Course description
In this course we introduce the basic mathematical concepts of the finite element method, with the aim of modeling engineering systems in different field of application (civil engineering, biomechanics, structural design, aerospace engineering,…). The finite element method consists in a mathematical approximation of the field of stresses and strains of a system subjected to various solicitations, when classical material resistance modeling becomes irrelevant or when analytical solutions of the continuum mechanics are unavailable. In addition, in this course a general overview of finite element method implementation in classical software is presented. The final part of the course is a simulation workshop with Finite Element software, in which students will design and conduct several numerical experiments oriented to solve different current research or industrial issues. Students will learn how to perform a detailed finite element analysis including modeling, meshing, resolution, evaluation of results and validation by writing a report and presenting the results. The course is ideal for people interested in understanding the general concept of Finite Element in static cases.
Learning Outcomes
Upon completion of the course, the student is expected to be able to:
- Understand the concepts behind formulation methods in Finite Element Method.
- Develop element characteristic equation and generation of global equation in the case of bars and beams.
- Introduce the general procedures that are necessary to carry out an analysis.
- Present basic information that is necessary for the safe use of Finite Element Method.
Program
- Introduction and generalities
- Numerical approximation of balance equations (variational analysis)
- The Galerkin Method trough 1D example.
- FEM in one dimension: bars element
- FEM in one dimension: beams element
- FEM in two/three dimension: generality
- Project