Chapter 1
Introduction and Principles
Basic concept and steps of FEM
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Calculus of variations and Rayleigh-Ritz method
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Weak formulation and Galerkin's weighted residual method
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Element shapes, nodes, and degrees of freedom
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Convergence requirements for displacement fields
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Chapter 2
1D and 2D Elements
Bar and beam elements formulation
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Constant Strain Triangle (CST) and Linear Strain Triangle (LST)
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Rectangular elements and bilinear interpolation
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Shape functions using natural coordinates
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Assembly of global matrices and boundary conditions
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Chapter 3
Isoparametric Elements
Concept of isoparametric, subparametric, and superparametric elements
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Quadrilateral elements and numerical integration
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Gauss quadrature rules
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Jacobian matrix and coordinate transformation
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Evaluation of element stiffness and force vectors
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Chapter 4
Plates, Shells, and 3D Elements
Chapter 5
Advanced FEM Applications
Dynamic analysis using FEM (Mass matrices)
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Buckling analysis and geometric stiffness matrix
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Heat transfer and steady-state thermal analysis
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Nonlinear FEA basics (material and geometric)
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Error estimation and adaptive mesh refinement
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