Introduction to Finite Element Analysis
As the name says, Computational Mechanics 1 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