Finite element simulation

The aim of this course is to introduce students to the finite element method as applied to one-, two- and three-dimensional problems in engineering and applied science. This presentation is made within the framework 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 approaches of Ritz and Gallerkine for one-dimensional media. Next, the problem of numerical integration is approached using the Gauss method. Meshing and validation of computational models is then addressed in the study of surface modeling with 2D elements. Finally, these notions will be used to set up the complete formalism of the finite element method within the framework of bar and beam elements, then triangle-type elements. A practical application of these important theoretical notions is carried out on an industrial calculation code (ANSYS) during practical work and a project.

• Give students an understanding of the 'mechanics' of finite elements.
• Enable the student 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.

- Continuum mechanics course.

- Linear algebra.