Finite Element Method (FEM)

  1. Application in Structural and Solid Mechanics
    1. Fundamental Concepts in Solid Mechanics
      1. Stress and Strain Tensors
        1. Constitutive Relations
          1. Equilibrium Equations
            1. Compatibility Conditions
            2. Truss Elements
              1. 2D Truss Elements
                1. Element Formulation
                  1. Coordinate Transformations
                    1. Assembly Process
                    2. 3D Truss Elements
                      1. Space Truss Formulation
                        1. Direction Cosines
                        2. Truss Structure Analysis
                          1. Static Analysis
                            1. Stability Considerations
                          2. Beam and Frame Elements
                            1. Euler-Bernoulli Beam Theory
                              1. Basic Assumptions
                                1. Governing Equations
                                  1. Shape Functions for Beams
                                    1. Stiffness Matrix Derivation
                                    2. Timoshenko Beam Theory
                                      1. Shear Deformation Effects
                                        1. Rotary Inertia
                                          1. Comparison with Euler-Bernoulli
                                          2. Frame Element Formulation
                                            1. Combined Axial and Bending
                                              1. 2D Frame Elements
                                                1. 3D Frame Elements
                                                2. Beam-Column Elements
                                                3. Plane Problems
                                                  1. Plane Stress Problems
                                                    1. Assumptions and Applications
                                                      1. Stress-Strain Relations
                                                        1. Element Formulation
                                                        2. Plane Strain Problems
                                                          1. Assumptions and Applications
                                                            1. Stress-Strain Relations
                                                              1. Element Formulation
                                                              2. Generalized Plane Strain
                                                              3. Axisymmetric Problems
                                                                1. Axisymmetric Geometry and Loading
                                                                  1. Cylindrical Coordinate System
                                                                    1. Axisymmetric Element Types
                                                                      1. Stress-Strain Relations
                                                                        1. Element Formulation
                                                                        2. Plate and Shell Elements
                                                                          1. Plate Theory Fundamentals
                                                                            1. Kirchhoff Plate Theory
                                                                              1. Thin Plate Assumptions
                                                                                1. Governing Equations
                                                                                  1. Element Formulation Challenges
                                                                                  2. Mindlin-Reissner Plate Theory
                                                                                    1. Thick Plate Effects
                                                                                      1. Shear Deformation
                                                                                        1. Element Formulation
                                                                                      2. Shell Theory Fundamentals
                                                                                        1. Shell Geometry
                                                                                          1. Membrane and Bending Actions
                                                                                            1. Shell Element Types
                                                                                            2. Implementation Considerations
                                                                                              1. C1 Continuity Requirements
                                                                                                1. Discrete Kirchhoff Elements
                                                                                                  1. Assumed Strain Formulations

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                                                                                              4. Analysis of 2D and 3D Problems

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                                                                                              6. Application in Heat Transfer and Other Field Problems