Finite element simulation

The aim of this course is to introduce students to the finite element method applied to one-, two-, and three-dimensional problems in engineering and applied science. This introduction is given in the context of linear elasticity and small perturbations in statics. Starting with prerequisites in mathematics and solid mechanics, the principle of discretization is first addressed through the Ritz and Gallerkine approaches for one-dimensional media. Next, the issue of numerical integration is approached using the Gauss method. Meshing and validation of calculation models are then addressed during the study of surface modeling with 2D elements. Finally, these concepts will be used to implement the complete formalism of the finite element method in the context of bar and beam elements, then triangle-type elements. A practical application of these important theoretical concepts is carried out on an industrial calculation code (ANSYS) during practical work and a project.

• Help students understand the "mechanics" of finite elements.
• Enable students to understand the finite element method applied to linear problems.
• Train students to use several types of finite element software.
• Be able to model and calculate simple structures using finite elements and critically analyze the results obtained.

- Course on continuum mechanics.

- Linear algebra.