Courses Detail Information
ME6104JH – Finite Element Methods
Instructors:
Credits: 3 credits
Pre-requisites: Vm211 and Vm311
Description:
This course is for graduate students to get all necessary knowledge in order to write from scratch, or adapt, finite element programs for specific needs. Fields of applications
are mainly mechanics problems, although problems in other fields such as heat transfer will be discussed. Note: How to use or program with a commercial finite element soft-
ware will not be discussed, which is the topic of another course, Vm405
Course Topics:
Basic information. The finite element method in 1D (strong form and weak
form). Equivalence of strong and weak forms.Galerkin approximation. Finite element shape functions. Three-element exam
ple. Sparsity. Element point of view. The case of inhomogeneous Dirichlet boundary conditions. Gauss integration.Lagrange polynomials. Lagrange and non-Lagrange families of elements.Element arrays. Algorithm for computing element stiffness matrix.Heat conduction problem: Weak form.
Linear elasticity: Principles of stationary potential energy and of virtualwork, Euler-Bernoulli beam formulation.Hermite cubic polynomials. Linear elasticity: Implementation aspects.Best approximation property and error estimates.Weak form for the time-dependent heat equation. Semi-discretization. Generalized trapezoidal rule. Stability of a single degree of freedom problem. Local truncation error. Stability + Consistency = Convergence.Formulation and the Newmark family of methods for hyperbolic problems. Strong
form and weak form. Semi-discretization. Stability and consistency of theNewmark family of methods. Modal reduction.Introduction to nonlinear problems. Newton-Raphson method. Snap-through.Implementation of nonlinear problems.Introduction to iterative solvers to sparse systems. Preconditioners. Par
allelization by domain decomposition.Formulation for finite strain problems.Total Lagrangian and updated Lagrangian formulations.Implementation of finite strain finite elements.