Advanced Finite Element Method
This graduate-level course provides an in-depth treatment of advanced finite element formulations for solid mechanics and engineering applications. The course emphasizes theoretical foundations, numerical implementation, and modern research-oriented developments in computational mechanics.
Course Topics
- Variational Formulations and Weak Forms of Boundary Value Problems
- Weighted Residual Methods and Galerkin Approximation
- Isoparametric Formulation and Higher-Order Elements
- Nonlinear Finite Element Analysis (Material and Geometric Nonlinearity)
- Newton–Raphson and Incremental-Iterative Methods
- Finite Element Implementation and Numerical Integration
- Error Estimation and Adaptive Mesh Refinement
- Mixed and Hybrid Finite Element Formulations
- Stabilized Methods and Locking Phenomena
- Introduction to Extended Finite Element Method (XFEM)
- Multiscale and Advanced Computational Techniques
Learning Objectives
- Develop and derive advanced finite element formulations from first principles.
- Implement nonlinear and advanced FEM algorithms.
- Understand convergence, stability, and numerical consistency.
- Analyze complex engineering systems using research-level FEM tools.
Software and Implementation
Students develop finite element codes in MATLAB and/or Python. Emphasis is placed on algorithmic clarity, modular implementation, and extension toward research-level applications.
