finite elements , ABAQUS, discretization, stiffness matrices, flexibility matrices

Pedagogic informations

Training objectives

The aim of this course is to learn to solve a solid mechanical problem (or structures) deformable by the finite element method.

Learning objectives

This course focuses on methods of numerical approximation in general and on the finite element method in particular, applied mainly to solid mechanics problems (or structures), linear elastic-static at first.
It focuses on key steps in building a finite element model, namely the concepts of geometric discretization, interpolation finite element and assembly, as well as associated mathematical tools (geometric transformation, numerical integration) for the approximate solution of a problem in geometry and loading complex, from the Principle of Virtual Works.

Learning context

Course materials

Handouts of tutorials and practical work on software .
ABAQUS software

Prerequisites

- Elasticity (Continuum Mechanics)
- Vibration
- Strength of Materials

Course content

Chapter 1: Approximation methods
Method of weighted residues.
Approximation concepts.
Principle of Virtual Works.

Chapter 2: Finite Element Method
Discretization. Interpolation. Reference Chart.
Elementary matrices and vectors. Assembly. Resolution.
Geometric transformation. Numerical integration.

Chapter 3: Examples of finite elements
Finite Element bar. Precast beam.
Finite Element 2D plane elasticity.

Chapter 4: Numerical modeling
Introduction to commercial software ABAQUS.
Data layout. Calculation. Postprocessing.
Modeling choices.

As part of the supervised work, the construction of conventional finite elements (bar, beam, 2D ...) and the "manual" solving simple problems in linear elasticity, static or dynamic (lattice porticoes plates. ..) allow students to better appreciate the operation of a code of finite elements, whose use is the purpose of this teaching.

Personal work

Exams

Label (French)

Label (English)

Eléments finis 2A

Finite Element Method

Exam description

Written exam : analytical resolution, using the finite element methodology, a simple problem of elastostatic.
- Written report and oral presentation of a case study involving the use of a computer code (ABAQUS).