This document outlines a presentation that demonstrates Mathematica's capabilities for finite element analysis and data visualization. The presentation contains two proposals: Proposal 1 focuses on using Mathematica for finite element modeling, including forming matrices, performing calculations, and solving an example problem of buckling of a frame. Proposal 2 demonstrates Mathematica's graphical capabilities for pre- and post-processing finite element results, including data and dynamic visualization techniques.

1. Prepared by
Md. Saniul Haque Mahi
Presentation on capabilities of Mathematica software in implementing finite element
algorithm and graphical capabilities of Mathematica to pre-process and post-process the
results obtained from a finite element procedure.
Presentation

2. 2
Preparing an outline of presentation to demonstrate live the
capabilities of Mathematica software in implementing finite
element algorithm.
• Proposal 01
Preparing an outline of presentation to demonstrate live the
graphical capabilities of Mathematica to pre-process and post-
process the results obtained from a finite element procedure.
• Proposal 02

3. 3
Proposal 01

4. 4
01. Function
02. Matrix
03. Calculus
04. Numerical Computation
05. Problem Solution
Contents

5. Function
Single variable Multiple variable
Function
5

6. 1. Formation through a list
2. Manual formation of matrix
*To create new column press "ctrl + ,"
*To create new row press "ctrl + Enter"
Formation of Matrix
6

7. Standard Matrix Multiplication
Matrix Operations
7

8. Element wise multiplication
Matrix Operations
8

9. A^2 =A.A Cautionary : Never do this
We can use MatrixPower
function to compute this
problems
Matrix Powers
Matrix Operations
9

10. Sum Subtract
The trace of a
matrix : It is
the sum of
the diagonal
elements
Trace
Matrix Operations
10

11. Extract an element Extract the entire row
Extract the entire column
Extracting Submatrices
Matrix Operations
11

12. Transpose of a matrix
finding out determinant of
the square matrix
row reduction of a matrix
Matrix Operations
12

13. Several Forms of Matrix
13

14. Differentiation
D Function Manual Command
Calculus
14

15. Integration
Using Integrate Function Manual Command
Calculus
15

16. Numerical Computations
16

17. Numerical Computations
17
Data Manipulation
A={10,55,44,-69,80}

18. Numerical Computations
18
Data Manipulation
A={10,55,44,-69,80}

19. Solution of Problem with Mathematica (Buckling of a frame)
19
Question

20. Solution of Problem with Mathematica (Buckling of a frame)
20

21. Solution of Problem with Mathematica (Buckling of a frame)
21

22. Solution of Problem with Mathematica (Buckling of a frame)
22

23. Solution of Problem with Mathematica (Buckling of a frame)
23

24. Solution of Problem with Mathematica (Buckling of a frame)
24

25. Solution of Problem with Mathematica (Buckling of a frame)
25

26. Solution of Problem with Mathematica (Buckling of a frame)
26

27. 27
Proposal 02

28. 28
01. Data visualization
02. Dynamic visualization
03. Problem Solution
Contents

29. Data Visualization
29
Plot
Parametric
Plot

30. Data Visualization
30
Aspect Ratio

31. Data Visualization
31
Example Data &
Texture
Plot Style

32. Data Visualization
32
Plot 3D
Texture
Coordinate
Scale

33. Data Visualization
33
Mesh

34. Data Visualization
34
Plot range

35. Data Visualization
35
Plot Labeling & Legending

36. Data Visualization
36
Row Boxed

37. Dynamic Visualization
37
Manipulate Plot
Manipulate
Parametric Plot

38. Dynamic Visualization
38
Appearance
Control

39. Dynamic Visualization
39
Module
Module allows to set up local variables with names that are local to the module.

40. Solution of Problem with Mathematica (Tunnel volume)
40

41. Solution of Problem with Mathematica (Tunnel volume)
41

42. 42
Reference:
** Chapter 15 Geometric Nonlinearity--Saouma V.E. - Finite element I.
Framed structures (2002)
** https://www.wolfram.com

43. 43
Thank you