This lesson focuses on the finite element modeling of mechanical problems of solid or structures in a non-linear context.
There is a deepening of teaching on the finite element method under the elastic-static or linear elastic-dynamic and consists mainly of practical work on computer code. Beforehand, during some concepts are presented, they concern general information on the methods of calculating incremental necessary for the resolution of non-linear mechanical problems.
Stability problems are also presented.
Much space is left to use the software.

Learning objectives

Learning context

Course materials

training exercises
ABAQUS software

Prerequisites

- Finite elements (linear mechanics)
- Numerical analysis
- Plasticity

Course content

Part 1: Numerical methods in non-linear mechanics
Incremental resolution principles.
Newton-Raphson.
Application to large displacements (geometric nonlinearities).

Part 2: Non-linearities material
Nonlinear Elasticity.
Plasticity. Isotropic and kinematic work hardening. Cyclic plasticity (adaptation, accommodation).

Part 3: linearization of a problem in large transformations
Tangent stiffness matrix. Geometric stiffness matrix.
Linearized behavior (static or vibration) a pre-stressed structure.
Application to the ropes and stretched membranes.

Part 4: Buckling
Linearized buckling. Eigenvalue problem. Loading and critical bifurcation mode.
Incremental resolution of a mechanical problem in the presence of instabilities (geometric).
Methods of arc length. Imperfections / branch-switching.
Application to breakdown and post-buckling.

Personal work

Exams

Label (French)

Label (English)

Eléments finis 3A

Finite Element Method

Exam description

Project : Solving, using ABAQUS software, a nonlinear problem (linearization calculation or incremental), static or dynamic.