The first part of the course is joint with MEC552A. It will deal with basic computational methods to solve:
- Ordinary differential equations (numerical integration schemes);
- Nonlinear equations and minimization problems (Newton-Raphson method);
- Systems of algebraic equations (direct & iterative methods).
The second part will focus on the finite element method, which is a very general approximation method for boundary value problems and partial differential equations. It was originated and is widely used in mechanics, but is also present in many fields of science and engineering. We will introduce and analyze the main theoretical ingredients of the method:
- Variational formulation;
- Discretization (convergence results);
As well as the practical ingredients of any efficient implementation of the method:
- Meshes/Triangulation;
- Shape functions and degrees of freedom;
- Numerical integration;
- Assembly;
- Post-processing.
Every aspect will be illustrated on actual mechanical problems of beams (1D), plates (2D) and solid (3D) structures. We will study static as well as dynamic problems, linear and nonlinear problems. Course sessions followed by implementation in Python in Jupyter notebooks. As time goes by, we use open source computational libraries to perform efficiently the calculation bricks studied previously; at the end, students can use the most efficient calculation tools while mastering all the stages of the calculation.
- Teaching coordinator: Genet Martin