Finite Element Analysis of Continuum Structures in Python
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1. Welcome and Preliminaries
1. Introduction and course overview
2. What you should cover before this ...
Support and Lecture Q&A (Please read!)
2. The Isoparametric Finite Element Method
3. Section overview
4. Bar stiffness using generalised co...
5. Bar stiffness using shape functions
6. Quad elements and shape functions
7. The strain-displacement matrix, B
8. The Jacobian Matrix, J
9. Calculating the strain-displacemen...
9.1 Jupyter Notebook - (lecture 9)
10. Accounting for plane-stress/strain
11. The equivalent surface force vector
12. The equivalent body force vector
12.1 Jupyter Notebook - (lectures 11-...
3. Gauss-Legendre Numerical Integration
13. Section overview
14. Gauss numerical integration scheme
15. Numerical integration in 2D
15.1 Jupyter Notebook - (lecture 15)
16. Calculating the element stiffness...
17. Stiffness matrix convergence
17.1 Jupyter Notebook - (lectures 16-17)
4. Generating Structure and Mesh Data
18. Section overview
19. Generating a simple quad mesh in ...
20. Exporting mesh data from Blender
21. Exporting support and point load ...
21.1 Blender File (lectures 19-21)
22. Importing support, loading and me...
22.1 Jupyter Notebook - (lecture 22)
5. Implementing the Isoparametric Finite Element Method
23. Section overview
24. Analysis parameters and plotting ...
25. Building the global force vector
26. Defining the element stiffness ma...
27. Assigning element stiffness coeff...
28. Building the structure stiffness ...
29. Solving the structure
30. Visualising the deformed structure
31. Generating detailed text output
32. Euler-Bernoulli deflection valida...
32.1 Jupyter Notebook - (lectures 24-32)
Mid-course check-in
6. Visualising the Strain and Stress Fields
33. Section overview
34. Generating the stress calculation...
35. Visualising the stress calculatio...
36. Calculating the strain and stress...
37. Visualising the normal stress dis...
38. Building normal strain/stress con...
39. Building shear stress/strain cont...
40. Building a stress/strain interpol...
41. Visualising stress distributions ...
42. Euler-Bernoulli stress comparison
42.2 Jupyter Notebook - (lectures 34-42)
7. Implementing Area and Volume Forces
43. Section overview
44. Implementing self-weight in our a...
45. Correcting reactions for self-weight
46. Distributed loading - Interpolati...
47. Distributed loading - Data export...
48. Importing distributed loading data
49. Surface force vector - Setup
50. Surface force vector - Integration
51. Updating the global force vector ...
52. Orthogonal surface forces
52.1 Jupyter Notebook - (lectures 44-52)
8. Principal Stresses and von Mises stress
53. Section overview
54. A recap of principal stresses
55. Calculating principal angles and ...
56. Sorting principal stresses
57. Identifying max ten/comp principa...
58. Visualising the principal stress ...
59. Visualising the principal stress ...
60. Combining the magnitude and vecto...
60.1 Jupyter Notebook - (lectures 55-60)
61. The von Mises failure theory
62. Visualising the von Mises stress ...
62.1 Jupyter Notebook - (lecture 62)
63. Perimeter stresses and updating p...
64. Perimeter stresses and updating p...
64.1 Jupyter Notebook - (lecture 64)
9. Generating and Analysing Complex Meshes
65. Section overview
66. Generating 2D geometry in Blender
67. Meshing complex geometries
68. Exporting an irregular mesh
68.1 Blender File (lectures 66-68)
69. Generalising our solver
70. Stress distribution masks
70.1 Jupyter Notebook - (lecture 69-70)
71. Course wrap up and Certificate of...
72. [BONUS] Cantilever model and anal...
72.1 Blender File (lecture 72)
72.2 Jupyter Notebook - (lecture 72)
Appendix 1: Fundamentals of 2D Stress Analysis and Mohr's Circle
A1. The 2D stress element
A2. The stress transformation equations
A3. Visualising the transformation eq...
A4. Principal stresses and principal ...
A5. Maximum shear stress
A6. Stress analysis worked example
A7. Stress analysis worked example - ...
A8. Mohr's circle of stress
A9. Mohr's circle example solution
Jupyter Notebook - 2D stress analysis...
Products
Course
Section
Lesson
29. Solving the structure
29. Solving the structure
Finite Element Analysis of Continuum Structures in Python
Buy now
Learn more
1. Welcome and Preliminaries
1. Introduction and course overview
2. What you should cover before this ...
Support and Lecture Q&A (Please read!)
2. The Isoparametric Finite Element Method
3. Section overview
4. Bar stiffness using generalised co...
5. Bar stiffness using shape functions
6. Quad elements and shape functions
7. The strain-displacement matrix, B
8. The Jacobian Matrix, J
9. Calculating the strain-displacemen...
9.1 Jupyter Notebook - (lecture 9)
10. Accounting for plane-stress/strain
11. The equivalent surface force vector
12. The equivalent body force vector
12.1 Jupyter Notebook - (lectures 11-...
3. Gauss-Legendre Numerical Integration
13. Section overview
14. Gauss numerical integration scheme
15. Numerical integration in 2D
15.1 Jupyter Notebook - (lecture 15)
16. Calculating the element stiffness...
17. Stiffness matrix convergence
17.1 Jupyter Notebook - (lectures 16-17)
4. Generating Structure and Mesh Data
18. Section overview
19. Generating a simple quad mesh in ...
20. Exporting mesh data from Blender
21. Exporting support and point load ...
21.1 Blender File (lectures 19-21)
22. Importing support, loading and me...
22.1 Jupyter Notebook - (lecture 22)
5. Implementing the Isoparametric Finite Element Method
23. Section overview
24. Analysis parameters and plotting ...
25. Building the global force vector
26. Defining the element stiffness ma...
27. Assigning element stiffness coeff...
28. Building the structure stiffness ...
29. Solving the structure
30. Visualising the deformed structure
31. Generating detailed text output
32. Euler-Bernoulli deflection valida...
32.1 Jupyter Notebook - (lectures 24-32)
Mid-course check-in
6. Visualising the Strain and Stress Fields
33. Section overview
34. Generating the stress calculation...
35. Visualising the stress calculatio...
36. Calculating the strain and stress...
37. Visualising the normal stress dis...
38. Building normal strain/stress con...
39. Building shear stress/strain cont...
40. Building a stress/strain interpol...
41. Visualising stress distributions ...
42. Euler-Bernoulli stress comparison
42.2 Jupyter Notebook - (lectures 34-42)
7. Implementing Area and Volume Forces
43. Section overview
44. Implementing self-weight in our a...
45. Correcting reactions for self-weight
46. Distributed loading - Interpolati...
47. Distributed loading - Data export...
48. Importing distributed loading data
49. Surface force vector - Setup
50. Surface force vector - Integration
51. Updating the global force vector ...
52. Orthogonal surface forces
52.1 Jupyter Notebook - (lectures 44-52)
8. Principal Stresses and von Mises stress
53. Section overview
54. A recap of principal stresses
55. Calculating principal angles and ...
56. Sorting principal stresses
57. Identifying max ten/comp principa...
58. Visualising the principal stress ...
59. Visualising the principal stress ...
60. Combining the magnitude and vecto...
60.1 Jupyter Notebook - (lectures 55-60)
61. The von Mises failure theory
62. Visualising the von Mises stress ...
62.1 Jupyter Notebook - (lecture 62)
63. Perimeter stresses and updating p...
64. Perimeter stresses and updating p...
64.1 Jupyter Notebook - (lecture 64)
9. Generating and Analysing Complex Meshes
65. Section overview
66. Generating 2D geometry in Blender
67. Meshing complex geometries
68. Exporting an irregular mesh
68.1 Blender File (lectures 66-68)
69. Generalising our solver
70. Stress distribution masks
70.1 Jupyter Notebook - (lecture 69-70)
71. Course wrap up and Certificate of...
72. [BONUS] Cantilever model and anal...
72.1 Blender File (lecture 72)
72.2 Jupyter Notebook - (lecture 72)
Appendix 1: Fundamentals of 2D Stress Analysis and Mohr's Circle
A1. The 2D stress element
A2. The stress transformation equations
A3. Visualising the transformation eq...
A4. Principal stresses and principal ...
A5. Maximum shear stress
A6. Stress analysis worked example
A7. Stress analysis worked example - ...
A8. Mohr's circle of stress
A9. Mohr's circle example solution
Jupyter Notebook - 2D stress analysis...
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