Finite Element Analysis of 3D Structures using Python
by
Dr Seán Carroll
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64. Section overview
Finite Element Analysis of 3D Structures using Python
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Bridge Analysis Case Study
Finite Element Analysis of 3D Structures using Python
Build your own complete 3D structural analysis software in Python using the Direct Stiffness Method
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Table of contents
Finite Element Analysis of 3D Structures using Python
by
Dr Seán Carroll
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Welcome and Preliminaries
Welcome and Preliminaries
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1. Introduction and course overview
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1. Introduction and course overview
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2. What you should cover before this course
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2. What you should cover before this course
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The 3D Beam Stiffness Matrix
The 3D Beam Stiffness Matrix
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3. Section overview
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3. Section overview
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4. Review of the 2D stiffness matrix
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4. Review of the 2D stiffness matrix
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5. 3D beam elements
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5. 3D beam elements
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5.1 3D beam elements [PDF Slides]
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5.1 3D beam elements [PDF Slides]
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6. Minor axis bending and transverse shear
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6. Minor axis bending and transverse shear
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7. Torsion & completing the stiffness matrix
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7. Torsion & completing the stiffness matrix
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7.1 Torsion & completing the stiffness matrix [PDF Slides]
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7.1 Torsion & completing the stiffness matrix [PDF Slides]
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Rotations in 3D Space
Rotations in 3D Space
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8. Section overview
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8. Section overview
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9. An introduction to 3D reference frames
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9. An introduction to 3D reference frames
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9.1 An introduction to 3D reference frames [PDF Slides]
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9.1 An introduction to 3D reference frames [PDF Slides]
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10. Direction cosines & the 3D bar transformation matrix
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10. Direction cosines & the 3D bar transformation matrix
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11. Building the 3D beam transformation matrix
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11. Building the 3D beam transformation matrix
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Generating 3D Frame Data in Blender
Generating 3D Frame Data in Blender
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12. Section overview
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12. Section overview
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13. Building and exporting a basic frame
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13. Building and exporting a basic frame
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14. Exporting frame data from Blender
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14. Exporting frame data from Blender
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15. Exporting structural supports
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15. Exporting structural supports
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16. Exporting point load data
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16. Exporting point load data
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16.1 Blender File - (lectures 13-16)
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16.1 Blender File - (lectures 13-16)
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17. Importing our frame data
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17. Importing our frame data
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18. Building the force vector
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18. Building the force vector
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19. Visualising our structure with matplotlib
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19. Visualising our structure with matplotlib
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19.1 Jupyter Notebook - (lectures 17-19)
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19.1 Jupyter Notebook - (lectures 17-19)
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Building the Transformation Matrix
Building the Transformation Matrix
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20. Section overview
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20. Section overview
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21. Defining a default member orientation
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21. Defining a default member orientation
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22. How to define a local member reference frame
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22. How to define a local member reference frame
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23. Building the local member reference frame
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23. Building the local member reference frame
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24. Calculating member reference frames and lengths
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24. Calculating member reference frames and lengths
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24.1 Jupyter Notebook - (lectures 21-24)
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24.1 Jupyter Notebook - (lectures 21-24)
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Building and Solving the Stiffness Matrix
Building and Solving the Stiffness Matrix
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25. Section overview
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25. Section overview
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26. Building the global element stiffness matrix
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26. Building the global element stiffness matrix
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27. Building the primary stiffness matrix
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27. Building the primary stiffness matrix
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28. Extracting the structure stiffness matrix
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28. Extracting the structure stiffness matrix
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29. Solving for displacements and reactions
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29. Solving for displacements and reactions
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30. Solving for member actions
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30. Solving for member actions
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30.1 Jupyter Notebook - (lectures 26-30)
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30.1 Jupyter Notebook - (lectures 26-30)
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Visualising Results in 3D
Visualising Results in 3D
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31. Section overview
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31. Section overview
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32. Plotting the deflected shape
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32. Plotting the deflected shape
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33. Plotting the axial force heat map
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33. Plotting the axial force heat map
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34. Build the local bending moment diagram
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34. Build the local bending moment diagram
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34.1 Jupyter Notebook - (lectures 32-34)
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34.1 Jupyter Notebook - (lectures 32-34)
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35. Plotting the 3D bending moment diagram
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35. Plotting the 3D bending moment diagram
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35.1 Blender File
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35.1 Blender File
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36. Build the local shear force diagram
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36. Build the local shear force diagram
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37. Plotting the 3D shear force diagram
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37. Plotting the 3D shear force diagram
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38. Generating detailed text output
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38. Generating detailed text output
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39. Exporting deflections to Blender
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39. Exporting deflections to Blender
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39.1 Blender File
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39.1 Blender File
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39.2 Jupyter Notebook - (lectures 35-39)
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39.2 Jupyter Notebook - (lectures 35-39)
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Implementing Bar Bracing Elements
Implementing Bar Bracing Elements
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40. Section overview
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40. Section overview
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41. Exporting bar elements from Blender
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41. Exporting bar elements from Blender
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41.1 Blender File
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41.1 Blender File
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42. Identifying rotational releases
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42. Identifying rotational releases
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43. Assigning areas to bar elements
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43. Assigning areas to bar elements
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44. Bar element stiffness matrix
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44. Bar element stiffness matrix
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45. Adding bars to the primary stiffness matrix
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45. Adding bars to the primary stiffness matrix
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46. The structure stiffness matrix with bars
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46. The structure stiffness matrix with bars
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47. - Solving for axial forces in bar elements
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47. - Solving for axial forces in bar elements
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47.1 Jupyter Notebook - (lectures 40-47)
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47.1 Jupyter Notebook - (lectures 40-47)
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Implementing Pinned Members
Implementing Pinned Members
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48. Section overview
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48. Section overview
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49. Constructing a fixed-pinned stiffness matrix
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49. Constructing a fixed-pinned stiffness matrix
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49.1 Fixed-pinned stiffness matrix [PDF Slides]
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49.1 Fixed-pinned stiffness matrix [PDF Slides]
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50. Exporting pinned elements from Blender
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50. Exporting pinned elements from Blender
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50.1 Blender File
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50.1 Blender File
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51. Identifying pinned members in our code
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51. Identifying pinned members in our code
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52. Element stiffness matrix with pin at node i
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52. Element stiffness matrix with pin at node i
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53. Element stiffness matrix with pin at node j
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53. Element stiffness matrix with pin at node j
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54. Adding pinned elements to the primary stiffness matrix
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54. Adding pinned elements to the primary stiffness matrix
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55. Solving for pinned member actions
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55. Solving for pinned member actions
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55.1 Jupyter Notebook - (lectures 51-55)
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55.1 Jupyter Notebook - (lectures 51-55)
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Implementing Distributed Loading
Implementing Distributed Loading
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56. Section overview
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56. Section overview
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57. Identifying distributed loads in Blender
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57. Identifying distributed loads in Blender
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57.1 Blender File
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57.1 Blender File
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58. Importing distributed loading information
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58. Importing distributed loading information
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59. Equivalent nodal actions - Part 1
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59. Equivalent nodal actions - Part 1
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60. Equivalent nodal actions - Part 2
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60. Equivalent nodal actions - Part 2
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61. Updating the global force vector
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61. Updating the global force vector
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62. Removing ENA from reactions
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62. Removing ENA from reactions
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63. Removing ENA from member actions
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63. Removing ENA from member actions
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63.1 Jupyter Notebook - (lectures 58-63)
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63.1 Jupyter Notebook - (lectures 58-63)
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Bridge Analysis Case Study
Bridge Analysis Case Study
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64. Section overview
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64. Section overview
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65. Reviewing the bridge structure
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65. Reviewing the bridge structure
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66. Building the structural bridge model
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66. Building the structural bridge model
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66.1 Blender File
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66.1 Blender File
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67. Model data export/import
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67. Model data export/import
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68. Reviewing our results
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68. Reviewing our results
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68.1 Jupyter Notebook - (lectures 67-68)
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68.1 Jupyter Notebook - (lectures 67-68)
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69. Course wrap-up & Certificate of Completion
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69. Course wrap-up & Certificate of Completion
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Appendix: Building 3D structures in Blender
Appendix: Building 3D structures in Blender
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A1. Section overview
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A1. Section overview
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A2. How can Blender help us?
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A2. How can Blender help us?
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A3. Downloading and installing Blender
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A3. Downloading and installing Blender
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A4. Blender overview and interface basics
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A4. Blender overview and interface basics
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A5. Object versus Edit mode
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A5. Object versus Edit mode
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A6. Basic modelling - rectilinear structures
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A6. Basic modelling - rectilinear structures
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A7. Basic modelling - organic/curved structures
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A7. Basic modelling - organic/curved structures
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Course Updates
Course Updates
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70. Self-weight part 1 - bar elements
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70. Self-weight part 1 - bar elements
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71. Self-weight part 2 - beam elements
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71. Self-weight part 2 - beam elements
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71.1 Jupyter Notebook - (lectures 70-71)
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71.1 Jupyter Notebook - (lectures 70-71)
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72. Member rotations part 1 - Identifying members to rotate
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72. Member rotations part 1 - Identifying members to rotate
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72.1 Blender File
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72.1 Blender File
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73. Member rotations part 2 - Implementing rotation overrides
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73. Member rotations part 2 - Implementing rotation overrides
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73.1 Jupyter Notebook - (lectures 72-73)
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73.1 Jupyter Notebook - (lectures 72-73)