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ME300H Introduction to Finite Element Methods

ME300H Introduction to Finite Element Methods. Finite Element Analysis of Plane Elasticity. Review of Linear Elasticity. Linear Elasticity: A theory to predict mechanical response of an elastic body under a general loading condition. Stress: measurement of force intensity. with. 2-D.

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ME300H Introduction to Finite Element Methods

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  1. ME300H Introduction to Finite Element Methods Finite Element Analysis of Plane Elasticity

  2. Review of Linear Elasticity Linear Elasticity: A theory to predict mechanical response of an elastic body under a general loading condition. Stress: measurement of force intensity with 2-D

  3. Review of Linear Elasticity Traction (surface force) : Equilibrium – Newton’s Law

  4. Review of Linear Elasticity Strain: measurement of intensity of deformation Generalized Hooke’s Law

  5. Plane Stress and Plane Strain Plane Stress - Thin Plate:

  6. Plane Stress and Plane Strain Plane Strain - Thick Plate: Plane Strain: Plane Stress: Replace E by and by

  7. Equations of Plane Elasticity Governing Equations (Static Equilibrium) Strain-Deformation (Small Deformation) Constitutive Relation (Linear Elasticity)

  8. Specification of Boundary Conditions EBC: Specify u(x,y) and/or v(x,y) on G NBC: Specify tx and/or ty on G where is the traction on the boundary G at the segment ds.

  9. Weak Formulation for Plane Elasticity are components of traction on the boundary G where

  10. Finite Element Formulation for Plane Elasticity Let where and

  11. Constant-Strain Triangular (CST) Element for Plane Stress Analysis Let

  12. Constant-Strain Triangular (CST) Element for Plane Stress Analysis

  13. 4-Node Rectangular Element for Plane Stress Analysis Let

  14. 4-Node Rectangular Element for Plane Stress Analysis For Plane Strain Analysis: and

  15. Loading Conditions for Plane Stress Analysis

  16. Evaluation of Applied Nodal Forces

  17. Evaluation of Applied Nodal Forces

  18. Element Assembly for Plane Elasticity 5 6 B 3 4 4 3 A 1 2

  19. Element Assembly for Plane Elasticity 5 6 B 4 3 A 2 1

  20. Comparison of Applied Nodal Forces

  21. Discussion on Boundary Conditions • Must have sufficient EBCs to suppress rigid body • translation and rotation • For higher order elements, the mid side nodes cannot be • skipped while applying EBCs/NBCs

  22. Plane Stress – Example 2

  23. Plane Stress – Example 3

  24. Evaluation of Strains

  25. Evaluation of Stresses Plane Strain Analysis Plane Stress Analysis

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