Lecture 80: Understanding Mohr's circle of stress | Finite Element Analysis of Continuum Structures in Python | EngineeringSkills.com

ACCESS THE COMPLETE LIBRARY OF COURSES & TUTORIALS

Section 1

Welcome and preliminaries

1. Introduction and course overview

08:11 (Preview)

2. What you should cover before this course

04:58 (Preview)

Section 2

The Isoparametric Finite Element Method

3. Section 2 overview

01:39 (Preview)

4. Bar stiffness using generalised coordinates

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-displacement matrix

10. Accounting for plane-stress/strain

11. The equivalent surface force vector

12. The equivalent body force vector

Section 3

Gauss-Legendre Numerical Integration

13. Section 3 overview

01:25 (Preview)

14. Gauss numerical integration scheme

15. Numerical integration in 2D

16. Calculating the element stiffness matrix

17. Stiffness matrix convergence

Section 4

Generating Structure and Mesh Data

18. Section 4 overview

01:11 (Preview)

19. Generating a simple quad mesh in Blender

20. Exporting mesh data from Blender

21. Exporting support and point load data

22. Importing support, loading and mesh data

Section 5

Implementing the Isoparametric Finite Element Method

23. Section 5 overview

01:18 (Preview)

24. Setting analysis parameters and plotting the structure

25. Building the global force vector

26. Defining the element stiffness matrix

27. Assigning the element stiffness coefficients

28. Building the structure stiffness matrix

29. Solving the structure

30. Visualising the deformed structure

31. Generating detailed text output

32. Euler-Bernoulli deflection validation

Section 6

Visualising the Strain and Stress Fields

33. Section 6 overview

02:24 (Preview)

34. Generating the stress calculation grid

35. Visualising the stress calculation grid

36. Calculating the strain and stress fields

37. Visualising the normal stress distribution

38. Building normal strain/stress contour plots

39. Building shear stress/strain contour plots

40. Building a stress/strain interpolation query function

41. Visualising stress distributions at a vertical section

42. Euler-Bernoulli stress validation

Section 7

Implementing Area and Volume Forces

43. Section 7 overview

01:13 (Preview)

44. Implementing self-weight in our analysis

45. Correcting self-weight reactions

46. Distributed loading - Interpolation limits

47. Distributed loading - Data export from Blender

48. Importing distributed loading data

49. Surface force vector - Setup

50. Surface force vector - Integration

51. Updating the global force vector and validating

52. Orthogonal surface forces

Section 8

Principal Stresses and von Mises Failure Theory

53. Section 8 overview

01:47 (Preview)

54. A recap of principal stresses

55. Calculating principal angles and stresses

56. Sorting principal stresses

57. Identifying max ten/comp principal stresses

58. Visualising the principal stress magnitude field

59. Visualising the principal stress vector field

60. Combining the magnitude and vector fields

61. The von Mises failure theory

62. Visualising the von Mises stress field

63. Perimeter stresses and updating plot edges - Planning

64. Perimeter stresses and updating plot edges - Coding

Section 9

Generating and Analysing Complex Meshes

65. Section 9 overview

01:37 (Preview)

66. Generating 2D geometry in Blender

67. Meshing complex geometries

68. Exporting an irregular mesh

69. Generalising our solver

70. Stress distribution masks

71. Course wrap up

72. [BONUS] Cantilever model and analysis walkthrough

22:28 (Preview)

Section 10

Appendix 1: Fundamentals of 2D Stress Analysis and Mohr's Circle

73. Understanding the 2D stress element

25:13 (Preview)

74. The stress transformation equations

23:25 (Preview)

75. Visualising transformation equations

30:59 (Preview)

76. Principal stresses and principal planes

28:32 (Preview)

77. Finding maximum shear stresses

25:21 (Preview)

78. 2D stress analysis worked example

15:40 (Preview)

79. Stress analysis Python worked example

21:35 (Preview)

80. Understanding Mohr's circle of stress

16:51 (Preview)

81. Mohr's circle worked example in Python

26:29 (Preview)

Full Preview

80. Understanding Mohr's circle of stress

Appendix 1: Fundamentals of 2D Stress Analysis and Mohr's Circle

Please log in or enroll to access resources

Please log in or enroll to continue

If you've already enrolled, please log in to continue.

Finite Element Analysis of Continuum Structures in Python

Use the Isoparametric Finite Element Method to build an analysis tool for 2D structures in Python.

After completing this course...

You will have the tools to analyse continuum structures using your own Isoparameteric Finite element Python code, developed from the ground up.
You will understand how the assumptions of plane stress and plane strain allow us to analyse 3D structures accurately with 2D planar models.
You will be able to use open source tools to generate structural models and mesh data that can be analysed with your FE code.

Next Lesson

81. Mohr's circle worked example in Python