MFG 513 Advanced Topics in Finite Element Analysis Select Term:
Advanced Finite Element Analysis aims at teaching advanced level finite element concepts in a mechanics perspective to graduate level students. The course starts with a complete review of fundamental finite element concepts like discretization of equilibrium equation, interpolation functions, line-surface-volume integrals, Gauss-Quadrature, isoparametric elements, application of essential and natural boundary conditions. Later, finite element elastic analysis concepts and principals for plate & shell elements would be introduced. In the course modeling of the orthotropic (anisotropic) elastic behavior of composites and how to incorporate this material behavior to the finite element models will be shown with worked examples. Next topic is the material and geometric non- linearities and the numerical solution methods of non-linear finite element analysis will be studied. Finally, meshless interpolation concepts such as moving least squares and element free Galerkin methods will be introduced. Matlab will be used as the coding environment during the course. Students will be asked to implement finite element codes in order to get a better understanding of finite element working principles of a commercial finite element software. In the course project, the students would prepare their own finite element analysis code for a given plate\shell type element type in MATLAB environment. In addition working principals and development of user-defined subroutines will be illustrated using “UMAT” of ABAQUS as a commercial finite element software.