User:EML4500.f08.JAMAMA/LectureNotes1

 The material from Wikipedia page was transfered to the Wikiversity page see Submission 1

Arunas Janulevicius --Eml4500.f08.jamama.jan 14:41, 8 December 2008 (UTC)

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TOPIC: Course Introduction and Introduction to Wiki
IN CLASS ASSIGNMENT

* Form 5-6 people groups. * Give a name for a group and decide upon the representative (leader) of the group. * Create Wikipedia/Wikiversity account (follow an identified pattern of naming the Wiki accounts). * Share information about the members within the group and present the info to the Instructor/TAs.

How to create the wiki account: use the user account Eml4500.f08.group_name.student_name. The homework will be submitted every Wednesday at 5p.m. Homework consist of:

1. Lecture Notes;

2. Homework Problems;

Directions/specifications upon the report submission:

Every student is responsible for doing at least one problem of the homework assignment + understanding upon how to do the other homework problems. Moreover, the students will be responsible for checking each other's work before the submission time. When submitting, the report material will be sent to the group leader. Each group member should make sure that his/her written part has his/her name associated with it. The group leader will gather all of the reports (including his/her own) and will send the appropriate web page to the TAs and the instructor. The leader will submit the history saved report, not the web page where the report was written. This will prevent the vandalism of the material. Final step is that students will have to evaluate each other anonymously. The homework grade will be assigned for the reports that will be scaled for each student by ratio of : grade_{homework}\frac {points_{evaluation}}{points_}

Plan:

* Vision: Big Picture Mediawiki & Wikipedia:

1. Textbooks >> in comparison of Wikipedia to the Britannica Encyclopedia, it was determined that Wikipedia is at least as accurate as Britannica Encyclopedia while Wikipedia has more recent and sometimes more (quantitavely) material about the subject; 2. Wikiversity >> it is a great place to get acquainted with other Universities' work and the presented material, such as (MIT's Open Course Ware); 3. MIT's Open Course Ware >> the material discussed in classes and the text book material are printed on this Course Ware, so that it could be accessible to entire world. It is especially profitable for the poor countries, where majority of students are not able to purchase the text-books. 4. Old approach >> homework (10%) + 3 exams (30% each) is subjected to change allowing the homework to be weighted more. New approach: homework (40%) + 3 exams (20% each). 5. Confidentiality >> the students will create a certain accounts, which will be known only to the other group members + these accounts should not be used to edit other material on the web for the reasons of the probable vandalism acts. 6. Method of work >> each student is expected to "pull his/her own weight." Every student is responsible for checking each other's work. When submitting, each student should add his/her name upon the material that he/she worked on + no late submissions are accepted (past Wednesday 5 p.m.). 7. e-learning >> e-learning will not be used, since it does not have a capacity to connect to the whole world at any time, it might not allow for the quick/real time peer review of the content, and a student said that e-learning "crashed" on him/her.

* MediaWiki (very important software)

1. Wikiversity, MIT's Open Course Ware >> allows the access to Wikiversity, MIT's Open Course Ware; 2. Collaboration >> allows the effective interation between:

* Member of a team; * Teams in the class; * Professor + student;

TOPIC: Trusses, Matrix Method (Chapter 4)
The following image is of a truss with two elastic (deformable) bars.



Note: The displacement at points 1 and 3 is fixed (constrained) to zero, in both the x and the y direction.

Global Free Body Diagram:

The below image illustrates the 4 unknown reactions. This example is statically indeterminate because it has 3 equations and 4 unknown variables. The key to solving this example is to look at the individual bars' deformation.



2 Free Body Diagrams of Separate Bar Elements


 * Bar Element 1:



The unknown solutions at the nodes are the nodal degrees of freedom. The choice of nodal degrees depend on the governing differential equation.


 * Bar Element 2:



Next step: Force Displacement relationship

Recall:

The force distance relationship of a 1 dimensional spring element (with one end fixed) is F=KD. (K is the spring constant)



The force displacement relationship of a 1D spring with 2 ends free is as shown above. To solve this more complex problem one needs to use a matrix to relate F=Kd. The matrix for this example is shown below.

Stiffness Matrix:



Case 1: Observer sits on node 1.
 * F2=K(d2-d1)

Case 2: Observer sits on node 2, or equilibrium f1+f2=0.
 * F1=-F2=-K(d2-d1)=K(d1-d2)

TOPIC: Steps to Solve a Simple Truss System. (Chapter 1)
1. Global Picture (description)
 * At structure level:
 * Global degrees of freedom (displacement unknowns)
 * Global forces


 * Actually, the displacement Dofs are partitioned into:
 * a known part, e.g., fixed Dof, contraints
 * an unknown part: solved by using the finite element method (FEM)


 * Similarly, for the forces:
 * known part: applied forces
 * an unknown part: reactions

2. Element Picture (draw)
 * Element Dof (displacements)
 * Element forces
 * Note: it can be either in global or local coordiante system

3. Global Force-Displacement (FD) relationships
 * Element stiffness matrix in global coordinates
 * Element force matrices in global coordinates.
 * Assembley of element stiffness matrices and element force matrices into global FD relation: $$K*d$$ = $$F$$

4. Elimination of known Dof to eliminate/reduce the global FD relations (if stiffness matrix is non-singular >> invertable >> det(K) &ne; 0);

Km &times; m*dm &times; 1 =  F m &times; 1, where $$m < n $$ m = n 0 of unknown displacement Dof n = n 0 of known and unknown displacement Dof K is non-singular matix >> K -1 (invertable)>> d m &times; 1 =  K -1 m &times; m * F m &times; 1

5. Compute element forces form now known d >> element stresses

6. Compute the reactions (unknown forces)

Example:



1) Globlal Picture:



Numbering of displacement DOF:
 * Follow the order of global node numbering. Assume x - axes are horizontal: If horizontal force was considered first in the first global node, then in the consequent nodes the horizontal force should be numbered first as well(vertical force follows the horizontal force in each node force/displacement numbering).

Matlab Tutorial
Matlab Tutorial

Contributing Team Members
Megan Alvarez --EML4500.f08.jamama.megan 23:55, 16 September 2008 (UTC)

Justin McIntire --Eml4500.f08.jamama.justin 19:10, 19 September 2008 (UTC)

William Mueller --Eml4500.f08.jamama.mueller 19:12, 19 September 2008 (UTC)

Arunas Janulevicius --Eml4500.f08.jamama.jan 19:51, 19 September 2008 (UTC)

Chris Alford --Eml4500.f08.jamama.chris 19:53, 19 September 2008 (UTC)

Cedric Adam--Eml4500.f08.jamama.adam 20:00, 19 September 2008 (UTC)