logic" and

simply number systems is ambiguous and doesn't specify its a part of the ee111 class this also allows for a auto generated back link and helps keep it together as a part of this class thoughts ideas ? Eadthem 18:41, 29 September 2007 (UTC)

title: Talk:Lecture Digital Logic Gates


text:
Elasticity/Homogeneous and inhomogeneous displacements

Homogeneous Displacement Field
A displacement field $$\textstyle \mathbf{u}(\mathbf{X})$$ is called homogeneous if

 * $$ \mathbf{u}(\mathbf{X}) = \mathbf{u}_0 + \boldsymbol{A}\bullet[\mathbf{X} - \mathbf{X}_0] $$

where $$\textstyle \mathbf{X}_0, \mathbf{u}_0, \boldsymbol{A}$$ are independent of $$\textstyle \mathbf{X}$$.

Pure Strain
If $$\textstyle \mathbf{u}_0 = 0$$ and $$\textstyle \boldsymbol{A} = \boldsymbol{\varepsilon}$$, then $$\textstyle \mathbf{u}$$ is called a pure strain from $$\textstyle \mathbf{X}_0$$, i.e.,

 * $$ \mathbf{u}(\mathbf{X}) = \boldsymbol{\varepsilon}\bullet[\mathbf{X} - \mathbf{X}_0] $$

{| cellspacing="0" cellpadding="0" style="margin:0em 0em 1em 0em; width:80%"  Examples of pure strain If $$\textstyle \mathbf{X}_0$$ is a given point, $$\textstyle \mathbf{p}_0(\mathbf{X}) = \mathbf{X} - \mathbf{X}_0$$, and $$\textstyle \{\mathbf{e}_1, \mathbf{e}_2, \mathbf{e}_3\}$$ is an orthonormal basis, then
 * colspan="2" style="width:80%; horizontal-align:right; vertical-align:top; border:1px solid Sienna; background-color:White;" |

Simple Extension
For a simple extension $$\textstyle e$$ in the direction of the unit vector $$\textstyle \mathbf{n}$$

 * $$ \mathbf{u} = e ({\mathbf{n}}\bullet{\mathbf{p}_0}) \mathbf{n} $$

and
 * $$ \boldsymbol{\varepsilon} = e \mathbf{n}\otimes\mathbf{n} $$

If $$\textstyle \mathbf{n} = \mathbf{e}_1$$ and $$\textstyle \mathbf{X}_0 = \{0,0,0\}$$, then (in matrix notation)

 * $$ \mathbf{u} = \{e, 0, 0\} $$

and
 * $$ \boldsymbol{\varepsilon} = \begin{bmatrix}e&0&0\\0&0&0\\0&0&0 \end{bmatrix} $$

The volume change is given by $$\textstyle \text{Tr}(\boldsymbol{\varepsilon}) = e$$.

Uniform Dilatation
For a uniform dilatation $$\textstyle e$$,

 * $$ \mathbf{u} = e~ \mathbf{p}_0 $$

and
 * $$ \boldsymbol{\varepsilon} = e~ \boldsymbol{\it{1}} $$

If $$\textstyle \mathbf{X}_0 = \{0,0,0\}$$ and $$\textstyle \mathbf{X} = \{X_1,X_2,X_3\}$$, then (in matrix notation)
 * $$ \mathbf{u} = \{e X_1, e X_2, e X_3\} $$

and
 * $$ \boldsymbol{\varepsilon} = \begin{bmatrix}e&0&0\\0&e&0\\0&0&e \end{bmatrix} $$

The volume change is given by $$\textstyle \text{Tr}(\boldsymbol{\varepsilon}) = 3e$$.

Simple Shear
For a simple shear $$\textstyle \theta$$ with respect to the perpendicular unit vectors $$\textstyle \mathbf{m}$$ and $$\textstyle \mathbf{n}$$,

 * $$ \mathbf{u} = \theta[({\mathbf{m}}\bullet{\mathbf{p}_0}) \mathbf{n}+({\mathbf{n}}\bullet{\mathbf{p}_0})\mathbf{m}] $$

and
 * $$ \boldsymbol{\varepsilon} = \theta[{\mathbf{m}}\otimes{\mathbf{n}}+{\mathbf{n}}\otimes{\mathbf{m}}] $$

If $$\textstyle \mathbf{m} = \mathbf{e}_1$$, $$\textstyle \mathbf{n} = \mathbf{e}_2$$, $$\textstyle \mathbf{X}_0 = \{0,0,0\}$$, and $$\textstyle \mathbf{X} = \{X_1,X_2,X_3\}$$, then (in matrix notation)

 * $$ \mathbf{u} = \{\theta X_2, \theta X_1, 0\} ;   \boldsymbol{\varepsilon} = \begin{bmatrix}0&\theta&0\\\theta&0&0\\0&0&0 \end{bmatrix} $$

The volume change is given by $$\textstyle \text{Tr}(\boldsymbol{\varepsilon}) = 0$$.
 * }

Inhomogeneous Displacement Field
Any displacement field that does not satisfy the condition of homogeneity is inhomogenous. Most deformations in engineering materials lead to inhomogeneous displacements.

{| cellspacing="0" cellpadding="0" style="margin:0em 0em 1em 0em; width:80%"  Properties of inhomogeneous displacement fields
 * colspan="2" style="width:80%; horizontal-align:right; vertical-align:top; border:1px solid Sienna; background-color:White;" |

Average strain
Let $$\textstyle \mathbf{u}$$ be a displacement field, $$\textstyle \boldsymbol{\varepsilon}$$ be the corresponding strain field. Let $$\textstyle \mathbf{u}$$ and $$\textstyle \boldsymbol{\varepsilon}$$ be continuous on B. Then, the mean strain $$\textstyle \overline{\boldsymbol{\varepsilon}}$$ depends only on the boundary values of $$\textstyle \mathbf{u}$$.

 * $$ \overline{\boldsymbol{\varepsilon}} = \frac{1}{V}\int_B\boldsymbol{\varepsilon} ~dV = \frac{1}{V}\int_{\partial B}({\mathbf{u}}\otimes{\mathbf{n}}+{\mathbf{n}}\otimes{\mathbf{u}}) ~dA $$

where $$\textstyle \mathbf{n}$$ is the unit normal to the infinitesimal surface area $$\textstyle dA$$.

Korn's Inequality
Let $$\textstyle \mathbf{u}$$ be a displacement field on B that is $$\textstyle C^2$$ continuous and let $$\textstyle \mathbf{u} = \mathbf{0}$$ on $$\textstyle \partial B$$. Then,

 * $$ \int_B |\boldsymbol{\nabla}\mathbf{u}|^2 ~dV \le 2 \int_B |\boldsymbol{\varepsilon}|^2 ~dV $$

 * }


text:
Elasticity/Rigid body motions

Rigid Deformation
A rigid deformation has the form

\boldsymbol{\varphi}(\mathbf{X}) = \mathbf{X}_1 + \boldsymbol{Q}\bullet[\mathbf{X}-\mathbf{X}_0] $$ where $$\textstyle \mathbf{X}_0, \mathbf{X}_1$$ are fixed material points and $$\textstyle \boldsymbol{Q}$$ is an orthogonal (rotation) tensor.

Therefore

\boldsymbol{F} = \boldsymbol{Q} $$ and

\boldsymbol{\nabla}\mathbf{u} = \boldsymbol{Q} - \boldsymbol{1} $$.

The strain tensors in this case are given by
 * $$ \boldsymbol{E} = 0

$$ but
 * $$ \boldsymbol{\epsilon} = \cfrac{1}{2}(\boldsymbol{Q}+\boldsymbol{Q}^T)-\boldsymbol{1} $$.

Hence the infinitesimal strain tensor does not measure the correct strain when there are large rotations though the finite strain tensor can.

Rigid Displacement
Rigid displacements involve motions in which there are no strains.

Finite Rigid Displacement
If the displacement is rigid we have

\begin{align} \mathbf{u}(\mathbf{X}) &= \mathbf{X}_1 + \boldsymbol{\nabla}\mathbf{u}\bullet[\mathbf{X}-\mathbf{X}_0] + \boldsymbol{1}[\mathbf{X}-\mathbf{X}_0] - \mathbf{X} \\ & = (\mathbf{X}_1-\mathbf{X}_0) + \boldsymbol{\nabla}\mathbf{u}\bullet[\mathbf{X}-\mathbf{X}_0] \\ &= \mathbf{u}_0 + \boldsymbol{\nabla}\mathbf{u}\bullet[\mathbf{X}-\mathbf{X}_0] \end{align} $$

Infinitesimal Rigid Displacement
An infinitesimal rigid displacement is given by

\mathbf{u}(\mathbf{X}) = \mathbf{u}_0 + \boldsymbol{W}\bullet[\mathbf{X}-\mathbf{X}_0] $$

where $$\textstyle \boldsymbol{W}$$ is a skew tensor.

title: Elasticity/Rigid body motions


text:
Elasticity/Disk with hole

Disk with a central hole
Under general loading, for the stresses and displacements to be single-valued and continuous, they must be periodic in $$\theta$$, e.g., $$\sigma_{11}(r,\theta) = \sigma_{11}(r,\theta + 2m\pi)$$.

An Airy stress function appropriate from this situation is
 * $$ \text{(83)} \qquad

\varphi = \sum^{\infty}_{n=0} f_n(r) \cos(n\theta) + \sum^{\infty}_{n=0} g_n(r) \sin(n\theta) $$ In the absence of body forces,
 * $$ \text{(84)} \qquad

\nabla^4{\varphi} = \nabla^2{(\nabla^2{\varphi})} = 0 ~; \nabla^2{} = \left(\cfrac{\partial^2}{\partial r^2} + \cfrac{1}{r}\cfrac{\partial}{\partial r} +                  \cfrac{1}{r^2}\cfrac{\partial^2}{\partial \theta^2}\right) $$ Plug in $$\varphi$$.
 * $$\begin{align}

\nabla^2{\varphi} = & \sum^{\infty}_{n=0} \left[ f^{''}_n(r) \cos(n\theta) + \cfrac{1}{r} f^{'}_n(r) \cos(n\theta) - \cfrac{n^2}{r^2} f_n(r) \cos(n\theta) \right] + \\ & \sum^{\infty}_{n=0} \left[ g^{''}_n(r) \sin(n\theta) + \cfrac{1}{r} g^{'}_n(r) \sin(n\theta) - \cfrac{n^2}{r^2} g_n(r) \sin(n\theta) \right] \qquad \text{(85)} \end{align}$$ or,
 * $$ \text{(86)} \qquad

\nabla^2{\varphi} = \sum^{\infty}_{n=0} F_n(r) \cos(n\theta) + \sum^{\infty}_{n=0} G_n(r) \sin(n\theta) $$ Therefore,
 * $$\begin{align}

\nabla^4{\varphi} = & \sum^{\infty}_{n=0} \left[ F^{''}_n(r) \cos(n\theta) + \cfrac{1}{r} F^{'}_n(r) \cos(n\theta) - \cfrac{n^2}{r^2} F_n(r) \cos(n\theta) \right] + \\ & \sum^{\infty}_{n=0} \left[ G^{''}_n(r) \sin(n\theta) + \cfrac{1}{r} G^{'}_n(r) \sin(n\theta) - \cfrac{n^2}{r^2} G_n(r) \sin(n\theta) \right] \qquad \text{(87)} \end{align}$$ To satisfy the compatibility condition $$\nabla^4{\varphi} = 0$$, we need
 * $$\begin{align}

\text{(88)} \qquad F^{''}_n(r) + \cfrac{1}{r} F^{'}_n(r) - \cfrac{n^2}{r^2} F_n(r) & = 0 \\   \text{(89)} \qquad G^{''}_n(r) + \cfrac{1}{r} G^{'}_n(r) - \cfrac{n^2}{r^2} G_n(r) & = 0 \end{align}$$ The general solution of these Euler-Cauchy type equations is
 * $$\begin{align}

\text{(90)} \qquad F_n(r) & = A_1 r^n + B_1 r^{-n}  \\ \text{(91)} \qquad G_n(r) & = C_1 r^n + D_1 r^{-n} \end{align}$$ We can use either to determine $$f_n(r)$$. Thus,
 * $$ \text{(92)} \qquad

f^{''}_n(r) + \cfrac{1}{r} f^{'}_n(r) - \cfrac{n^2}{r^2} f_n(r) = A_1 r^n + B_1 r^{-n} $$ or,
 * $$ \text{(93)} \qquad

r^2 f^{''}_n(r) + r f^{'}_n(r) - n^2 f_n(r) = A_1 r^{n+2} + B_1 r^{-n+2} $$ The homogeneous and particular solutions of this equation are
 * $$\begin{align}

\text{(94)} \qquad f^h_n(r) & = A_2 r^n + B_2 r^{-n}  \\ \text{(95)} \qquad f^p_n(r) & = A_1 r^{n+2} + B_1 r^{-n+2} \end{align}$$ Hence, the general solution is
 * $$ \text{(96)} \qquad

f_n(r) = A_1 r^{n+2} + B_1 r^{-n+2} + A_2 r^n + B_2 r^{-n} $$ This form is valid for $$n > 1$$. If $$n = 0, 1$$, alternative forms are obtained. Thus,
 * $$\begin{align}

\text{(97)} \qquad f_0(r) & = A_O r^2 + B_0 r^2 \ln r + C_0 + D_0 \ln r \\ \text{(98)} \qquad f_1(r) & = A_1 r^3 + B_1 r + C_1 r \ln r + D_1 r^{-1}   \\ \text{(99)} \qquad f_n(r) & = A_n r^{n+2} + B_n r^n + C_n r^{-n+2} + D_n r^{-n} ~,n > 1 \end{align}$$ Terms in $$f_n$$ are chosen according to the specific problem of interest.

Traction BCs

 * at $$ r = a $$

\text{(100)} \qquad \sigma_{rr} = T_1(\theta) ~, \sigma_{r\theta} = T_2(\theta) $$
 * at $$ r = b $$

\text{(101)} \qquad \sigma_{rr} = T_3(\theta) ~, \sigma_{r\theta} = T_4(\theta) $$ Express $$T_i(\theta)$$ in Fourier series form.
 * $$ \text{(102)} \qquad

T_i(\theta) = \sum^{\infty}_{n=0} A_{ni}\cos(n\theta) + \sum^{\infty}_{n=0} B_{ni}\sin(n\theta) ~,i=1,2,3,4 $$ Terms in $$T_i$$ are chosen according to the specific problem of interest.

title: Elasticity/Disk with hole


text:
Elasticity/Plate with hole in shear

Circular hole in a shear field
Given:
 * Large plate in pure shear.
 * Stress state perturbed by a small hole.

The BCs are
 * at $$ r = a $$

\text{(103)} \qquad t_r = t_{\theta} = 0 ~; \widehat{\mathbf{n}} = -\widehat{\mathbf{e}}~r \Rightarrow \sigma_{rr} = \sigma_{r\theta} = 0 $$

 * at $$ r \rightarrow \infty $$

\text{(104)} \qquad \sigma_{12} \rightarrow S ~; \sigma_{11} \rightarrow 0 ~; \sigma_{22} \rightarrow 0 $$

We will solve this problem by superposing a perturbation due to the hole on the unperturbed solution. The effect of the perturbation will decrease with increasing distance from the hole, i.e. the effect will be proportional to $$r^{-n} \,$$.

Unperturbed Solution

 * $$ \text{(105)} \qquad

\sigma_{11} = \sigma_{22} = 0 ~; \sigma_{12} = S $$ Therefore,
 * $$\text{(106)} \qquad

\sigma_{12} = -\varphi_{,12} = S $$ Integrating,
 * $$\text{(107)} \qquad

\varphi_{,1} = -Sx_2 + f(x_1) \Rightarrow \varphi = -Sx_1x_2 + \int f(x_1) dx_1 $$ Since $$\varphi$$ is a potential, we can neglect the integration constants (these do not affect the stresses - which are what we are interested in). Hence,
 * $$ \text{(108)} \qquad

\varphi = -Sx_1x_2 = -S (r\cos\theta) (r\sin\theta) = -\cfrac{Sr^2}{2}\sin(2\theta) $$ or,
 * $$ \text{(109)} \qquad

\varphi = -\cfrac{Sr^2}{2}\sin(2\theta) $$ Note that we have arranged the expression so that it has a form similar to the Fourier series of the previous section.

Perturbed Solution
For this we have to add terms to $$\varphi$$ in such a way that

 * The unperturbed solution continues to be true as $$r\rightarrow\infty \,$$.
 * The terms have the same form as the unperturbed solution,i.e., $$sin(2\theta) \,$$ terms.
 * The new $$\varphi$$ leads to stresses that are proportional to $$r^{-n}\,$$.

Recall,

\varphi = \sum^{\infty}_{n=0} f_n(r) \cos(n\theta) + \sum^{\infty}_{n=0} g_n(r) \sin(n\theta) $$ where,
 * $$\begin{align}

f_0(r) & = A_0 r^2 + B_0 r^2 \ln r + C_0 + D_0 \ln r \\ f_1(r) & = A_1 r^3 + B_1 r + C_1 r \ln r + D_1 r^{-1} \\ f_n(r) & = A_n r^{n+2} + B_n r^n + C_n r^{-n+2} + D_n r^{-n} ~,n > 1 \end{align} $$ So the appropriate stress function for the perturbation is
 * $$\text{(110)}\qquad

\varphi = g_2(r) \sin(2\theta) = \left(C_2 r^{-2+2} + D_2 r^{-2}\right) \sin(2\theta) $$ or,
 * $$\text{(111)} \qquad

\varphi = \left(C_2 + D_2 r^{-2}\right)\sin(2\theta) $$ Hence, the stress function appropriate for the superposed solution is
 * $$\text{(112)}

\varphi = -\cfrac{Sr^2}{2}\sin(2\theta) + \left(C_2 + D_2 r^{-2}\right)\sin(2\theta) $$ We determine $$C_2$$ and $$D_2$$ using the boundary conditions at $$r=a$$.

The stresses are
 * $$\begin{align}

\text{(113)}\qquad\sigma_{rr} & = \cfrac{1}{r}\cfrac{\partial\varphi}{\partial r} + \cfrac{1}{r^2}\cfrac{\partial^2\varphi}{\partial \theta^2} = \left(S - 4C_2r^{-2} - 6D_2r^{-4}\right)\sin(2\theta) \\ \text{(114)}\qquad\sigma_{\theta\theta} & = \cfrac{\partial^2\varphi}{\partial r^2} = \left(-S + 6D_2r^{-4}\right)\sin(2\theta) \\ \text{(115)}\qquad\sigma_{r\theta} & = -\cfrac{\partial}{\partial r}      \left(\cfrac{1}{r}\cfrac{\partial\varphi}{\partial \theta}\right) = \left(S + 6D_2r^{-4}\right)\cos(2\theta) \end{align}$$ Hence,
 * $$\begin{align}

\text{(116)}\qquad\left.\sigma_{rr}\right|_{r=a} & = 0 = \left(S - 4C_2a^{-2} - 6D_2a^{-4}\right)\sin(2\theta) \\ \text{(117)}\qquad\left.\sigma_{r\theta}\right|_{r=a} & = 0 = \left(S + 2C_2a^{-2} + 6D_2a^{-4}\right)\cos(2\theta) \end{align}$$ or,
 * $$\begin{align}

\text{(118)}\qquad 4C_2a^{-2} + 6D_2a^{-4} & = S \\ \text{(119)}\qquad 2C_2a^{-2} + 6D_2a^{-4} & = -S \end{align}$$ Solving,
 * $$\text{(120)}\qquad

C_2 = Sa^2 ~; D_2 = -\cfrac{Sa^4}{2} $$ Back substituting,
 * $$\begin{align}

\text{(121)}\qquad \sigma_{rr} & = S\left(1 - 4\cfrac{a^2}{r^2} + 3\cfrac{a^4}{r^4}\right)\sin(2\theta) \\   \text{(122)}\qquad \sigma_{\theta\theta} & = S\left(-1 - 3\cfrac{a^4}{r^4}\right)\sin(2\theta) \\   \text{(123)}\qquad \sigma_{r\theta} & = S\left(1 + 2\cfrac{a^2}{r^2} - 3\cfrac{a^4}{r^4}\right)\cos(2\theta) \end{align}$$

Example homework problem
Consider the elastic plate with a hole subject to pure shear. The stresses close to the hole are given by
 * $$\begin{align}

\text{(29)} \qquad  \sigma_{rr} & = S\left(1 - 4\frac{a^2}{r^2} + 3\frac{a^4}{r^4}\right)\sin(2\theta) \\  \text{(30)} \qquad  \sigma_{\theta\theta} & = S\left(-1 - 3\frac{a^4}{r^4}\right)\sin(2\theta) \\  \text{(31)} \qquad   \sigma_{r\theta} & = S\left(1 + 2\frac{a^2}{r^2} - 3\frac{a^4}{r^4}\right)\cos(2\theta) \end{align}$$
 * Show that the normal and shear traction boundary conditions far from the hole are satisfied by these stresses.
 * Calculate the stress concentration factors at the hole, i.e., ($$\tau_{\text{max}}/S$$) (shear) and ($$\sigma_{\text{max}}/\sigma_0$$) (normal).
 * Calculate the displacement field corresponding to this stress field (for plane stress). Plot the deformed shape of the hole.

Solution
Far from the hole, $$r = \infty$$. Therefore,
 * $$\begin{align}

\text{(32)} \qquad  \sigma_{rr} & = S\sin(2\theta) \\ \text{(33)} \qquad \sigma_{\theta\theta} & = -S\sin(2\theta)  \\ \text{(34)} \qquad  \sigma_{r\theta} & = S\cos(2\theta) \end{align}$$ To rotate the stresses back to the $$(x_1,x_2)$$ coordinate system, we use the tensor transformation rule
 * $$\text{(35)} \qquad

\begin{bmatrix} \sigma_{11} & \sigma_{12} & \sigma_{13} \\ \sigma_{21} & \sigma_{22} & \sigma_{23} \\ \sigma_{31} & \sigma_{32} & \sigma_{33} \end{bmatrix} = \begin{bmatrix} \cos\theta & -\sin\theta & 0 \\ \sin\theta & \cos\theta & 0 \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} \sigma_{rr} & \sigma_{r\theta} & \sigma_{rz} \\ \sigma_{r\theta} & \sigma_{\theta\theta} & \sigma_{\theta z} \\ \sigma_{rz} & \sigma_{\theta z} & \sigma_{zz} \end{bmatrix} \begin{bmatrix} \cos\theta & \sin\theta & 0 \\ -\sin\theta & \cos\theta & 0 \\ 0 & 0 & 1 \end{bmatrix} $$ Setting $$\sigma_{rz} = 0$$ and $$\sigma_{\theta z} = 0$$, we get the simplified set of equations
 * $$\begin{align}

\text{(36)} \qquad \sigma_{11} &= \sigma_{rr}\cos^2\theta + \sigma_{\theta\theta}\sin^2\theta - \sigma_{r\theta}\sin(2\theta) \\ \text{(37)} \qquad \sigma_{22} &= \sigma_{rr}\sin^2\theta + \sigma_{\theta\theta}\cos^2\theta + \sigma_{r\theta}\sin(2\theta) \\ \text{(38)} \qquad \sigma_{12} &= \frac{\sigma_{rr}-\sigma_{\theta\theta}}{2}\sin(2\theta) + \sigma_{r\theta}\cos(2\theta) \end{align}$$ Plugging in equations (32-34) in the above, we have
 * $$\begin{align}

\text{(39)} \qquad \sigma_{11} &= -S\left[\sin(2\theta)\cos(2\theta)-\sin(2\theta)\cos(2\theta) \right] = 0 \\ \text{(40)} \qquad \sigma_{22} &= S\left[\sin(2\theta)\cos(2\theta)-\sin(2\theta)\cos(2\theta) \right] = 0 \\ \text{(41)} \qquad \sigma_{12} &= S\left[\sin(2\theta)\sin(2\theta)+\cos(2\theta)\cos(2\theta) \right] = S \end{align}$$ Hence, the far field stress BCs are satisfied.

The stresses at the hole ($$r = a$$) are
 * $$\begin{align}

\text{(42)} \qquad \sigma_{rr} & = S\left(1 - 4 + 3\right)\sin(2\theta) = 0 \\   \text{(43)} \qquad \sigma_{\theta\theta} & = S\left(-1 - 3\right)\sin(2\theta) = -4S\sin(2\theta) \\   \text{(44)} \qquad \sigma_{r\theta} & = S\left(1 + 2 - 3\right)\cos(2\theta) = 0 \end{align}$$

The maximum (or minimum) hoop stress at the hole is at the locations where $$d\sigma_{\theta\theta}/d\theta = -8S\cos(2\theta) = 0$$. These locations are $$\theta = \pi/4$$ and $$\theta = 3\pi/4$$. The value of the hoop stress is
 * $$\begin{align}

\text{(45)} \qquad \text{at}~ \theta = \frac{\pi}{4} & & \sigma_{\theta\theta} = -4S \\ \text{(46)} \qquad \text{at}~ \theta = \frac{3\pi}{4} &  &\sigma_{\theta\theta} = 4S \end{align}$$ The maximum shear stress is given by
 * $$ \text{(47)} \qquad

\tau_{\text{max}} = \frac{1}{2}\left|\sigma_{rr}-\sigma_{\theta\theta}\right| = 2S $$ Therefore, the stress concentration factors are
 * $$\text{(48)} \qquad

\frac{\sigma_{\text{max}}}{S} = 4 ~; \frac{\tau_{\text{max}}}{S} = 2 $$

The stress function used to derive the above results was
 * $$\text{(49)} \qquad

\varphi = -\frac{S}{2}r^2\sin(2\theta) + Sa^2 \sin(2\theta) - \frac{Sa^4}{2}r^{-2}\sin(2\theta) $$ From Michell's solution, the displacements corresponding to the above stress function are given by
 * $$\begin{align}

\text{(50)} \qquad 2\mu u_r & = -\frac{S}{2}\left[-2r\sin(2\theta)\right] +Sa^2\left[(\kappa+1)r^{-1}\sin(2\theta)\right] -\frac{Sa^4}{2}\left[2r^{-3}\sin(2\theta)\right] \\  \text{(51)} \qquad 2\mu u_{\theta} & = -\frac{S}{2}\left[-2r\cos(2\theta)\right] +Sa^2\left[(\kappa-1)r^{-1}\cos(2\theta)\right] -\frac{Sa^4}{2}\left[-2r^{-3}\cos(2\theta)\right] \end{align}$$ or,
 * $$\begin{align}

\text{(52)} \qquad u_r & = \frac{Sr\sin(2\theta)}{2\mu}\left[ 1 + (\kappa+1)\frac{a^2}{r^2} - \frac{a^4}{r^4}\right] \\  \text{(53)} \qquad u_{\theta} & = \frac{Sr\cos(2\theta)}{2\mu}\left[ 1 + (\kappa-1)\frac{a^2}{r^2} + \frac{a^4}{r^4}\right] \end{align}$$ For plane stress, $$\kappa = (3-\nu)/(1+\nu)$$. Hence,
 * $$\begin{align}

\text{(54)} \qquad u_r & = \frac{Sr\sin(2\theta)}{2\mu}\left[ 1 + \left(\frac{4}{1+\nu}\right)\frac{a^2}{r^2} - \frac{a^4}{r^4}\right] \\  \text{(55)} \qquad u_{\theta} & = \frac{Sr\cos(2\theta)}{2\mu}\left[ 1 + 2\left(\frac{1-\nu}{1+\nu}\right)\frac{a^2}{r^2} + \frac{a^4}{r^4}\right] \end{align}$$ At $$r = a$$,
 * $$\begin{align}

\text{(56)} \qquad u_r & = \frac{Sa\sin(2\theta)}{\mu}\left(\frac{2}{1+\nu}\right) \\  \text{(57)} \qquad u_{\theta} & = \frac{Sa\cos(2\theta)}{\mu}\left(\frac{2}{1+\nu}\right) \end{align}$$ Now $$\mu = E/2(1+\nu)$$. Hence, we have
 * $$\begin{align}

\text{(58)} \qquad u_r & = \frac{4Sa\sin(2\theta)}{E} \\ \text{(59)} \qquad u_{\theta} & = \frac{4Sa\cos(2\theta)}{E} \end{align}$$ The deformed shape is shown below

title: Elasticity/Plate with hole in shear


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User:SalinaT91

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title: User:SalinaT91


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text:
Michell solution

The Michell solution is a general solution to the elasticity equations in polar coordinates ($$ r, \theta \,$$). The solution is such that the stress components are in the form of a Fourier series in $$ \theta \, $$.

Michell showed that the general solution can be expressed in terms of an Airy stress function of the form

\begin{align} \varphi &= A_0~r^2 + B_0~r^2~\ln(r) + C_0~\ln(r) + D_0~\theta \\ & + \left(A_1~r + B_1~r^{-1} + B_1^{'}~r~\theta + C_1~r^3 +      D_1~r~\ln(r)\right) \cos\theta \\ & + \left(E_1~r + F_1~r^{-1} + F_1^{'}~r~\theta + G_1~r^3 +      H_1~r~\ln(r)\right) \sin\theta \\ & + \sum_{n=2}^{\infty} \left(A_n~r^n + B_n~r^{-n} + C_n~r^{n+2} + D_n~r^{-n+2}\right)\cos(n\theta) \\ & + \sum_{n=2}^{\infty} \left(E_n~r^n + F_n~r^{-n} + G_n~r^{n+2} + H_n~r^{-n+2}\right)\sin(n\theta) \end{align} $$

The terms $$A_1~r~\cos\theta\,$$ and $$E_1~r~\sin\theta\,$$ define a trivial null state of stress and are ignored.

Stress components
The stress components can be obtained by substituting the Michell solution into the equations for stress in terms of the Airy stress function (in cylindrical coordinates). A table of stress components is shown below [from J. R. Barber (2002) ].

Displacement components
Displacements can be obtained from the Michell solution by using the stress-strain and strain-displacement relations. A table of displacement components corresponding the the terms in the Airy stress function for the Michell solution is given below. In this table

\kappa = \begin{cases} 3 - 4~\nu & \rm{for~plane~strain} \\ \cfrac{3 - \nu}{1 + \nu} & \rm{for~plane~stress} \\ \end{cases} $$

Note that you can superpose a rigid body displacement on the Michell solution of the form

\begin{align} u_r &= A~\cos\theta + B~\sin\theta \\ u_\theta &= -A~\sin\theta + B~\cos\theta + C~r\\ \end{align} $$ to obtain an admissible displacement field.

title: Michell solution


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Elasticity/Plate with hole in tension

Plate with hole in a tensile field
The BCs are
 * $$\begin{align}

\text{(124)} & \qquad \text{at}~  r = a & &  t_r = t_{\theta} = 0 ~; \widehat{\mathbf{n}} = -\widehat{\mathbf{e}}~{r} \Rightarrow \sigma_{rr} = \sigma_{r\theta} = 0 \\ \text{(125)} & \qquad \text{at}~ r \rightarrow \infty & & \sigma_{11} \rightarrow T ~; \sigma_{12} \rightarrow 0 ~; \sigma_{22} \rightarrow 0 \end{align}$$

Unperturbed Solution
The unperturbed part of the Michell solution gives us

\varphi = \cfrac{Tx_2^2}{2} = \cfrac{T (r\sin\theta)^2}{2} = \cfrac{Tr^2}{4} - \cfrac{Tr^2\cos(2\theta)}{4} $$ or,
 * $$\text{(126)} \qquad

\varphi = \cfrac{Tr^2}{4} - \cfrac{Tr^2\cos(2\theta)}{4} $$ The first term is the axisymmetric term while the second term is the periodic term.

Perturbation
Similar to previous problem, but we simply choose terms from the Michell solution of the same form (i.e. containing $$\cos(2\theta)$$) and such that the stresses decay with increasing radius. The relevant terms from the table are:
 * $$ \text{(127)} \qquad

\ln(r) ~, \theta ~, r^{-2+2}\cos(2\theta) ~,r^{-2}\cos(2\theta) $$

Perturbed Solution
The perturbed solution is
 * $$ \text{(128)} \qquad

\varphi = \cfrac{Tr^2}{4} - \cfrac{Tr^2\cos(2\theta)}{4} + A\ln(r) + B\theta + C\cos(2\theta) + Dr^{-2}\cos(2\theta) $$ After applying the BCS, we get
 * $$ \begin{align}

\text{(129)}\qquad\sigma_{rr} & = \cfrac{T}{2}\left(1-\cfrac{a^2}{r^2}\right) + \cfrac{T\cos(2\theta)}{2} \left(\cfrac{3a^4}{r^4} - \cfrac{4a^2}{r^2} + 1\right)\\ \text{(130)}\qquad\sigma_{\theta\theta} & = \cfrac{T}{2}\left(1+\cfrac{a^2}{r^2}\right) - \cfrac{T\cos(2\theta)}{2} \left(\cfrac{3a^4}{r^4} + 1\right)\\ \text{(131)}\qquad\sigma_{r\theta} & = \cfrac{T\sin(2\theta)}{2} \left(\cfrac{3a^4}{r^4} - \cfrac{2a^2}{r^2} - 1\right) \end{align}$$

The stress concentration factor, often referred to as Kt, in this case is $$3$$ and is the same in both tension and shear.

Example homework problem
Consider the elastic plate with a hole subject to uniaxial tension.
 * Show that the stress function

\varphi = \frac{Tr^2}{4} - \frac{Tr^2\cos(2\theta)}{4} + A\ln(r) + B\theta               + C\cos(2\theta) + Dr^{-2}\cos(2\theta) $$ leads to the stresses

\begin{align} \sigma_{rr} & = \frac{T}{2}\left(1-\frac{a^2}{r^2}\right) +       \frac{T\cos(2\theta)}{2}        \left(\frac{3a^4}{r^4} - \frac{4a^2}{r^2} + 1\right) \\ \sigma_{\theta\theta} & = \frac{T}{2}\left(1+\frac{a^2}{r^2}\right) -       \frac{T\cos(2\theta)}{2}        \left(\frac{3a^4}{r^4} + 1\right)\\ \sigma_{r\theta} & = \frac{T\sin(2\theta)}{2}       \left(\frac{3a^4}{r^4} - \frac{2a^2}{r^2} - 1\right) \end{align} $$ or, in cartesian coordinates:

$$ \begin{align} \sigma_{xx}(r,\theta)&=T-T\frac{a^{2}}{r^{2}}(\frac{3}{2}\cos 2\theta+\cos 4\theta)+T\frac{3a^4}{2r^4}\cos 4\theta,\\ \sigma_{yy}(r,\theta)&=-T\frac{a^2}{r^2}(\frac{1}{2}\cos 2\theta-\cos 4\theta)-T\frac{3a^4}{2r^4}\cos 4\theta,\\ \tau_{xy}(r,\theta)&=-T\frac{a^2}{r^2}(\frac{1}{2}\sin 2\theta+\sin 4\theta)+T\frac{3a^4}{2r^4}\sin 4\theta \end{align} $$
 * Calculate the stress concentration factors at the hole, both in shear and in tension, and show that they are the same.  How far from the hole (in units of hole diameters) does the stress reach 95% of the far field (unperturbed) value?
 * Calculate the displacement field corresponding to this stress field (for plane stress). Plot the deformed shape of the hole.

Solution
We can use the following Maple code to show the above results. phi := T*r^2/4*(1 - cos(2*theta)) + A*ln(r) + B*theta + C*cos(2*theta) + D/r^2*cos(2*theta);

srr := 1/r*diff(phi,r) + 1/r^2*diff(phi,theta,theta); stt := diff(phi,r,r); srt := -diff((1/r*diff(phi,theta)),r);

srra := collect(simplify(eval(srr, r=a)),{cos}); srta := collect(simplify(eval(srt, r=a)),{cos});

eq1 := coeff(srra, cos(2*theta)); eq2 := coeff(srta, sin(2*theta)); eq3 := 1/2*(T*a^4+2*A*a^2)/a^4; eq4 := 1/a^2*B;

BB := solve({eq4=0},{B}); AA := solve({eq3=0},{A});

sol := solve({eq1=0,eq2=0},{C,D});

phi := subs(BB, phi); phi := subs(AA, phi); phi := subs(sol, phi);

srr2 := 1/r*diff(phi,r) + 1/r^2*diff(phi,theta,theta); stt2 := diff(phi,r,r); srt2 := -diff((1/r*diff(phi,theta)),r);

srr3 := collect(simplify(srr2),{cos}); stt3 := collect(simplify(stt2),{cos}); srt3 := collect(simplify(srt2),{cos});

The stresses at the hole ($$r=a$$) are

\begin{align} \sigma_{rr} & = 0 \\ \sigma_{\theta\theta} & = T - 2T\cos(2\theta) \\ \sigma_{r\theta} & = 0 \end{align} $$ The maximum hoop stress is given at $$\theta = 0$$ or $$\theta = \pi/2$$.

At $$\theta = 0$$, $$\sigma_{\theta\theta} = -T$$.

At $$\theta = \pi/2$$, $$\sigma_{\theta\theta} = 3T$$.

The maximum shear stress at $$r = a$$ is $$\tau_{\text{max}} = 1.5T$$ while that at $$r = \infty$$ is $$0.5T$$.

Therefore, the stress concentration factor in tension is $$3T/T = 3$$, while that in shear is $$1.5T/0.5T = 3$$.

Both stress concentration factors are equal.

Let us look at the ratio of the hoop stress at $$\theta = \pi/2$$ to the far field hoop stress

\sigma_{\theta\theta} = T/2(1-\cos 2\theta) $$ The ratio is

\text{ratio} = 1 + \frac{3a^4}{2r^4} + \frac{a^2}{2r^2} $$ This ratio is 0.95 when $$r \approx 3.5a$$, i.e., at a distance of $$1.75$$ diameters from the center.

The given stress function is

\varphi = \frac{Tr^2}{4} - \frac{Tr^2\cos(2\theta)}{4} + A\ln(r) + B\theta + C\cos(2\theta) + Dr^{-2}\cos(2\theta) $$ Therefore, the displacement field from the Michell solution is
 * $$\begin{align}

2\mu u_r & =  \frac{T}{4}\left[(\kappa-1)r\right] -  \frac{T}{4}\left[-2r\cos(2\theta)\right] +  A\left[-\frac{1}{r}\right] +  C\left[(\kappa+1)r^{-1}\cos(2\theta)\right] +  D\left[2r^{-3}\cos(2\theta)\right]   \\ 2\mu u_{\theta} & = -  \frac{T}{4}\left[2r\sin(2\theta)\right] +  C\left[-(\kappa-1)r^{-1}\sin(2\theta)\right] +  D\left[2r^{-3}\sin(2\theta)\right] \end{align} $$ From the stress calculation step, we have

A = -\frac{Ta^2}{2} ~; B = 0 ~; C = \frac{Ta^2}{2} ~; D = -\frac{Ta^4}{4} $$ After substituting the constants and collecting terms,
 * $$\begin{align}

2\mu u_r & = \frac{Tr\cos(2\theta)}{2}\left[ 1 + (\kappa+1)\frac{a^2}{r^2} - \frac{a^4}{r^4}\right] + \frac{Tr}{4}\left[(\kappa-1) + 2\frac{a^2}{r^2}\right] \\ 2\mu u_{\theta} & =  -\frac{Tr\sin(2\theta)}{2}\left[ 1 + (\kappa-1)\frac{a^2}{r^2} + \frac{a^4}{r^4}\right] \end{align}$$ Replacing $$\mu$$ with $$\frac{E}{2(1+\nu)}$$, and $$\kappa$$ with $$\frac{3-\nu}{1+\nu}$$ (for plane stress conditions), we get
 * $$\begin{align}

u_r & = \frac{Tr\cos(2\theta)}{2E}\left[ (1+\nu)+4\frac{a^2}{r^2}-(1+\nu)\frac{a^4}{r^4}\right] + \frac{Tr}{2E}\left[(1-\nu)+(1+\nu)\frac{a^2}{r^2}\right] \\ u_{\theta} & =  -\frac{Tr\sin(2\theta)}{2E}\left[ (1+\nu) + 2(1-\nu)\frac{a^2}{r^2}+(1+\nu)\frac{a^4}{r^4}\right] \end{align}$$ At $$r = a$$,
 * $$\begin{align}

u_r & = \frac{Ta}{E}\left[1+2\cos(2\theta)\right] \\ u_{\theta} & = - \frac{2Ta}{E} \sin(2\theta) \end{align}$$ The deformed shape is shown below: In cartesian coordinates, the displacement field is given by
 * $$\begin{align}u_{x}(r,\theta)&=&\frac{Ta}{8\mu}\left[\frac{r}{a}(\kappa+1)\cos\theta + \frac{2a}{r}((1+\kappa)\cos\theta + \cos3\theta) - \frac{2a^3}{r^3}\cos3\theta\right],\\

u_{y}(r,\theta)&=&\frac{Ta}{8\mu}\left[\frac{r}{a}(\kappa-3)\sin\theta + \frac{2a}{r}((1-\kappa)\sin\theta + \sin3\theta) - \frac{2a^3}{r^3}\sin3\theta\right]\end{align}$$

title: Elasticity/Plate with hole in tension


text: File:Tension hole deform.png

title: File:Tension hole deform.png


text:
File:Mok Previs overview N2a.png

Used with the WikiU Film School Lesson on how to create 3D storyboards with FrameForge 3D Studio Demo Version.

title: File:Mok Previs overview N2a.png


text:
User:Kumaarps

 * welcome
 * Hi, i have just started to creat. Wait for some time to finish!!

title: User:Kumaarps


text:
User:Emimurphy

I am new to wikiversity and very interested in learning more

title: User:Emimurphy


text:
User talk:Hazel~enwikiversity

Hello Hazel, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. When leaving comments for others to read, remember to sign and date; it helps everyone keep track of who is writing messages. The signature icon in the edit window makes it simple. To help you get started:
 * Take a guided tour and learn how to edit;
 * Explore our learning projects;
 * Browse our portals, schools, and research pages; and
 * Read and help develop our community policies.

Also, don't forget to experiment with the links to your left. Be bold, and see you around Wikiversity! SB_Johnny | PA! 09:43, 4 August 2007 (UTC)

Bloom Clock category
Hi Hazel. I'm afraid I don't know much about Oregon geology and ecology, but I'd imagine that like Pennsylvania it probably has some rather distinct regions as far as flora and bloom times are concerned (since, like here, you're in a large state with a mountain range running through the middle). Do you think it makes more sense to have your logs categorized as "Southwestern Oregon", or just "Oregon"? I strongly suspect that Northwestern Oregon's bloom times will be very different than from Jackson County, especially in early spring and late autumn :). --SB_Johnny | PA! 14:45, 4 August 2007 (UTC)

Key is up
Here ya go: Bloom Clock/Flowers seen in August in Southwest Oregon. :-) --SB_Johnny | PA! 14:42, 8 August 2007 (UTC)

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Hazel. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Hazel~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:37, 17 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 06:10, 19 April 2015 (UTC)

title: User talk:Hazel~enwikiversity


text: Category:BCP/Family/Lamiaceae

title: Category:BCP/Family/Lamiaceae


text:
BCP/Lobelia siphilitica

Lobelia siphilitica

title: BCP/Lobelia siphilitica


text:
BCP/Lobelia siphilitica/Logs

2007 Logs

 * --SB_Johnny | PA! 11:06, 14 July 2007 (UTC)
 * --SB_Johnny | PA! 10:14, 4 August 2007 (UTC)
 * --SB_Johnny | talk 10:57, 1 September 2007 (UTC)
 * --SB_Johnny | talk 09:08, 14 September 2007 (UTC)
 * --SB_Johnny | talk 07:18, 1 October 2007 (UTC)
 * --Jomegat 14:59, 14 October 2007 (UTC)
 * --SB_Johnny | talk 13:04, 24 October 2007 (UTC)
 * --Jomegat 02:17, 27 October 2007 (UTC)
 * --Jomegat 23:17, 30 October 2007 (UTC)
 * --Jomegat 21:04, 8 November 2007 (UTC)

2008 Logs

 * (no archived logs yet)

Recent Logs

 * --Jomegat 19 July, 2008 (from photo)
 * --Jomegat 26 July, 2008 (from photo)
 * Jomegat 20:32, 9 August 2008 (UTC)
 * --SB_Johnny talk 22:36, 9 August 2008 (UTC)

title: BCP/Lobelia siphilitica/Logs


text:
BCP/Liatris spicata/Logs

2007 Logs

 * SB Johnny-LM 18:34, 6 July 2007 (UTC)
 * --SB_Johnny | PA! 10:26, 4 August 2007 (UTC)
 * SB Johnny-LM 00:11, 6 August 2007 (UTC) (from a datestamped photograph)
 * --Luai lashire 17:51, 15 August 2007 (UTC)
 * SB Johnny-LM 09:27, 8 September 2007 (UTC)

2008 Logs

 * --SB_Johnny | talk 10:13, 9 July 2008 (UTC)
 * --SB_Johnny | talk 10:04, 20 July 2008 (UTC)

Recent Logs

 * --Clarinetguy097 (discuss • contribs) 01:45, 8 July 2020 (UTC)
 * --Clarinetguy097 (discuss • contribs) 19:07, 18 July 2021 (UTC)

title: BCP/Liatris spicata/Logs


text:
BCP/Plantago major/Logs

2007 Logs

 * SB Johnny-LM 09:09, 6 June 2007 (UTC)
 * SBJ 16:16, 7 June 2007 (UTC)
 * --SB_Johnny | talk 09:52, 18 June 2007 (UTC)
 * --SB_Johnny | talk 10:37, 4 July 2007 (UTC)
 * --SB_Johnny | PA! 10:34, 4 August 2007 (UTC)
 * --Luai lashire 17:53, 15 August 2007 (UTC)
 * SB Johnny-LM 10:39, 25 August 2007 (UTC)
 * --Luai lashire 18:31, 22 September 2007 (UTC)

2008 Logs

 * --Jomegat 23:56, 9 June 2008 (UTC)
 * --Jomegat 17:45, 17 June 2008 (UTC)
 * --SB_Johnny | talk 22:01, 17 June 2008 (UTC)
 * --Jomegat 22:40, 1 July 2008 (UTC)
 * --Jomegat 18:38, 12 July 2008 (UTC)
 * --SB_Johnny | talk 10:24, 14 July 2008 (UTC)
 * Jomegat 19:50, 26 July 2008 (UTC)
 * Jomegat 00:32, 2 August 2008 (UTC)
 * --SB_Johnny talk 09:24, 5 September 2008 (UTC)

Recent Logs

 * Jomegat 00:16, 15 July 2009 (UTC)
 * Jomegat 00:55, 22 July 2009 (UTC)
 * Jomegat 03:47, 2 August 2009 (UTC)
 * l_d_allan 20:00, 30 July 2013 (UTC)

title: BCP/Plantago major/Logs


text:
BCP/Cirsium vulgare

Cirsium vulgare

title: BCP/Cirsium vulgare


text:
BCP/Cirsium vulgare/Logs

2007 Logs

 * Hazel 16:40, 3 August 2007 (UTC)
 * --SB_Johnny | PA! 11:12, 4 August 2007 (UTC)
 * --Jomegat 13:01, 5 August 2007 (UTC)
 * --Luai lashire 02:18, 23 August 2007 (UTC)
 * --SB_Johnny | talk 10:03, 1 September 2007 (UTC)
 * --Jomegat 17:01, 3 October 2007 (UTC)

2008 Logs

 * --SB_Johnny talk 11:24, 10 August 2008 (UTC)

Recent Logs

 * Trinity507 20:53, 5 October 2009 (UTC)
 * --Anna reg 12:45, 20 October 2011 (UTC)

title: BCP/Cirsium vulgare/Logs


text:
BCP/Cucurbita maxima/Logs

2007 Logs

 * --SB_Johnny | talk 11:31, 4 July 2007 (UTC)
 * --SB_Johnny | PA! 11:02, 4 August 2007 (UTC)

2008 Logs

 * (no archived logs yet)

Recent Logs

 * --SB_Johnny | talk 09:52, 14 July 2008 (UTC)
 * Jomegat 31 August 2008
 * Jomegat 23:13, 1 September 2008 (UTC)
 * Jomegat 16:09, 21 September 2008 (UTC)
 * Jomegat 22:18, 6 October 2008 (UTC)

title: BCP/Cucurbita maxima/Logs


title: Category:BCP/NHAMP/8


text:
BCP/Phlox paniculata/Logs

2007 Logs

 * --SB_Johnny | talk 16:27, 19 August 2006 (UTC)
 * SB Johnny-LM 10:39, 25 August 2007 (UTC)
 * --SB_Johnny | talk 12:23, 28 August 2006 (UTC)
 * --SB_Johnny | talk 08:56, 2 July 2007 (UTC)
 * SB Johnny-LM 19:32, 2 July 2007 (UTC)
 * --SB_Johnny | PA! 11:54, 4 August 2007 (UTC)
 * --SB_Johnny | PA! 10:16, 12 August 2007 (UTC)
 * --SB_Johnny | PA! 11:10, 25 August 2007 (UTC)
 * --SB_Johnny | talk 10:37, 1 September 2007 (UTC)
 * SBJ 18:24, 4 September 2007 (UTC)
 * --SB_Johnny | talk 07:15, 1 October 2007 (UTC)
 * --SB_Johnny | talk 10:02, 2 November 2007 (UTC)
 * --SB_Johnny | talk 10:16, 17 November 2007 (UTC)
 * --SB_Johnny | talk 12:35, 26 November 2007 (UTC)

2008 Logs

 * (no archived logs yet)

Recent Logs

 * --SB_Johnny | talk 11:57, 1 December 2007 (UTC)
 * --SB_Johnny | talk 12:18, 28 June 2008 (UTC)
 * --SB_Johnny | talk 10:23, 14 July 2008 (UTC)
 * --SB_Johnny talk 12:50, 26 September 2008 (UTC)
 * ˜˜˜˜ TristanDolciano 16:30, 21 July 2019 (UTC)

title: BCP/Phlox paniculata/Logs


text:
C++/More Functions

As mentioned in the previous lesson, functions are building blocks of C++. A function is a named part of a program that can be invoked from other parts of the program as often needed. This chapter introduces the ways by which we pass values to a function.

Function Arguments Passed By Value
In C++, by default variables are passed by value to functions. This means that a copy of the data is made and passed to the function. This is in contrast to passing by reference or by pointer, in which case the address of the object itself is passed to the function. However, let's first look at what passing arguments by value means:

Consider the following program that accepts a number and prints its cube:

If you want the cube of 19, the output should look like this:

Enter a number : 19

The cube of 19 is 6859

That was quite a basic example. I think you got an idea of what a function can do anyways. Let us go a little more complex.

Before looking below, think what the output should be. Probably as the function should work, num1 should be 5 and num2 should be 4. Let's see what the compiler has to say. Number 1 : 4 Number 2 : 5 What? Doesn't that look like the complete opposite to the rules of the language? Seems to be, but isn't. Let us discuss what actually took place. We will need to go into the works of the compiler. A little knowledge is essential to properly understand the functions of the pass by reference and pointers.

Pass By Reference
Now, let's redefine the  function from the above example. The change will be explained in more detail in a later lesson, but let's look briefly at what passing data by reference means.

First the change in the type of the data passed into. Previously the arguments were of type  but they are now of type. The additional  is very important: it tells the compiler that the data is a reference to an int value rather than simply an int value.

The default C++ behavior is to copy the function arguments. The use of a reference type changes this behavior and a copy is no longer made. As an analogy, think of asking someone to proof-read and markup a printed document. You can either give them a photocopy (pass by value) or hand them the original document (pass by reference). In the same way, you can tell the compiler whether to pass a copy of the arguments or the original variables themselves depending on whether you want the originals to be changed or not.

This time the result of the program using pass by reference semantics will be:

Number 1 : 5 Number 2 : 4

title: C++/More Functions


text:
Template:Bcp+

 Wikipedia | Commons | Wikibooks | Quiz page | Log page
 * (please use the Log page for additional entries)

title: Template:Bcp+


text:
BCP/Trifolium pratense/Logs

2007 Logs

 * --SB_Johnny | talk 17:31, 27 May 2007 (UTC)
 * --SB_Johnny | talk 23:49, 31 May 2007 (UTC)
 * --SB_Johnny | talk 10:47, 3 June 2007 (UTC)
 * --SB_Johnny | talk 14:34, 9 June 2007 (UTC)
 * --SB_Johnny | talk 09:52, 18 June 2007 (UTC)
 * --SB_Johnny | talk 16:57, 1 July 2007 (UTC)
 * --SB_Johnny | PA! 12:25, 4 August 2007 (UTC)
 * --SB_Johnny | PA! 11:51, 25 August 2007 (UTC)
 * Luai lashire 18:54, 25 August 2007 (UTC)
 * --Jomegat 03:16, 1 September 2007 (UTC)
 * --Jomegat 16:54, 10 September 2007 (UTC)
 * --SB_Johnny | talk 06:58, 11 September 2007 (UTC)
 * --Jomegat-UPNY 00:44, 16 September 2007 (UTC)
 * --Jomegat 23:09, 21 September 2007 (UTC)
 * --SB_Johnny | talk 06:57, 1 October 2007 (UTC)
 * --Jomegat 03:03, 2 October 2007 (UTC)
 * --Juan 14:49, 4 October 2007 (UTC)
 * --Jomegat 18:17, 15 October 2007 (UTC)
 * --Luai lashire 20:41, 17 October 2007 (UTC)
 * --Jomegat 12:33, 24 October 2007 (UTC)
 * --SB_Johnny | talk 13:11, 24 October 2007 (UTC)
 * --Jomegat 23:11, 30 October 2007 (UTC)
 * --Jomegat 23:08, 1 November 2007 (UTC)
 * --SB_Johnny | talk 10:17, 2 November 2007 (UTC)
 * --Jomegat 22:54, 5 November 2007 (UTC)
 * --Jomegat 22:45, 14 November 2007 (UTC)
 * --Jomegat 21:37, 16 November 2007 (UTC)

2008 Logs

 * --Jomegat 17:05, 16 May 2008 (UTC)
 * --SB_Johnny | talk 15:30, 18 May 2008 (UTC)
 * --Jomegat 03:23, 21 May 2008 (UTC)
 * --Jomegat 00:25, 28 May 2008 (UTC)
 * --Jomegat 00:34, 3 June 2008 (UTC)
 * --SB_Johnny | talk 11:32, 4 June 2008 (UTC)
 * --Jomegat 23:45, 9 June 2008 (UTC)
 * --Jomegat 21:24, 21 June 2008 (UTC)
 * --Jomegat 22:49, 1 July 2008 (UTC)
 * --Jomegat 02:59, 8 July 2008 (UTC)
 * --Jomegat 18:39, 12 July 2008 (UTC)
 * --SB_Johnny | talk 10:08, 20 July 2008 (UTC)
 * Jomegat 19:49, 26 July 2008 (UTC)
 * Jomegat 00:58, 2 August 2008 (UTC)
 * Jomegat 03:11, 21 August 2008 (UTC)
 * Jomegat 21:32, 1 September 2008 (UTC)
 * Jomegat 20:06, 20 September 2008 (UTC)
 * Jomegat 21:03, 29 September 2008 (UTC)
 * Jomegat 23:16, 3 October 2008 (UTC)
 * Jomegat 04:33, 19 October 2008 (UTC)
 * Jomegat 17:54, 4 November 2008 (UTC)

2009 Logs

 * Jomegat 22:24, 14 May 2009 (UTC)
 * Jomegat 00:25, 25 May 2009 (UTC)
 * Jomegat 00:28, 2 June 2009 (UTC)
 * Jomegat 00:13, 15 July 2009 (UTC)
 * Jomegat 04:01, 2 August 2009 (UTC)

2010 Logs

 * Jomegat 00:32, 8 May 2010 (UTC)
 * Anna reg 23:39, 20 May 2010 (UTC)

Recent Logs

 * Anna reg 19:17, 12 May 2011 (UTC)
 * Anna reg 18:13, 19 October 2011 (UTC)

title: BCP/Trifolium pratense/Logs


text:
BCP/Solanum dulcamara/Logs

2007 Logs

 * --SB_Johnny | talk 10:30, 3 June 2007 (UTC)
 * --SB_Johnny | talk 09:52, 18 June 2007 (UTC)
 * --SB_Johnny | talk 13:22, 2 July 2007 (UTC)
 * --Jomegat 17:21, 1 August 2007 (UTC)
 * --SB_Johnny | PA! 13:07, 4 August 2007 (UTC)
 * Hazel 18:07, 5 August 2007 (UTC)
 * --Jomegat 00:45, 10 August 2007 (UTC)
 * --Jomegat 00:38, 21 August 2007 (UTC)
 * --SB_Johnny | talk 09:34, 1 September 2007 (UTC)
 * --Luai lashire 14:10, 9 September 2007 (UTC)
 * --Jomegat 16:04, 12 September 2007 (UTC)
 * --Jomegat 17:08, 17 September 2007 (UTC)
 * --Jomegat 17:56, 20 September 2007 (UTC)
 * --SB_Johnny | talk 10:37, 10 September 2007 (UTC)
 * --SB_Johnny | talk 07:01, 1 October 2007 (UTC)
 * --Jomegat 04:22, 10 October 2007 (UTC)
 * --Jomegat 21:37, 29 October 2007 (UTC)
 * --Jomegat 22:58, 5 November 2007 (UTC)
 * --Jomegat 22:44, 14 November 2007 (UTC)

2008 Logs

 * --Jomegat 17:59, 10 June 2008 (UTC)
 * --SB_Johnny | talk 18:38, 10 June 2008 (UTC)
 * --Jomegat 17:35, 17 June 2008 (UTC)
 * --SB_Johnny | talk 09:19, 28 June 2008 (UTC)
 * --Jomegat 22:56, 1 July 2008 (UTC)
 * --SB_Johnny | talk 10:31, 14 July 2008 (UTC)
 * Jomegat 02:45, 15 July 2008 (UTC)
 * Jomegat 00:52, 2 August 2008 (UTC)
 * Jomegat 04:18, 9 August 2008 (UTC)
 * Jomegat 02:26, 13 August 2008 (UTC)
 * Jomegat 20 August, 2008
 * Jomegat 23:32, 4 September 2008 (UTC)
 * Jomegat 18:08, 7 October 2008 (UTC)

2009 Logs

 * Jomegat 04:03, 5 June 2009 (UTC)
 * Jomegat 00:13, 26 June 2009 (UTC)
 * Jomegat 00:18, 15 July 2009 (UTC)
 * Jomegat 00:45, 22 July 2009 (UTC)
 * Jomegat 02:48, 23 October 2009 (UTC)

Recent Logs

 * Jomegat 11:22, 22 June 2010 (UTC)

title: BCP/Solanum dulcamara/Logs


text:
User:KnowCycle Editor

This is the home page of the editor of the Wikiversity project KnowCycle.

title: User:KnowCycle Editor


text:
User talk:KnowCycle Editor

Hello KnowCycle Editor, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. When leaving comments for others to read, remember to sign and date; it helps everyone keep track of who is writing messages. The signature icon in the edit window makes it simple. To help you get started:
 * Take a guided tour and learn how to edit;
 * Explore our learning projects;
 * Browse our portals, schools, and research pages; and
 * Read and help develop our community policies.

Also, don't forget to experiment with the links to your left. Be bold, and see you around Wikiversity! --JWSchmidt 14:42, 4 August 2007 (UTC)

title: User talk:KnowCycle Editor


text:
BCP/Solanum carolinense/Logs

2008 Logs

 * (no archived logs yet)

Recent Logs

 * --SB_Johnny | talk 12:12, 4 July 2007 (UTC)
 * --SB_Johnny | talk 10:23, 8 July 2007 (UTC)
 * --SB_Johnny | PA! 14:51, 4 August 2007 (UTC)
 * Pfthom01 15:27, 6 August 2007 (UTC)
 * --SB_Johnny | talk 13:51, 17 September 2007 (UTC)
 * --SB_Johnny | talk 09:17, 28 June 2008 (UTC)
 * --SB_Johnny | talk 10:31, 14 July 2008 (UTC)

title: BCP/Solanum carolinense/Logs


text:
BCP/Oxalis stricta/Logs

2007 Logs

 * SBJ 12:08, 12 May 2007 (UTC)
 * --SB_Johnny | talk 23:17, 20 May 2007 (UTC)
 * SBJ 09:18, 25 May 2007 (UTC)
 * --SB_Johnny | talk 10:21, 26 May 2007 (UTC)
 * --SB_Johnny | talk 17:31, 27 May 2007 (UTC)
 * SBJ 19:25, 31 May 2007 (UTC)
 * --SB_Johnny | talk 23:49, 31 May 2007 (UTC)
 * --SB_Johnny | talk 10:47, 3 June 2007 (UTC)
 * SBJ 16:16, 7 June 2007 (UTC)
 * SB Johnny-LM 09:37, 9 June 2007 (UTC)
 * --SB_Johnny | talk 14:34, 9 June 2007 (UTC)
 * SBJ 10:16, 13 June 2007 (UTC)
 * --SB_Johnny | talk 20:00, 1 July 2007 (UTC)
 * --SB_Johnny | PA! 09:53, 16 July 2007 (UTC)
 * --SB_Johnny | PA! 14:59, 4 August 2007 (UTC)
 * SB Johnny-LM 10:39, 25 August 2007 (UTC)
 * --Luai lashire 15:43, 26 August 2007 (UTC)
 * --SB_Johnny | talk 10:44, 1 September 2007 (UTC)
 * --Luai lashire 21:51, 1 September 2007 (UTC)
 * --Luai lashire 22:04, 6 September 2007 (UTC)
 * --Jomegat 02:25, 15 September 2007 (UTC)
 * --Jomegat-UPNY 00:42, 16 September 2007 (UTC)
 * --Jomegat 23:06, 21 September 2007 (UTC)
 * --Luai lashire 18:30, 22 September 2007 (UTC)
 * --Jomegat 02:58, 2 October 2007 (UTC)
 * SBJ 08:48, 3 October 2007 (UTC)
 * --Jomegat 01:53, 7 October 2007 (UTC)
 * --Luai lashire 23:16, 9 October 2007 (UTC)
 * --SB_Johnny | talk 13:07, 24 October 2007 (UTC)
 * --SB_Johnny | talk 09:42, 2 November 2007 (UTC)

2008 Logs

 * SBJ 10:29, 26 April 2008 (UTC)
 * --Jomegat 17:07, 20 May 2008 (UTC)
 * --SB_Johnny | talk 10:32, 27 May 2008 (UTC)
 * --Jomegat 00:24, 28 May 2008 (UTC)
 * --SB_Johnny | talk 11:08, 4 June 2008 (UTC)
 * --Jomegat 00:33, 6 June 2008 (UTC)
 * --Jomegat 23:46, 9 June 2008 (UTC)
 * --Jomegat 17:35, 17 June 2008 (UTC)
 * --Jomegat 22:41, 1 July 2008 (UTC)
 * Jomegat 02:55, 8 July 2008 (UTC)
 * --SB_Johnny | talk 10:21, 14 July 2008 (UTC)
 * Jomegat 02:45, 15 July 2008 (UTC)
 * Jomegat 00:48, 23 July 2008 (UTC)
 * Jomegat 19:42, 26 July 2008 (UTC)
 * Jomegat 00:49, 2 August 2008 (UTC)
 * Jomegat 20:28, 9 August 2008 (UTC)
 * Jomegat 02:25, 13 August 2008 (UTC)
 * Jomegat 03:14, 21 August 2008 (UTC)
 * Jomegat 20 August, 2008
 * Jomegat 00:05, 30 August 2008 (UTC)
 * Jomegat 21:34, 1 September 2008 (UTC)
 * Jomegat 22:44, 10 September 2008 (UTC)
 * Jomegat 12:34, 25 September 2008 (UTC)
 * Jomegat 21:03, 29 September 2008 (UTC)

2009 Logs

 * Jomegat 22:34, 7 May 2009 (UTC)
 * Jomegat 00:42, 12 May 2009 (UTC)
 * Jomegat 00:14, 21 May 2009 (UTC)
 * Jomegat 00:31, 2 June 2009 (UTC)
 * Jomegat 00:27, 9 June 2009 (UTC)
 * Jomegat 00:09, 15 July 2009 (UTC)
 * Jomegat 00:56, 22 July 2009 (UTC)
 * Jomegat 04:01, 2 August 2009 (UTC)

Recent Logs

 * Jomegat 17:01, 27 May 2010 (UTC)
 * Anna reg 29 May 2010 (Photo)

title: BCP/Oxalis stricta/Logs


text:
Bloom Clock/Keys/Southeastern Pennsylvania/August/Pink Flowers/DPL

This page is used to help create a graphical list.

 category=Pink flowered plants category=BCP/SEPA/8 order=descending ordermethod=lastedit


text:
File talk:ABC-Song.ogg

This is very quiet... consider a louder version?

title: File talk:ABC-Song.ogg


text:
Bloom Clock/Keys/Southeastern Pennsylvania/August/Pink Flowers

The plants pictured below have been recorded as blooming during the month of August in Southeastern Pennsylvania.

last updated 09:24, 18 October 2007 (UTC) with 28 plants


text:
Bloom Clock/Keys/Southeastern Pennsylvania/August/Blue Flowers/DPL

This page is used to help create a graphical list.

 category=Blue flowered plants category=BCP/SEPA/8 order=descending ordermethod=lastedit


text:
Bloom Clock/Keys/Southeastern Pennsylvania/August/Blue Flowers

The plants pictured below have been recorded as blooming during the month of August in Southeastern Pennsylvania.

last updated 09:41, 18 October 2007 (UTC) with 11 plants


text:
Bloom Clock/Keys/Southeastern Pennsylvania/August/Purple Flowers/DPL

This page is used to help create a graphical list.

 category=Purple flowered plants category=BCP/SEPA/8 order=descending ordermethod=lastedit


text:
Bloom Clock/Keys/Southeastern Pennsylvania/August/Purple Flowers

The plants pictured below have been recorded as blooming during the month of August in Southeastern Pennsylvania.

last updated 09:44, 18 October 2007 (UTC) with 34 plants


text:
Bloom Clock/Keys/Southeastern Pennsylvania/August/Yellow Flowers/DPL

This page is used to help create a graphical list.

 category=Yellow flowered plants category=BCP/SEPA/8 order=descending ordermethod=lastedit


text:
Bloom Clock/Keys/Southeastern Pennsylvania/August/Yellow Flowers

The plants pictured below have been recorded as blooming during the month of August in Southeastern Pennsylvania.

last updated 09:34, 18 October 2007 (UTC) with 36 plants