The Direct Stiffness Method for Truss Analysis with Python
by
Dr Seán Carroll
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32. Section overview
The Direct Stiffness Method for Truss Analysis with Python
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Direct Stiffness Method on Larger Structures
The Direct Stiffness Method for Truss Analysis with Python
Build your own finite element truss analysis software using Python and tackle large scale structures
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Table of contents
The Direct Stiffness Method for Truss Analysis with Python
by
Dr Seán Carroll
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Introduction
Introduction
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1. Introduction and course overview
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1. Introduction and course overview
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2. Our approach to Python in this course
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2. Our approach to Python in this course
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3. Getting started with Jupyter Notebooks and Python
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3. Getting started with Jupyter Notebooks and Python
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Modelling Elastic Behaviour
Modelling Elastic Behaviour
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4. Section overview
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4. Section overview
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5. Stress and strain in 2D
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5. Stress and strain in 2D
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6. Strain and displacement in 2D
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6. Strain and displacement in 2D
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7. 3-dimensions and matrix notation
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7. 3-dimensions and matrix notation
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8. Plane Stress condition
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8. Plane Stress condition
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9. Plane Strain condition
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9. Plane Strain condition
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10. Material matrix summary
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10. Material matrix summary
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Finite Element Equations & Stiffness Matrices
Finite Element Equations & Stiffness Matrices
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11. Section overview
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11. Section overview
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12. Finite Element equations and the Direct Stiffness Method
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12. Finite Element equations and the Direct Stiffness Method
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13. The Principle of Minimum Potential Energy
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13. The Principle of Minimum Potential Energy
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14. The Finite Element equations
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14. The Finite Element equations
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15. Stiffness matrix for bar element
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15. Stiffness matrix for bar element
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16. Finite Element equation review
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16. Finite Element equation review
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17. Transformation from local to global coordinates
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17. Transformation from local to global coordinates
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Direct Stiffness Method: Step-by-Step
Direct Stiffness Method: Step-by-Step
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18. Section overview
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18. Section overview
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Section 4 - Direct Stiffness Method Step by Step - Slides
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Section 4 - Direct Stiffness Method Step by Step - Slides
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19. Analysis procedure overview
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19. Analysis procedure overview
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20. Calculating element stiffness matrices
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20. Calculating element stiffness matrices
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21. Building the primary stiffness matrix
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21. Building the primary stiffness matrix
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22. Reducing to the structure stiffness matrix
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22. Reducing to the structure stiffness matrix
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23. Solving for unknown displacements
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23. Solving for unknown displacements
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24. Solving for unknown reactions
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24. Solving for unknown reactions
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25. Finding element forces
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25. Finding element forces
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Direct Stiffness Method in Python
Direct Stiffness Method in Python
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26. Section overview
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26. Section overview
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Jupyter notebooks.zip
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Jupyter notebooks.zip
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27. Element stiffness matrices
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27. Element stiffness matrices
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28. Whole structure stiffness matrix
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28. Whole structure stiffness matrix
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29. Reactions, element forces and nodal displacements
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29. Reactions, element forces and nodal displacements
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30. Visualising our output
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30. Visualising our output
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31. Refactor - Tidying up with functions
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31. Refactor - Tidying up with functions
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Direct Stiffness Method on Larger Structures
Direct Stiffness Method on Larger Structures
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32. Section overview
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32. Section overview
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Question Jupyter notebook
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Question Jupyter notebook
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Section 6 - Direct Stiffness Method on Larger Structures - Slides
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Section 6 - Direct Stiffness Method on Larger Structures - Slides
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33. Calculating element stiffness matrices
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33. Calculating element stiffness matrices
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34. Building the primary stiffness matrix
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34. Building the primary stiffness matrix
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35. Reducing to structure stiffness matrix
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35. Reducing to structure stiffness matrix
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36. Solving for unknown displacements
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36. Solving for unknown displacements
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37. Solving for unknown reactions
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37. Solving for unknown reactions
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38. Finding element forces
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38. Finding element forces
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Optimising for Larger Structures in Python
Optimising for Larger Structures in Python
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39. Section overview
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39. Section overview
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Jupyter notebook
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Jupyter notebook
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40. Building the primary stiffness matrix
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40. Building the primary stiffness matrix
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41. Extracting the structure stiffness matrix
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41. Extracting the structure stiffness matrix
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42. Displacements and reactions
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42. Displacements and reactions
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43. Calculating member forces
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43. Calculating member forces
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44. Visualising our output
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44. Visualising our output
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Building a Generalised Truss Solver in Python
Building a Generalised Truss Solver in Python
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45. Section overview
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45. Section overview
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Jupyter notebook
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Jupyter notebook
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46. Establishing input data
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46. Establishing input data
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47. Calculating member orientation and length
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47. Calculating member orientation and length
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48. Primary and Structure Stiffness matrices
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48. Primary and Structure Stiffness matrices
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49. Displacements, reactions and member forces
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49. Displacements, reactions and member forces
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50. Automating the output visualisation
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50. Automating the output visualisation
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51. Automating the text summary
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51. Automating the text summary
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Taking your Solver for a Test Drive
Taking your Solver for a Test Drive
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52. Section overview
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52. Section overview
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Jupyter notebooks
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Jupyter notebooks
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53. Test Question #1
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53. Test Question #1
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54. Test Question #2
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54. Test Question #2
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55. Test Question #3
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55. Test Question #3
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56. Course wrap up and debrief
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56. Course wrap up and debrief
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