Single-Course English 10 ECTS

Finite Element Methods

Overall Course Objectives

Computational modelling of the mechanical response of engineering parts, structures and devices is a basic engineering discipline with ever-growing applications, also within Industry 4.0, Digital Twins, biomechanics, life sciences and Additive Manufacturing (AM). The Finite Element Method (FEM) constitutes the all-dominating computational approach to modelling of solids and also covers applications and couplings to multiple other physical domains like fluids, acoustics, thermodynamics and electromagnetism. The goal of the course is to teach the students basic and advanced FEM through theory development, extensive programming of own FE codes and applications within linear and non-linear elasticity. The final part of the course constitutes a larger programming project, where students can choose between subjects including, but not limited to: transient analysis, coupled thermomechanical problems, fluid-structure interaction, plates, plasticity or acoustic-structure interaction, some of them possibly combined with structural design through topology optimization.

Use the principle of virtual work to set up finite element equations
Program Finite Element Methods for truss and continuum problems
Apply Finite Element Methods to the solution of static and dynamic mechanical problems
Solve material and geometrically non-linear problems by use of explicit and implicit solution methods
Optimize simple mechanical structures based on Finite Element calculations
Program iso-parametric Finite Elements based on numerical integration
Verify correctness of calculations based on test problems and comparisons with analytical solutions
Evaluate the quality of a Finite Element model when the exact solution is unknown
Evaluate the quality of Finite Element calculations based on convergence analyses
Present results of Finite Element analyses in a transparent, easily accessible and efficient form
Set up continuous and discrete forms of the principle of virtual work for arbitrary partial differential equations
Plan a larger Finite Element programming project and in an independent way suggest and implement test examples.

The course “Finite Element Methods” focuses on theoretical lectures combined with computer exercises in Matlab and Fortran in groups of two. Subjects covered include: the principle of virtual work; truss elements; isoparametric elements and numerical integration; solution of large systems of equations, explicit and implicit non-linear incremental solution methods; geometric and material non-linearities and topology optimization. As a part of the course, the students will build their own finite element code and apply it to model simple geometries. Commercial finite element codes will only be used for pre-processing. Choice of final project (see suggestions above) may depend on prerequisites.

Basic understanding of stresses and strains in two and three dimensions and programming experience f.ex. 41502 and 02631.
Other courses in solid mechanics, e.g. 41560 and 41516.

Lectures and computer exercises