Introduction to Finite Element Analysis
As the name says, this course offers an Introduction to Finite Element Analysis (FEA) for undergraduate students and interested graduate students. It is designed as an entry-level course that discuss the fundamental theory behind the finite element method as well as the implementation and usage of finite element code. Rather than discussing a particular software, we write our own finite element code in MATLAB, which we grow throughout the course into a simple stand-alone finite element toolbox capable of handling 1D, 2D and 3D simulations in small-strain linear elasticity, applicable to both quasistatic problems and dynamic scenarios (covering vibrations as well as time integration).
Course Contents
The following gives a brief overview of topics that are covered:
- Introduction, review of continuum mechanics
- Dimensionless forms, direct and indirect numerical methods
- Finite differences, finite difference stability analysis (CFL/von Neumann/phase error analysis)
- Variational principles (calculus of variations, energy methods, Rayleigh-Ritz)
- Strong form vs. weak form
- Finite element method (FE terminology, interpolation spaces, completeness)
- Structural elements: bar and beam elements
- Solid elements: isoparametric mapping, various 2D and 3D element types, simplicial elements
- Numerical quadrature (focus on Gauss-Legendre quadrature)
- Finite element technology: assembly, iterative solvers, boundary conditions
- Dynamics: vibrations, eigenfrequencies/-modes, modal anlaysis, expicit and impicit time integration
- Thermal problems (linear heat conduction problem)
- Error analysis, mesh adaptivity, common FEA mistakes