Finite Element Analysis

Catalog description

The objective of this course is to equip students with the necessary background needed to carry out finite elements-based simulations of various engineering and science problems using finite elements packages. The first part of the course will outline the theory of finite element methods. The objective is to acquaint the students with the theory rather than to equip them with the programming skills needed to write multi-dimensional finite elements codes. The second part of the course will address the solution of the classical equations of mathematical physics such as the Laplace, Poisson, Helmholtz, wave, and heat equations. The general properties of the solutions will be described, and potential pitfalls will be addressed. This part of the course will also address issues such as code verification and convergence. The students will gain hands-on experience working with COMSOL Multiphysics (finite element analysis, solver and simulation software / FEA software package for various physics and engineering applications). This part of the course will also address relevant topics of numerical analysis such as the solution of initial value problems and their precision, the solution of algebraic equations, and the calculation of eigenvalues and eigenvectors. The third part of the course will consist of case studies taken from various areas of engineering and sciences. Presentation of each case study will start with a description of the pertinent physical and engineering background and how finite elements are being used to solve the problem. The case studies will also address the verification issue (how do we know that the solution is right) and the analysis and post-processing of the computed data. Prerequisites: Calculus, introductory level fluid & solid mechanics and heat transfer