1. ECIV 720 A Advanced Structural Mechanics and Analysis Solid Modeling

2. Summary of Procedure Discretize domain -point loads - start & end of distributed loads T Nodes should be placed at

3. Summary of Procedure 3 q6 v u q5 1 2 x h q4 q2 q3 q1 For Every Element Compute • Strain-Displacement Matrix B

4. Summary of Procedure • Element Stiffness Matrix • Node Equivalent Body Force Vector • Node Equivalent Traction Vector

5. Summary of Procedure Py1 Px1 1 PyN PxN N Collect ALL Point Loads in Nodal Load Vector

6. Summary of Procedure Form Stiffness Equations

7. Summary of Procedure Solve Apply Boundary Conditions For Every Element Compute Stress

8. Modeling Issues • Data Preparation • The three modes of typical FE software • Pre-Processing • Processing • Post-Processing • Solid Modeling • Meshing • Solution Convergence

9. Data Processing Beam Plane Stress For a given physical problem select an appropriate mathematical model e.g.

10. Set Up General Model Data

11. Set Up General Model Data

12. Finite Element Mesh May be Defined in Direct Way Solid Modeling approach • Nodes • Elements • Loads • BC • Geometry of Solid • Loads • BC Automatic Mesh Generation

13. Direct FEM Mesh Manually define nodes, elements, BC & loads

14. Direct FEM Mesh Typical Input Data (Text File or GUI) Actual depends on software

15. Direct FEM Mesh

16. Solid Modeling Point Line Surface Volume • Describe Geometry of FE Domain as a collection of Primitive Entities

17. Solid Modeling Point Do not confuse with FEM node Line Any two points define a line Points belong to line

18. Solid Modeling Surface Any closed loop of lines define surface Points belong to lines Points AND lines belong to surface 2 faces are defined

19. Solid Modeling Volume Any closed loop of faces defines volume Points belong to lines Points AND lines belong to surface Points AND lines AND Surfacesbelong to volume

20. Solid Modeling Primitive Entities can be used to form more complex solid geometries Boolean Operations

21. Solid Modeling Boolean Operations

22. Solid Modeling Each of the primitive or the derived entities (objects) is assigned a set of properties such as material, FEM type, etc. Typically, derived objects inherit properties of parents. At any point, such properties can be changed

23. Solid Modeling Loads and Boundary Conditions can now be applied on primitive objects regardless of the specific Finite Elements.

24. Automatic Meshing Solid Model Structured Mesh (Mapped) Free Mesh Triangulation Techniques Based on Geometric Transformations

25. Structured Mesh Map to Parent Transformation Through Shape Functions

26. Structured Mesh

27. Free Mesh Triangulation Technique Suitable for arbitrary geometries

28. Example Using ANSYS thickness=1” 10” 10” Plane Stress With Thickness E=29x106 5” 5”

29. Define Element Groups

30. Define Element Options

31. Define Thickness

32. Define Material

33. Define Key points

34. Defining Areas

35. Deleting Entities

36. Automatic Meshing - Coarse

37. Applying Boundary Conditions

38. Applying Loads

39. Applying Loads Positive Value Towards line

40. Processing…

41. Deformed Shape

42. Vertical Displacement

43. sx

44. sy

45. Medium Mesh

46. Vertical Displacement Uy = 0.002042 in Compare to Uy = 0.001905 in

47. sx & sy

48. Refine Mesh

49. Refined Mesh

50. Displacement Uy