Finite Element Method: Theory and Applications in Mechanics and Multiphysics

Catalog description

This class is an intermediate-level course on the linear Finite Element Method (FEM) for graduate engineering students. The students will learn to: set up the strong formulation of mechanical, hydraulic, thermal, and coupled problems, write the variational formulation, discretize the weak form in space and time, choose a resolution algorithm, write an input file for a FEM software, and interpret numerical results. Applications will focus on climate change and energy. First, one-dimensional problems will be solved for one dependent variable, e.g., elongation, fluid flow, heat transfer. Second, hydro-mechanical equations for two-phase porous media will be introduced and applied to consolidation problems. Next, 2D space discretization and numerical integration will be explained and applied through simulation and analysis of problems of plane elasticity and seepage. The course will conclude with the modeling unsaturated porous media with applications to geological storage, evapo-transpiration, and subsidence.