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User:Yongtao-Li/HW4.7

=Problem 4.7=

Given
Introduction to Calculix - A non-linear Finite Element Analysis Code

Calculix is an open source Finite Element Analysis code with the authors acknowledging that naming conventions and input style formats for CalculiX are based on those used by ABAQUS, a proprietary and commercial, general purpose finite element code but the results obtained from CalculiX are in no way connected to ABAQUS.

Website for informational and software download (Linux executable) purposes - http://dhondt.de/ Website for informational and software download (Windows executable) purposes - www.bconverged.com/calculix

Calculix in all has 2 major modules, namely- 1. CGX ( Calculix Graphics Module ) - This program is designed to generate and display finite elements (FE) and results coming from CalculiX CrunchiX (ccx).The Concept and File Format sections give some background on functionality and mesher capabilities. The Getting Started section describes how to run the verification examples you should have obtained along with the code of the program.

2. CCX (Calculix CrunchiX (Solver) Module) - This is a theoretical section giving some background on the analysis types, elements, materials etc. Then, an overview is given of all the available keywords in alphabetical order, followed by detailed instructions on the format of the input deck. If CalculiX does not run because your input deck has problems, this is the section to look at. The last section contains a description of the verification examples you should have obtained along with the code of the program. If you try to solve a new kind of problem you haven't dealt with in the past, check this section for examples. You can also use this section to check whether you installed CalculiX correctly (if you do so with the compare script and if you experience problems with some of the examples, please check the comments at the start of the corresponding input deck). Finally, the User's Manual ends with some references used while writing the code.

Find
a) Installation of the Calculix Graphics Module and to explain the installation process for layman(CGX) b) To access the CGX manual c) To sign up with used group for asking the queries,if any and to gain access to the archives where we can access the email conversation from various users,a source of possible learning d) To reproduce the basic inbuilt examples from CGX data base installed on your machine, with a detailed report, about entities such as - 1. Dics 2. Cylinder 3. Sphere 4. Sphere Volume 5. Airofoil The report shall include explanation to all the CGX commands used to generate above example geometries along with their meshes using screen-shots of the useful explanatory steps.

For Linux
For a naiver Linux user now using Windows, we strongly recommend using Ubuntu as your linux operating system which can be easily downloaded and installed at Ubuntu

To install Calculix for Linux, start by downloading the source code and examples available at http://dhondt.de/cgx_2.2.all.tar.bz2. Right now you need open a terminal by selecting that from Applications as in the following picture.

Before installation, you should check openGL on your system by typing the following words in your terminal:

find /usr/* -name libGL* -print

And the following results show that you have the openGL-library which is needed.

/usr/lib/mesa/libGL.so.1 /usr/lib/mesa/libGL.so.1.2 /usr/lib/libGLU.so.1 /usr/lib/libGLU.so.1.3.070701

Another thing you need is c++ complier since we have to compile the source code. You can check where is your c++ complier by typing

which c++

If you don't have these essential things, please typing the following to download and install them sudo apt-get install linux-kernel-headers sudo apt-get install build-essential

Then we start to install cgx.

1.Unpack the file cgx_2.2.all.tar.bz2 in "/usr/local". An easy way is first exacting the compressed file using your right mouse menu and then copy to the destination.

2.Then enter the folder where the source code located by typing

cd /usr/local/CalculiX/cgx_2.2/src/

3.Run "make" as a root and copy the binary "cgx" to "/usr/local/bin/cgx" with

cp cgx /usr/local/bin/cgx

4.Run "latex cgx" in "/usr/local/CalculiX/cgx_2.2/doc" for three times and then run "latex2html cgx".

5.Now your CalculiX has been installed and please enjoy

6.In order to check the installation, type

cgx -b dummy.fbd

and you can see a window appear on your screen as following.

Note:

1.If you are counting any problems for being unable to find any *.h, you can type the following to ensure that you have install all the essential libraries before building the source codes

sudo apt-get install build-essential libsdl1.2debian libsdl1.2-dev libgl1-mesa-dev libglu1-mesa-dev libsdl-image1.2 libsdl-image1.2-dev

For Windows
To install CalculiX for Windows, start by downloading the executable file available at http://www.bconverged.com/download.php.

Before installing CalculiX, we recommend that you create a folder that you will want to use as your workspace for CalculiX files.

Access the zip file, CalculiX_2_2_win_002.zip, and run the executable CalculiX_2_2_win_002.exe. Review the license agreement and select "I agree" when you are prompted to as shown below.

The next screen will ask you to select the directory to which Calculix will be installed. You may use the default directory or click "Browse" to select the directory of your choosing. Once you have the desired directory in the "destination folder" field (1) click the "next" button (2) to continue.

You will now be shown a prompt which allows you to choose which components and/or extensions of the program you wished to have installed. It is recommended to use the default settings unless you are an advanced user. Click "Install" to begin the installation.

When the installation begins you will be asked to specify a folder or directory to use as your workspace. Choose the folder you created prior to starting the installation on the file tree and click "OK"

CalculiX will now begin installing onto your computer. When completed you will be presented with the screen below. Specify if you'd like to view the help file by checking or un-checking the corresponding box and then click "Finish" to complete the installation process.

Congratulations !! You have completed installing CalculiX on your Windows based computer.

Access to CGX manual
To locate the user manual after installation of the software, begin by clicking on the windows start button. All programs will open and select the folder bConverge. This folder will open with all of the calculix programs listed, however to access the manual double-click on the help icon inside of the bConverged folder. This action will open a new window containing several folders. Expand the Calculix folder and then the CGX folder. This will bring you to the Calculix User's Manual -Calculix GraphiX, Version 2.2- as shown below.

To navigate through the manual any of the blue links in the initial index will take the user to that section of the the manual as shown in the above picture. Pressing ctrl+f will allow the user to find a particular word within the manual as well. At the top of the manual, there are four buttons Next, Up, Previous, and Contents as shown below. The function of these buttons is presented below.

Next: Flips to the next page of the manual. Up: Returns to the previously viewed screen before a link was clicked. Previous: Flips to the previous page of the manual. Contents: Takes the user to the index of links of all contents in the manual.

Additional help while Getting Started- The Calculix User Group
Student can join the yahoo user group dedicated to the forums related to knowledge sharing about Calculix. In the very friendly environment of these forums, the student can present their difficulties and queries and can get benefited by the knowledge of many other Calculix users. Student will be given a choice of joining this user group while in some final steps of the software installation. Even if the student misses to join it at the time of installation, he/she can join the group later using help on Calculix or from Calculix website online. With the help of this user group, the student will be able to have access to the email archives of the group members which at times can become useful to answer at least some of the queries or for informational purposes.

Reproducing the basic inbuilt examples from CGX- A report
Here we present the steps, codes, explanation to all the CGX commands used in the codes to generate the sample inbuilt example geometries in CGX database after installation, along with their meshes using screen-shots of the useful explanatory steps. Please refer to the CGX manual (as explained in the above section) for more details.

Figure
Following figure 4.7.1 shows the geometry and the mesh generated by CGX for a disc in four 90 degree segments-

Geometry generation code
Following figure 4.7.2 shows the code to generate the geometry and the mesh by CGX for the disc in Figure 4.7.1. Explanation of the commands used is given in the succeeding subsection.

Explanation of the commands used
This subsection provides the explanation of the CGX commands used in Figure 4.7.2

PNT
The format for entering a point in CGX is as follows -

'pnt' |'!' [  ]|

[  ]|

[  ]|

[]

This keyword is used to define or redefine a point. There are four possibilities to define a point.

To define a point just with coordinates:

pnt p1 11 1.2 34

or,

pnt ! 11 1.2 34

where the name is chosen automatically.

It is also possible to create points on a line or in the direction from P1 to P2 by defining a spacing (ratio) and number-of-points:

pnt ! L1 0.25 3

or

pnt ! P1 P2 0.25 3

This will create 3 new points at the positions 0.25, 0.5 and 0.75 times the length of the line or the distance from P1 to P2.

And it is also possible to create points on the positions of existing nodes. The command

pnt ! set

will create new points on the positions of the nodes included in the specified set.

Usually when points are defined interactive the command qpnt is used. Please refer to the CGX manual for its details

LINE
The format for entering a Line is as follows-

'line' |'!'

This keyword is used to define or redefine a line. A line depends on points.

A line can only be defined if the necessary points are already defined. There are three different types of lines available.

The straight line -

line l1 p1 p2 4

is defined by: its name l1 (the name could have up to 8 characters), by the points p1 and p2 and optionally by the division.

The arc

line ! p1 p2 cp 4

needs a center point cp. The radius changes linear from p1 to p2 if the center-point cp is excentric. The name is chosen automatically (triggered by the character !).

The spline

line l1 p1 p2 seq 4

needs a so called sequential-set, seq (use the command seqa to define such a set). This set seq stores the spline points between the end-points in the right order. The spline function is described in [14]. Usually, a line is defined interactively with qlin.

GSUR
The format for entering a surface is as follows-

'gsur' |'!' '+|-' 'BLEND| ' '+|-'  '+|-' ->  .. (3-5 times)

This keyword is used to define or redefine a surface in the most basic way (see also qsur). Each surface must have three to five lines or combined lines (see lcmb) to be mesh-able. However, the recommend amount of edges is four. For example,

gsur S004 + BLEND - L002 + L00E + L006 - L00C

will create the surface S004 with a mathematically positive orientation indicated by the + sign after the surface name.

The keyword BLEND indicates that the interior of the surface will be defined according to reference [12] given as- S. A. Coons, 'Surfaces for computer-aided design of space forms'. Project MAC, MIT (1964). Revised to MAC-TR-41 (1967) or a NURBS surface is referenced.

Use a + or - in front of the lines or lcmbs to indicate the orientation. These signs will be corrected automatically if necessary. If automatic name generation is desired, then use ! instead of a name.

ELTY
The format used to assign a specific element type to a set of entities and generating the mesh, is as follows-

'elty' [ ] ['be2'|'be3'|'tr3'|'tr3u'|'tr6'|'qu4'|-> 'qu8'|'he8'|'he8f'||'he8i'|'he8r'|'he20'|'he20r']

This keyword is used to assign a specific element type to a set of entities (see section Element Types in the appendix). The element name is composed of the following parts: The leading two letters define the shape (be: beam, tr: triangle, qu: quadrangle, he: hexahedra), then the number of nodes and at last an attribute describing the mathematical formulation or other features (u: unstructured mesh, r: reduced integration, i: incompatible modes, f: fluid element for ccx). If the element type is omitted, the assignment is deleted. If all parameters are omitted, the actual assignments are posted:

elty

will print only the sets with assigned elements. Multiple definitions are possible. For example,

elty all

deletes all element definitions. If the geometry was already meshed, the mesh will NOT be deleted. If the mesh command is executed again after new assignments has taken place, additional elements will be created.

elty all he20

assigns 20 node brick-elements to all bodies in the set all.

elty part1 he8 <p?

redefines that definition for all bodies in the set part1.

elty part2 qu8

assigns 8 node shell elements to all surfaces in set part2.

Figure
Following figure 4.7.3 shows the geometry and the mesh generated by CGX for a cylinder in four 90 degree segments-

Geometry generation code
Following figure 4.7.4 shows the code to generate the geometry and the mesh by CGX for the cylinder in Figure 4.7.3.

Explanation of the commands used is given in the succeeding subsection.

Explanation of the commands used
Please refer to the 'Disc' section above for explanation of all the following CGX commands used to build the geometry and mesh of the cylinder Following commands are used to generate the geometry and mesh of the cylinder in figure 4.7.3 -

' PNT  For entering a point - (refer to the 'Disc' subsection above for explanation)

' LINE  For entering a Line - (refer to the 'Disc' subsection above for explanation)

' GSUR  For entering a surface - (refer to the 'Disc' subsection above for explanation)

' ELTY  To assign a specific element type to a set of entities and generating the mesh - (refer to the 'Disc' subsection above for explanation)

Figure
Following figure 4.7.5 shows the geometry and the mesh generated by CGX for a sphere created from 32 blended surfaces.-

Geometry generation code
Following code was used to generate the geometry by the CGX for the sphere in Figure 4.7.5.

Explanation of the commands used is given in the succeeding subsection.

Explanation of the commands used
Please refer to the 'Disc' section above for explanation of all the following CGX commands used to build the geometry and mesh of the sphere Following commands are used to generate the geometry and mesh of the sphere in figure 4.7.5 -

' PNT  For entering a point - (refer to the 'Disc' subsection above for explanation)

' LINE  For entering a Line - (refer to the 'Disc' subsection above for explanation)

' GSUR  For entering a surface - (refer to the 'Disc' subsection above for explanation)

' ELTY  To assign a specific element type to a set of entities and generating the mesh - (refer to the 'Disc' subsection above for explanation)

Figure
Following figure 4.7.l3 and figure 4.7.l4 show the geometry and the mesh generated by CGX for an airfoil using many 4 nodes element-

Geometry generation code
Following codes show how to generate the geometry and the mesh by CGX for the cylinder in Figure 4.7.l3.

Explanation of the commands used is given in the succeeding subsection.

Explanation of the commands used
Please refer to the 'Disc' section above for explanation of all the following CGX commands used to build the geometry and mesh of the airfoil Following commands are used to generate the geometry and mesh of the airfoil in figure 4.7.l3 -

' PNT  For entering a point - (refer to the 'Disc' subsection above for explanation)

' LINE  For entering a Line - (refer to the 'Disc' subsection above for explanation)

' GSUR  For entering a surface - (refer to the 'Disc' subsection above for explanation)

' ELTY  To assign a specific element type to a set of entities and generating the mesh - (refer to the 'Disc' subsection above for explanation)

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User:Merwan~enwikiversity

Hello. Here is a brief list of things that I am interested in:

 * Criticism of school
 * Mathematics
 * Computer programming
 * Music
 * Linguistics
 * Philology - Spanish, Japanese, Latin, Chinese (Cantonese and Mandarin) to name a few
 * Games (Ludology? - sounds a bit stuffy)
 * Philosophy
 * Economics
 * Marxism

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Nucleotide Synthesis

Nucleotides are the building blocks of amino acids. They can either be synthesized in a process called "de novo" synthesis--which means "beginning again" in Latin--or they can be recycled through salvage pathways after the RNA or DNA harboring them has been degraded (most likely via DNase or RNase). This article will specifically cover de novo synthesis.

All five nucleotides (including the RNA base "uracil") are synthesized through complex metabolic pathways involving several multi-subunit enzymes. The pathways differ for both purines and pyrimidines (uracil falling in the pyrimidine category since it is thymine's counterpart.)

Contrary to common belief, the nucleotides are not synthesized as bases first then attached to a sugar. As seen in the first step of purine synthesis, sugars usually attach themselves to a base very early on in the process if not in the middle (as with pyrimidine synthesis).

Purine Synthesis:

Reaction Mechanism 1: The purine synthesis pathway begins with 5-phosphoribosyl 1-pyrophosphate (synthesized from ribose 5-phosphate). 5-phosphoribosyl 1-pyrophosphate (from henceforth "PRPP") binds to the first enzyme in this pathway, glutamine-PRPP amidotransferase. This changes the conformation of the enzyme to allow for glutamine binding in another active site. Through this enzyme, glutamine is hydrolyzed to glutamate, and the ammonia (readily turned into a weakly nucleophilic ammonium ion in an aqueous environment) that was hydrolyzed off then travels down a hydrophobic channel to attack PRPP's 1' carbon. Since the O-P-P already on the 1' carbon is a good leaving group, PRPP is stable enough to accept the attack and becomes 5-phospho-beta-D-ribosylamine.

Reaction Mechanism 2: 5-phospho-beta-D-ribosylamine attacks a phosphorylated glycine (the phosphate is a good leaving group). GAR synthetase is the enzyme that catalyzes this reaction. Glycinamide ribonucleotide (GAR) is produced.

Reaction Mechanism 3: GAR is formylated on the newly added amine group (the N terminus of the glycine residue) by N10-Formyl H4 folate. GAR transformylase catalyzes this reaction.

Reaction Mechanism 4: The formylated GAR (known as formylglycinamide ribonucleotide or FGAM) is attacked by another ammonia on the first carbon from the glycine residue. The ammonia is again released after hydrolysis of glutamine. Before ammonia can attack, however, ATP activates the oxygen of the carbonyl from the glycine. After phosphorylation, the O-P substituent becomes a good leaving group, and the nucleophile ammonia can perform an SN2 reaction. The reaction is catalyzed by FGAR amidotransferase (similar mechanism to glutamine-PRPP amidotransferase; the FGAR is activated in tandem with glutamine hydrolysis). The intermediate is now a formylglycinamine and is thus known as FGAM.

Reaction Mechanism 5: FGAM is phosphorylated by ATP through FGAM cyclase to form a five-membered ring. The ATP activates the remaining carbonyl group (from formylation in step 3). That carbon is then attacked by the amine from reaction 1, forming a ring with O-P as a leaving group. The molecule that remains is known as 5-aminoimidazole ribonucleotide (AIR).

Reaction Mechanism 6a: AIR can now by processed in different ways (higher eukaryotes like humans use AIR carboxylase to bypass step 7; mechanism will be covered as step 6b). In this mechanism, AIR can attacked an activated bicarbonate ion using the amine group from the second glutamine reaction (step 4). This steps is catalyzed by N5-CAIR synthetase.

Reaction Mechanism 7: The carboxyl group from the bicarbonate is transferred to the central carbon of the glycine residue from reaction 2. N5-CAIR from 6a now becomes CAIR (or carboxyaminoimidazole ribonucleotide). This is very similar to the glycine binding mechanism. This reaction is catalyzed by N5-CAIR mutase.

Reaction Mechanism 6b: This reaction involves bringing in a carbon dioxide to directly bond with the central carbon of the glycine residue. That carbon attacks the carbon dioxide using the help of AIR carboxylase, an enzyme that is homologous to N5-CAIR mutase.

A few more reactions follow. I will finish this later unless someone would like to finish for me.

title: Nucleotide Synthesis


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The History of the Paralympic Movement in Australia/Request for Proposals

APC Request for Proposals
The Australian Paralympic Committee (APC) seeks costed proposals from suitably qualified individuals or organisations to document the history of the Paralympic movement in Australia in a format which meets the needs of the APC for online and possible print publication.

Project name
History of the Paralympic Movement in Australia

Purpose
Create a well-researched and referenced multi-media document which can be published online - and linked to video, audio and photographic content - or adapted for print publication, which tells the story of:
 * The development of Paralympic sport and, where the two intersect, the wider story of sport for people with a disability in Australia.
 * Australia’s participation in the 13 summer and 10 winter Paralympic Games conducted to the end of 2010.
 * The foundation and growth of the Australian Paralympic Committee.
 * Key individuals in the growth of the Paralympic movement in Australia.

Time frame
Commence in the first six months of 2011. Delivery by 31 December 2012.

Background
The Australian Paralympic Committee helps Australians with disabilities participate in sport and compete at the Paralympic Games through partnerships with governments, business, sporting bodies and the community. The APC aims to be the leading National Paralympic Committee and one of Australia’s leading sport administration organisations. Through the Australian Centre for Paralympic Studies, the Australian Paralympic Committee is undertaking a range of activities to collect, manage and preserve the history of the Paralympic movement in Australia and to ensure its accessibility to future generations.

The Paralympic history project has the following elements: Hall of Fame – The APC will make inaugural inductions into the Australian Paralympic Hall of Fame in 2011, with subsequent inductions in 2012 and then every two years.
 * Audio-visual collection – Photos, newspaper clippings videos and audio recordings, including some historical materials. These are managed for the APC by the National Sports Information Centre.
 * Oral history – 23 oral histories will be recorded by the National Library of Australia under the Australian Centre for Paralympic Studies oral history program by mid-2011.
 * Video interviews – The APC records brief video interviews with the subjects of the oral histories.
 * Physical materials – The APC is conducting negotiations with several organisations to ensure the preservation of physical materials of significance to the history of the Paralympic movement in Australia.
 * Reunions and alumni - The APC is developing a strategy to conduct regular reunions for Paralympic Team members and to create an active alumni program for past Team members. A reunion of the 1960 Paralympic Team was held in 2010.

See Attachment A for more detail.

The APC seeks to draw these elements together through an online document, linked to images, video and audio, as well as websites, to create a rich, multi-dimensional history of the Paralympic movement in Australia, which can be added to over time and will grow as the Paralympic movement itself grows.

Scope of the project and role of the tenderer
The APC is seeking an individual, organisation or team of people to assemble an online document which tells the history of the Paralympic movement in Australia.It is anticipated that the successful tenderer will have:
 * demonstrated writing skills and experience;
 * networking skills;
 * experience in historical research;
 * an understanding of sport in Australia;
 * an understanding of sport for people with disabilities and the Paralympic movement;
 * an understanding of modern information technologies and the capacity or resources to create a document which exploits the opportunities available through the Web environment;
 * an openness to input.

The role will involve:
 * the creation of an initial framework document, based on research and utilisation of existing materials, covering the history of the Paralympic movement in Australia;
 * setting up an online forum for input by a full range of people involved in the Paralympic movement in Australia;
 * monitoring and moderating input;
 * interviews with people who have played a significant role in Australian Paralympic sport
 * research;
 * liaison with representatives of the APC to source photographs, videos, audio, competition results, team lists and other materials relevant to the project;
 * creating a final text for the period up to 2010, within a structure which includes the following elements:
 * personal stories;
 * each Paralympic Games;
 * other key Games, such as the Stoke Mandeville Games, the Commonwealth Paraplegic Games and the FESPIC Games;
 * organisational history and changes;
 * some social and historical contexts.

 * linking the text to oral history interviews, other audio, video and photographs through a customised website.

It is anticipated that engagement with the Paralympic community will occur through direct contact, including face-to-face, telephone and email, and also through the creation of a “wiki” or other on-line forum which will allow input from a range of interested sources, anecdotes and discussion about events and activities. The project may involve the use of Facebook or other social networking sites for communication, as well as more traditional methods.

The aim of this approach is to draw upon the collective knowledge and memory of the Paralympic community, in addition to using historical records such as results and contemporaneous documents.

The APC is keen to ensure that the final document is as accurate as possible and that input is referenced or corroborated. The APC anticipates that the tenderer will create an initial framework document which can be put online to enable feedback and input from the community of those who were involved in the creation of the history.

Priority will be given to tenderers who can communicate a vision for how they will create an effective multi-media project and can demonstrate an understanding of the use of web- based techniques and a capacity to identify and engage stakeholders. Expressions of interest from historians who work in a more traditional format are welcomed. The APC also encourages collaborative approaches between historians and individuals or organisations with expertise in online communications. It is anticipated that the completed text for the project will be in the order of 100,000 to 150,000 words.

Existing resources and APC support for the project

 * 1) The Australian Paralympic Committee was formed in 1990, almost 30 years after the first Australian Paralympic Team competed at the first Paralympic Games in Rome, in September 1960. In those first 30 years, the Australian Paralympic Team was assembled through the collaborative efforts of state, and then national, disability organisations. The APC’s own records and documents date only from the time of its foundation and, more comprehensively, from the late 1990s.
 * 2) In 1999 a considerable amount of work was done to compile a written history of the Paralympic movement in Australia. At the time of its termination, the writer, Adrienne Smith, had drafted just over 40,000 words, covering the period from the beginning of the Paralympic movement until 1987. Ms Smith’s research materials and her document will be available to the successful tenderer. It is expected that the tenderer will make use of this material and that it may assist in the process. The APC has collected historical information, documents, images and other materials through its operations and especially since the initiation of the current history project in 2010.
 * 3) The APC will provide access to its archives and any materials that it possesses which are of relevance to the project.

Submission inclusions
1. Expressions of interest should include:
 * the name(s) of the proposed tenderers;
 * proposed timelines for the project;
 * an outline of how the project will be structured and managed;
 * any software or systems that will be utilised;
 * the proposed format of the finished product;
 * proposed contract cost;
 * any other details that will assist the APC to make a decision.

2. The successful tenderer will be expected to travel within Australia to conduct interviews and review original documents and other materials. Given the involvement of individuals and organisations around Australia in the Paralympic movement, it is anticipated that total stays of between one and two weeks during the project in each mainland capital except Darwin may be necessary. In the case of travel within Australia, the APC will meet all accommodation and transport costs and will pay the tenderer $100 a day for food and miscellaneous expenses. Hence, these costs should not be included in the tender.

3. Tenders should include the full cost of the tender and not assume any grants or subsidies from any organisation.

4. Tenders may be made by individuals, groups of two or more people working collaboratively, or organisations. The proposed organisation or structure of the project should form part of the expression of interest document.

Conditions

 * 1) The APC will base its selection of the successful tenderer on its evaluation of the tenderer’s capacity to deliver outcomes which match the APC’s needs, outlined in this document, at a reasonable cost.
 * 2) The APC will appoint an internal committee to recommend the tenderer to the APC Board, which will make the selection at its absolute discretion.
 * 3) The APC will enter into a formal agreement with the successful tenderer.
 * 4) A payment schedule will be negotiated with the successful tenderer. It will include progress payments dependent upon progress and a final payment on satisfactory delivery of the finished project.
 * 5) All content developed through the project, including any related online resources, will be the property of the APC.

Closing date for tenders
Written expressions of interest must be received by the APC by 5 PM (AEDT) on Friday 11 March, addressed to: Tony Naar General Manager Knowledge Services Australian Paralympic Committee PO Box 596 Sydney Markets NSW 2129 AUSTRALIA Electronic tenders will be accepted and should be emailed to tony.naar@paralympic.org.au.

Further information
For further information, including a copy of the existing, written partial history of the APC, contact Tony Naar at tony.naar@paralympic.org.au or (+61 2) 9704 0510.

The APC Paralympic History Project	ATTACHMENT A
The Australian Paralympic Committee is undertaking a range of activities to collect, manage and preserve the history of the Paralympic movement in Australia and to ensure its accessibility to future generations. The Paralympic historic project has the following elements:

Audio-visual
1. APC holdings The APC has an extensive collection of more than 45,000 photographs and more than 1,100 video items, which span the period from the creation of the APC in 1990 to the present. The APC has entered into a formal agreement with the National Sports Information Centre (NSIC), which is part of the Australian Sports Commission, and based at the AIS in Canberra, under which the NSIC is evaluating, cataloguing, labelling and managing the APC’s audio-visual collection. Through the NSIC, the collection is being preserved and made accessible to researchers, coaches and the general public.

2. Historical photos and clippings The APC is beginning to receive donations and loans of photos and newspaper clippings relating to the history of the Paralympic movement in Australia. These are forwarded to the NSIC, which scans these historical photos and newspaper clippings to ensure that permanent, high quality copies are stored. Where such items were loaned to the APC, they are then returned to the owners.

3. Historical film and other video The APC is aware of the existence of footage on film and other media, from Games prior to 1990, and is keen to ensure the preservation of this important historical Paralympic sport footage. To this end, the APC has initiated discussions with the National Film and Sound Archive (NFSA). The NFSA, a Division of the Australian Film Commission (AFC), is the national audiovisual archive of Australia. The NFSA plays a key role in documenting and interpreting the Australian experience. It aims to develop a collection of audiovisual and related materials of enduring cultural significance. The NFSA has indicated that it is interested in preserving and managing historical Paralympic film by making and storing high quality digital copies. The NFSA has also indicated its interest in accepting Paralympic materials for storage and preservation if they are offered to it.

Oral history
The APC has entered into a formal agreement with the National Library of Australia (NLA) for the NLA to collect the oral histories of people who have played a significant role in the development of Paralympic sport in Australia. These interviews are part of the NLA’s ongoing oral history project. In accord with its national heritage responsibilities, the NLA produces, collects and preserves recorded interviews and other forms of oral history to meet the documentation, research, publication and exhibition needs of the Australian research community. By July 2011, 23 interviews will be conducted, including interviews with all the eight surviving Paralympians from the first Games in Rome in 1960. (Interviews with six of the eight were conducted in 2010). The NLA has set up a page on its website for the Paralympic interviews and the first of these are on the site (http://www.nla.gov.au/digicoll/APConline.html). The project will be reviewed after the initial round of interviews, with the intention to conduct further interviews until a comprehensive overview of the story of the Paralympic movement in Australia is achieved.

Video interviews
The APC’s audio-visual manager, Shaun Giles, has started the process of recording short historical video interviews. This project commenced with the Rome Paralympians and will include interviews with all of those interviewed for the oral history project, to complement the oral history interviews. They will be used on the APC website, in the APC Paralympic Education Program and in other ways. For example, interviews with the Rome Paralympians were used in a video tribute to the first Games, which has since been used in a number of Australian and international forums and is posted on the APC’s YouTube site.

Written history
In 2011 the APC will call for tenders to write the history of the Paralympic movement in Australia, drawing on and completing work that was initiated in the late 1990s. Once written, this history will be published in an appropriate format and regularly updated.

Online
In recent years, the APC has developed a strong online presence. In addition to its main website (www.paralympic.org.au), the APC has created a website for its education program (www.paralympiceducation.org.au), a facebook site, a YouTube channel (http://www.youtube.com/ausparateam) and is active on Twitter (http://twitter.com/AUSParalympics). The elements of the Paralympic history project outlined in this document will be published through the APC’s website to maximise their accessibility to the widest possible audience.

Paralympic Hall of Fame
In 2011 the APC will launch the Australian Paralympic Hall of Fame and induct the inaugural athlete and associate members. Further inductions will be made in 2012 and thereafter. Over coming years, the APC will investigate options for a physical home for the Australian Paralympic Hall of Fame.

Equipment, uniforms and memorabilia
The APC is conducting discussions with relevant museums and historical organisations for the collection, management and preservation of Paralympic equipment, uniforms and memorabilia. The Powerhouse Museum holds a comprehensive collection of items associated with the 2000 Sydney Paralympic Games. The National Sports Museum holds a small collection of donated items. The APC is developing a collections policy and is looking at innovative ways to preserve and display Paralympic items of historical value, while respecting the wishes of the owners.

Reunions and alumni
In 2010 the APC invited all eight surviving 1960 Rome Paralympians to be its guests at the Paralympian of the Year dinner in Sydney on 18 October, to celebrate the 50th anniversary of the first Paralympic Games. The day after the dinner, the APC hosted an informal lunch for the 1960 Paralympians. Seven members of the 1960 Team and their partners were able to attend. The APC is developing a strategy to conduct regular reunions for Paralympic Team members and to create an active alumni program for past Team members.


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User:EGM6341.s11.TEAM1.Yoon.HW4-1

Applying error bound by taking max and absolute sign on the both side,

We can define bound of each sub-f(x)s by,

Since the summation of each bound is equal or less than n times of M4,

Applying above relation onto our inequality yields,

In conclusion,
 * {| style="width:100%" border="0" align="left"

$$\displaystyle \displaystyle \left| {E}_{n}^{S} \right| \leq \frac{(b-a)^{5}}{2880 {\color{blue}{n^{4}}}} M_{4} = \frac{(b-a)h^{\color{red}{4}}}{2880} M_{4} $$
 * style="width:10%; padding:10px; border:2px solid #8888aa" |
 * style="width:10%; padding:10px; border:2px solid #8888aa" |
 * style = |
 * }
 * }

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User:Eml5526.sp11.team1.adam/HW4

=Homework Problem 4.2: Weak form for the equation of heat conduction= Fish and Belystschko page73, Problem 3.5.

Obtain the weak from for the equation of heat conduction with the boundary conditions $$ T\left(0\right) = 100$$ and $$ q\left(10\right) = h\bar{T} $$. The condition on the right is a convection condition.

Multiplying by the weight function
Multiplying the first two equations by the weight funtion we can write:

Applying integration by parts
Applying integration by parts to $$\left(4.2.2a\right)$$ we ca write:

Therefore we can write that:

Using the natural boundary condition we can write:

Which yields

Weak form for 1D heat conduction problems
Therefore the weak form for 1D heat conduction problems can be written as follows:

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User talk:Anandsuict

 * Total Quality Management
 * By
 * Dr. Daniel G. Fuchs

Gerber Products Company

Background: Gerber Products Company is one largest manufacturer and supplier of baby food offering more than 190 products in 80 countries using 16 languages in labeling. It dominates the baby food industry in USA having share of 83 percent. Gerber brand is well known in the world, the picture logo of Gerber baby food is recognized crossed the world. Let’s look at the brief history of Gerber Products Company.

Origin:

Gerber is well known baby food producer and supplier around the world which stated it first production in 1927 and marketed in 1928 (Wikipedia, 2011). The history of Gerber goes back in 1920s when Daniel Frank Gerber was working as Assistant General Manager in his parent’s company, Fremont Canning Company. Daniel and his wife Dorothy had ill child, Sally. Dorothy urged Daniel to convince his father to begin making and selling at their canning company strained baby foods in order to end the chore of cooking, straining and preparing solid foods for babies (Wikipedia, 2010). Dorothy had already fed her daughter strained food made by herself when Sally was just seven months. Daniel with his father began experiments on baby food production process and getting formulas for baby foods. There were baby food products in the market as liquid diet usually fed to 12 months baby and above. But their experiment and research was risky as they had no idea how mother would react on the new way of strained baby food. Gerber started advertising campaign in different magazines and journals to convince the parent attracting them towards the Gerber strained baby food in 1928 which work in 1930 expanding baby food product line.

Gerber focused on improvement since very beginning, the company introduced strained peas, prunes, carrots and spinach to the market with improved method for straining vegetables and fruits. Five varieties of baby food were prepared, tested, and were ready to market in 1928. Within six months, Gerber’s baby foods were on grocery shelves in most major areas throughout the United States. Gerber made survey how the products could be sold and found scope in grocery stores selling at very lower prices comparing baby food sold in pharmacies. Gerber sold six cans for a dollar. Gerber’s product was less than half of the pharmacy baby food as Gerber advertised in the magazine campaign. Gerber invented great face of baby, Ann Turner Cook at her five months of age for promote the campaign to represent Gerber’s baby food which became trademark of the company in 1931 and famous worldwide, even today that face is trusted symbol of Gerber. The campaign included a magazine ad with attached detachable coupons which customers filled with information of theirs grocers such as name and address. Gerber collected the database of his customers and understand trend from very starting.

Milestones of Gerber: Gerber enjoyed monopoly of the baby food industry; however by 1935 more 60 manufacturers launched their own vitamin-rich, pressure-cooked, sealed baby foods. (Funding, Universe, 2011). Gerber had advantage in this competitive environment that, Gerber received the loyalty of the customers and well earned perception Gerber was synonymous to quality and expert. Gerber symbol was famous among the US population, on other hand other no other company possessed a logo approaching the appeal of the "Gerber Baby," which was already famous; Gerber continuously conducted a research on parenting, feeding, and child psychology. Dorothy wrote articles in the newspapers "Bringing up Baby" held sway with thousands of mothers nationwide. During the American recession of the Great Depression, the Gerber was confident about its strength and vision for the future by introducing a state-of-the-art agricultural program, going beyond national borders; they entered into the Canadian market, increasing their production line to double making annual revenue of $1 million, topping industry. (Funding, Universe, 2011). Weekly sale of baby food in 1941, reached up to a million cans and renamed as the Gerber Products Company. In 1943 company opened a second baby food plant in Oakland, California. The year 1948 is considered to be the best time for the Gerber when tow million baby food cans were sold. That same year, the company adopted its trademark slogan: "Babies are our business ... our only business."

 * Three more new plants were added in 1950 locating in Asheville, North Carolina; Rochester, New York; and Niagara Falls, Ontario. The death of father replaced Daniel to Frank Gerber. Under the leadership of Daniel Gerber, the company embarked on a new mission of expansion and diversification. Gerber joined toy line in 1955, a listing on the New York Stock Exchange in 1956, the opening of a Mexican subsidiary in 1959, and the introduction of a large line of baby-related products in 1965. Gerber added Gerber Life Insurance as subsidiary in 1967. Daniel Frank Gerber passed away in 1974 leaving company as the world’s largest baby food manufacturer rising sale up to $ 278 million having 70 percent domestic market share.

 * Anderson, Clayton, and Company, a food products firm based in Houston aggressively launched a serious takeover attempt to Gerber in 1977. The probability of a long legal battle dissuaded Anderson from further action and preserved Gerber's independence. Within two years, Gerber began in earnest a major campaign of diversification and acquired CW Transport, a freight carrier based in Wisconsin. Although furniture, toy, and other subsidiaries followed, by 1989 Gerber had divested itself of many of these fringe ventures in order to refocus on its more profitable baby food, baby care, and clothing lines.

Class shard crisis, information center and expansion:
 * Gerber faced one of most serious threat which in 1980s, public relations crises of 1984 and 1986 proved to be even more dangerous than acquisition policy of board in 1980s. Gerber responded to the first of these two crises involving reports alleging the presence of glass fragments in jar of baby juice by recalling some 550,000 jars in a 15-state region. This cautionary action was viewed favorably by the public, and financial damage incurred by the company was limited to only a short-term, 4 percent drop in sales.
 * The second glass crisis which, like the first, sparked investigations that ultimately exonerated Gerber involved some 645 complaints spread over 40 states. This time Gerber, headed by William L. McKinley, chose to remain silent and to take no action other than offer its cooperation with federal investigators. The decision proved unpopular and contributed at least in part to a drop in profits from $69 million in 1985 to $54 million in 1987; McKinley departed shortly after the resolution of the glass scare and was replaced by Leo D. Goulet (Funding, Universe, 2011) . After second crisis Gerber learnt the lesson and understood the need of a system allowing consumers to contact it directly and give feedback. However the consumer relationship department had a flow of letter since 1938, but it was totally different than of 1986’s which related to quality and safety department. As a result of the crisis telephone service (free hotline) was launched in 1986 which brought about changes in quality discipline. It also helped to understand the consumer trend and gathered the database. In 1991company extended the operating hour to 24 a day taking daily average 2,400 call in all languages and letter correspond team answered the 45,000 letters received from consumers. In the same year In 1991 Gerber entered foreign markets including the USSR, Thailand, Brazil, Chile, and Sweden, in February 1992 purchased 60 percent of Alima, S.A., a Polish producer of food and juices.

Take over and today:
 * Sandoz, the Swiss pharmaceutical company took over Gerber in 1994 paying $3.7 billion. Two years, Sandoz merged with CIBA-Geigy and became Novartis one of the largest pharmaceutical company in the world. Today Nestle company is owner of Gerber, Nestle Company which bought Gerber for $5.5 billion in 2007 (Wikipedia, 2011).

Hazard Analysis and Critical Control Points (HACCP)

Meaning and Scope:

 * HACCP was developed by Pillsbury Company at NASA, National Aeronautics and Space Administration in 1960s to provide safe food for astronauts in the space program (Youtube, 2009) . It is a method of ensuring food safety and pharmaceutical safety by examining every step in a food operation, identifying those steps critical to food safety and implementing effective control and monitoring procedures at these steps. It deals with physical, chemical and biological hazards as a means of prevention rather than checking the finished product. HACCP is a preventative system that gives a high level of food safety assurance and is considered to be the best approach to producing safe food and thus preventing food-borne illness.
 * The method of preventing hazards increasing hygiene is widely used in all the steps of food production and food preparation processes such as packaging, distributing, storing, transporting etc. The system is a mandatory requirement of Food and Drug Administration (FDA) and the United States Department f Agriculture (USDA) for every small and large firm involved in food productions and processing. According to USDA HACCP program for juice and meat are an effect approach to food safety and protecting public health. Meat HACCP program is controlled by the USDA and seafood and juice are taken care by the FDA (Wikipedia, 2011).
 * HACCP method includes seven major steps:

 * 1) Identifying Hazards
 * 2) Identifying Critical Control Point
 * 3) Establishment Critical Limits
 * 4) Establishing Monitoring Procedures
 * 5) Establishment of Correct Actions
 * 6) Verifying that The System is Working
 * 7) Establish a Record Keeping System
 * If a small food processing plant sets up the HACCP first it needs to create recipe  or processing flow chart, step by step description that how the product is made from receiving the row ingredients through processing and storing the finished product watching what happens  to each of the ingredient. It includes keeping watch on ingredients at the time of delivery whether are properly cleaned and undamaged, chopping, cutting, grinding, weaving and measuring, way of mixing, cooing and packaging. When these all steps are surely included in the process, time comes to look at HACCP’s every single step.

 * Identifying food related hazards: what factors may make food unsafe to consume; biological hazards are bacteria, viruses, parasites including flatworms and roundworms cause sicknesses like Chinese Liver Fluke, Lever Fluke, Pinworm, Hookworm, Viral Gastroenteritis, Botulism, Salmonellosis and Brucellosis (Microbiologyprocedure, 2011) . Chemical risk occurs when food could be contaminated with chemical substances used kill harmful insects and small animals or when they might come into contact with cleaning compounds or sanitizing chemicals. Physical hazards include any unaware action resulting addition of unwanted, harmful outside substance in the product such as class shard.

Once hazards are identified in the recipe or processing of product, next step is to:

 * Identify critical control point: A critical control point is a step in operation, or procedure in a food manufacturing process at which control must be applied and, as a result, a food safety hazard can be prevented, eliminated, or reduced reasonably. For example, in food like tomatoes and peppers bacteria like Clostridium Botulinum can grow and produce deadly toxic. Adding an acid such as lemon juice is necessary to prevent spore grow. This adding of acid is critical control point, when food consumed will outbreak the Botulism. If the product requires heat treatment, that heat processing is critical control point, guidelines for temperature and time for particular product are given by the authorities. Looking through the product processing steps, it has to be determined whether any of steps is eliminating or reduce hazards at acceptable level, then that becomes the critical control point. Adding acid in above example is critical control point which is needed for safety. Whereas adding spices is matter of taste which not the critical control point since it has nothing to do with safety.

 * Establishment Critical Limits: After identifying critical control point the decision has to be made, what measure must be used to make sure that every risk is adequately control, this criteria is called critical limit. This most likely includes cooking or refrigeration temperature, acid levels. Since these limits are critical to the safety of the products consulting professionals to decide temperature and acid level makes sure that error may not occur.

 * Establishing Monitoring Procedures: How to know, meeting of critical limits; adding each critical control point for each critical limit monitoring the procedure. Some of the procedure may need only visual inspection. Does any of the jars has chips in the rim that prevent sealing them properly. Other may require simple instrumentations such as pH meter, thermometer and timer to see foods are cooked at correct temperature and in time period. Records of processing must be taken, what food is cooked at what temperature. If something goes wrong eventfully, like failure of the gas supply to stove. The temperature clearly notify the problem, where concerned expert will fix them and will bring back on the track.

 * Establish corrective actions. Identifying, monitoring, correcting; constant vigilance is the key of safety processed food products and to effective hazard program.  These are actions to be taken when monitoring indicates a deviation from an established critical limit. The final rule requires a plant's HACCP plan to identify the corrective actions to be taken if a critical limit is not met. Corrective actions are intended to ensure that no product injurious to health or otherwise adulterated as a result of the deviation enters commerce.

Verifying that The System is Working: Verification should include regular review of hazard plan by an outside source. Internal verification includes regular review of the processing, record and periodic collaboration of measuring instruments.

 * Establish a Record Keeping System: Final step of HACCP is record keeping, the records may be kept in the notebooks or file racks, it provides important information that the product is safely produced. Records made while monitoring critical limits at critical control point should be kept in permanent record keeping system after each batch or product lot has been processed. It is necessary to identify each batch with batch label or lot number. If the question arises about one of the products, that particular products can be identified and recalled affected product.

 * It is important to have HACCP in the plant which involves food production or food processing because this indicates that the firm is truly interested in producing a good, clean product and protecting the consumers.

Gerber Products Company, manufacturer of baby food meets almost all the definitions of quality discussed in chapter one. Gerber Products Company has higher standers set than of government. It has scientific research team to create baby food formulas and doctors to verify. They also test the product taste feeding babies to know they prefer or not. In the first chapter we discussed several quality definitions including:
 * Product based definition: quantities of product attribution.
 * User based definition: fitness for intended use.
 * Value based definition: Quality Vs price.
 * Manufacturing based definition: conformance to specifications.
 * Customer Driven Quality and Excellence.

Product based definition: quantities of product attribution
 * Gerber baby food is high in nutrition and great in taste. However, even if the food is highly nutritious and not tasty the baby will not like it. Gerber’s baby food is tasted on babies using a panel of 4,000 babies to taste the products. In 2003, along with scientific and medical team, Gerber established the Gerber Feeding Development Model (Gerber Products Company, 2011) . This ensures providing a wide array of baby foods that are the right sizes, textures, and shapes to encourage the development of proper feeding skills in young children at each developmental stage. The Gerber backs quality commitment with strict ingredient specifications, multiple sample tests, and strict safety programs to ensure that Gerber products comply with regulatory requirements and are unquestionably safe for babies.

User based definition: fitness for intended use
 * Gerber Baby Food is healthy, safe and convenient baby food. Gerber’s research team develops baby food formulas for different products indented for varying age groups of babies. The every product are medically tasted to make sure that the product will cause no side effects. Gerber’s organic baby foods makes sure that baby will not suffer from diseases based bacteria such as pesticides. Non organic baby food may cause active appearance of pesticides in baby urine (Dr. David Hill, 2008) . However this kind of bacteria is found in baby urine who takes Gerber organic baby food.

Gerber have single dose package which is contained in small bottles. It is time saving and easy to carry.

Value based definition: Quality Vs price

 * If we see the Gerber’s baby food product history they have started with very cheaper pricing strategy. In 1930s Gerber sold six cans of baby food just for a dollar whereas same amount of baby food was sold in pharmacies cost was more than doubled. Today the life has become even faster which seeks time saving in every actions. Preparing food for baby for every diet will lead a lot of time consumption, buying the vegetable and fruits, cleaning them, and process them including boiling, pilling, blending, cooking, cooling etc. After it is cooked it has to be kept in particular temperature. If the mother is working or traveling with baby it becomes inconvenient. These all steps have certain level of hazard. Therefore buying Gerber becomes cheaper and safer.

Manufacturing based definition: conformance to specifications

 * The Gerber Product Company has an extra ordinary process to produce the baby food. Gerber works hard to make sure it meets all the latest safety, quality, and regulatory standards for the products, ingredients, and packaging. To ensure that Gerber meets consumers’ expectations for quality and safety every time, Gerber often sets its internal standards even higher than those of the government.

Customer Driven Quality and Excellence.

 * The Gerber’s baby food market share in US proves that it satisfies the customers’ expectations and quality of Gerber goes beyond it. The Gerber is considered as synonymous to excellence (Funding, Universe, 2011) . The competitive US market is dominated by Gerber having 83 percentages. Gerber brand has become extremely popular producing baby food around the world. Nestle is an international giant which took over the Gerber in 2007 but kept Gerber name unchanged. This shows the Esteem of Gerber brand.

Total Quality Principles at Gerber Products Company
 * Various fundamental principles of quality has been demonstrated by Berber, let’s see some of the principles leading to total quality:

Product based definition: quantities of product attribution

 * Gerber baby food is high in nutrition and great in taste. However, even if the food is highly nutritious and not tasty the baby will not like it. Gerber’s baby food is tasted on babies using a panel of 4,000 babies to taste the products. In 2003, along with scientific and medical team, Gerber established the Gerber Feeding Development Model. This ensures providing a wide array of baby foods that are the right sizes, textures, and shapes to encourage the development of proper feeding skills in young children at each developmental stage. The Gerber backs quality commitment with strict ingredient specifications, multiple sample tests, and strict safety programs to ensure that Gerber products comply with regulatory requirements and are unquestionably safe for babies.

User based definition: fitness for intended use

 * Gerber Baby Food is healthy, safe and convenient baby food. Gerber’s research team develops baby food formulas for different products indented for varying age groups of babies. The every product are medically tasted to make sure that the product will cause no side effects. Gerber’s organic baby foods makes sure that baby will not suffer from diseases based bacteria such as pesticides. Non organic baby food may cause active appearance of pesticides in baby urine. However this kind of bacteria is found in baby urine who takes Gerber organic baby food.

Gerber baby food is convenient to carry and feed the babies anywhere with smart packaging. Gerber have single dose package which is contained in small bottles. It is time saving and easy to carry.

Value based definition: Quality Vs price

 * If we see the Gerber’s baby food product history they have started with very cheaper pricing strategy. In 1930s Gerber sold six cans of baby food just for a dollar whereas same amount of baby food was sold in pharmacies cost was more than doubled. Today the life has become even faster which seeks time saving in every actions. Preparing food for baby for every diet will lead a lot of time consumption, buying the vegetable and fruits, cleaning them, and process them including boiling, pilling, blending, cooking, cooling etc. After it is cooked it has to be kept in particular temperature. If the mother is working or traveling with baby it becomes inconvenient. These all steps have certain level of hazard. Therefore buying Gerber becomes cheaper and safer.

Manufacturing based definition: conformance to specifications

 * The Gerber Product Company has an extra ordinary process to produce the baby food. Gerber works hard to make sure it meets all the latest safety, quality, and regulatory standards for the products, ingredients, and packaging. To ensure that Gerber meets consumers’ expectations for quality and safety every time, Gerber often sets its internal standards even higher than those of the government.

Customer Driven Quality and Excellence.

 * The Gerber’s baby food market share in US proves that it satisfies the customers’ expectations and quality of Gerber goes beyond it. The Gerber is considered as synonymous to excellence. The competitive US market is dominated by Gerber having 83 percentages. Gerber brand has become extremely popular producing baby food around the world. Nestle is an international giant which took over the Gerber in 2007 but kept Gerber name unchanged. This shows the Esteem of Gerber brand.

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User:Eml5526.s11.team3.sahin/Homework 4

=Problem 4.2 Deriving of the Weak Form for One Dimensional Heat Conduction =

Given: Equations of heat conduction in one dimension
A first Course in Finite Elements, Fish & Belychtschko, John Wiley & Sons Ltd, 2007, p.73, problem 3.5

Strong form for 1D heat conduction problems

Essential boundary conditions, Natural boundary conditions, The condition on the right is a convection condition

Find
Derive the weak form for one dimensional heat conduction.

Solution
We multiply the first equation in the strong form (Eq 2.1) by the weight function and integrate over the domain on $$\Omega$$, which yields

Using Integration by Parts of the first term in (Eq 2.4) gives

Since $$w$$ is arbitrary, we select $$w$$ such that $$w(0)=0$$ to drop out the unknown term at x=0. As we remember we already have essential boundary conditions at x=0 and substitute natural boundary condition (Eq 2.3) into (Eq 2.6). So we get

If we rearrange the equation, we obtain the weak form

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User talk:Glen619

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You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! Jtneill - Talk - c 11:35, 2 March 2011 (UTC)

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User:Eml5526.s11.team7.snook/HW4

=Problem 4.6: Elastic Bar With a Variable Distributed Spring: F&B 3.9=

Problem Description
An elastic bar is subjected along its length to a variable distributed spring p(x) as seen in the figure below. An axial force proportional to the displacement is imposed by the spring on the bar. Adapted from "A First Course in Finite Elements" by Fish and Belytschko p. 74 pb.3.9

a. Construct the strong form.

b. Construct the weak form.

Given
This bar is of length l, cross-sectional area A(x), Young's modulus E(x) with body force b(x) and with boundary conditions:

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$$\displaystyle u(0)=0$$
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$$\displaystyle E(l)A(l)\frac{du(l)}{dx}=t$$
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As seen in the figure above.

Solution
Assumptions:
 * The bar must be in equilibrium
 * It satisfies Hooke's law
 * Compatible Displacement Field
 * The Strain-Displacement Equation must be Satisfied

a. Construct the Strong Form
Following a similar solution method as Team 2 used here with Eq. 1.1-1.10. Using the following diagram from Team 7 homework 1 to start creating the strong form:

Performing a force balance on the rod using the free body diagram above, the net force is equal to the internal forces plus the external, or applied, forces. Note, in this specific problem we will designate our body force as b(x+dx/2) (instead of f(x+dx/2 as seen in the diagram from Team 7) and have the additional body force in the opposite direction caused by the springs (as seen by the figure in the problem description) designated as p(x+dx/2)

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$$ \displaystyle \Sigma \text{ Internal Force } + \text{ Applied Force } = \text{ Net Force}$$ (4.6.1)
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$$ \displaystyle \Sigma \text{ Internal Force }=N(x) + N(x+\Delta x)$$ (4.6.2)
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$$ \displaystyle \text{ Applied Force }=b(x+\frac{dx}{2})dx-p(x+\frac{dx}{2})dx$$ (4.6.3)
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Since we are looking at the static case:

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$$ \displaystyle \text{ Net Force}= m*a =0$$ (4.6.4)
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Substituting equations 4.6.2-4.6.4 into the force balance equation, 4.6.1:

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$$ \displaystyle N(x) + N(x+dx) + b(x+\frac{dx}{2})dx-p(x+\frac{dx}{2})dx =0$$ (4.6.5)
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Plugging in for the direction of the surface normal, the balance of forces at position x can be expressed as:

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$$ \displaystyle N(x)=n(x)\sigma (x)A(x)=-\sigma (x)A(x)$$ (4.6.6)
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Also plugging in for the surface normal, the corresponding force at x + dx:

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$$ \displaystyle N(x+dx)=n(x+dx)\sigma (x+dx)A(x+dx)=\sigma (x+dx)A(x+dx)$$ (4.6.7)
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Using a Taylor Series:

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$$ \displaystyle \sigma (x+dx)=\sigma (x)+\frac{d\sigma (x)}{dx}dx+...$$ (4.6.8)
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$$ \displaystyle A(x+dx)=A(x)+\frac{dA(x)}{dx}dx+...$$ (4.6.9)
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Additionally, in Eq. 4.6.3 the body force $$b(x+\frac{dx}{2})$$ has been averaged for the differential volume we are considering to formulate the governing differential equation. The same has been done for the force caused by the variable distributed spring, given as $$p(x+\frac{dx}{2})$$. Taylor expanding for these as well:

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$$\displaystyle b(x+\frac{dx}{2})=b(x)+\frac{db(x)}{dx}\frac{dx}{2}....$$. (4.6.10)
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$$\displaystyle p(x+\frac{dx}{2})=p(x)+\frac{dp(x)}{dx}\frac{dx}{2}....$$. (4.6.11)
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Plugging in Eq.'s 4.6.8 and 4.6.9 into Eq. 4.6.7, and then plugging this and Eq.'s 4.6.6, 4.6.10 and 4.6.11 into Eq. 4.6.5 gives:
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$$\displaystyle \sigma (x)A(x) + \sigma (x)\frac{dA(x)}{dx}dx+A(x)\frac{d\sigma (x)}{dx}-\sigma (x)A(x)+b(x)dx-p(x)dx$$. (4.6.12)
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Using the product rule, canceling out terms, and dividing through by dx gives:
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$$\displaystyle \frac{d}{dx}\sigma (x)A(x)+b(x)-p(x)=0$$. (4.6.13)
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Noting that the strain-displacement equation is
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$$ \displaystyle
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\varepsilon \left( x \right) = \frac

$$     (4.6.14) And by Hooke ‘ s Law
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$$ \displaystyle
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\sigma \left( x \right) = E\left( x \right)\varepsilon \left( x \right) = E\left( x \right)\frac

$$     (4.6.15)
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Gives the following strong form:
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$$\displaystyle \frac{d}{dx}E(x)A(x)\frac{du}{dx}+b(x)-p(x)=0$$. (4.6.16)
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b. Construct the Weak Form
Following the same solutions as Team 7's previous work here.

In order to reduce the requirements or constraints on what trial solutions could be substituted in for u, we will generate the weak form which requires the basis solutions only be once differentiable. This occurs from the natural boundary condition being absorbed in the weak form, as will be seen shortly. Also, this creates a symmetric stiffness matrix.

As with Team 7's solution, the strong form and natural boundary condition are used in an inner product with an arbitrary weighting function giving the following equations:

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$$\displaystyle \int_{0}^{l}w(x)\big [\frac{d}{dx}E(x)A(x)\frac{du}{dx}+b(x)-p(x)\big ]dx=0$$. (4.6.17)
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$$\displaystyle w(l)E(l)A(l)\frac{du(l)}{dx}-w(l)t=0$$. (4.6.18)
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Distributing the weighting function w(x) and the integral of Eq. 4.6.17 and looking at the first term:

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$$\displaystyle \int_{0}^{l}w\frac{d}{dx}E(x)A(x)\frac{du}{dx}dx=w(x)E(x)A(x)|_{0}^{l}-int_{0}^{l}\frac{dw}{dx}E(x)A(x)\frac{du}{dx}dx$$. (4.6.19)
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In Eq. 4.6.19 integration by parts (derived and example of use here) was used. Now to remove the unknown flux at the essential boundary location (x=0), we will make the arbitrary weighting function be zero at x equal to zero, or

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$$\displaystyle w(0)=0$$. (4.6.20) Using Eq. 4.6.7 and 4.6.9, Eq. 4.6.8 becomes:
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$$\displaystyle w(x)E(x)A(x)|_{0}^{l}-\int_{0}^{l}\frac{dw}{dx}E(x)A(x)\frac{du}{dx}dx=w(l)t-\int_{0}^{l}\frac{dw}{dx}E(x)A(x)\frac{du}{dx}dx$$. (4.6.21)
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Combining Equations 4.6.18 and 4.6.21 gives the following weak form:

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$$\displaystyle w(l)t-\int_{0}^{l}\frac{dw}{dx}E(x)A(x)\frac{du}{dx}dx+\int_{0}^{l}w(x)p(x)dx+\int_{0}^{l}w(x)b(x)dx$$. (4.6.22)
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Note in equation 4.6.22 the weighting function must be zero at the essential boundary condition (w(0)=0). Also, the weighting function and the displacement are both first order derivatives and now a symmetric stiffness matrix can be formed.

Author
Braden Snook

title: User:Eml5526.s11.team7.snook/HW4


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