Descriptif

COURSE PHILOSOPHY:

This is an introduction to the finite element method (F.E.M.) applied to structural and continuum mechanics problems. The course is intended for M1-level students and is self-contained. Emphasis is placed on learning the fundamentals of the finite element method. As part of the course requirements, students are expected a) to write their own code to solve simple mechanics problems and b) use some software packages (FELT, CASTEM etc.) to solve more complicated problems.

TOPICS COVERED:

1. INTRODUCTION TO THE FINITE ELEMENT METHOD USING 1-D MODELS.
2. CHOLESKY METHOD FOR SOLVING LINEAR SYSTEMS.
3. TRUSSES AND FRAMES IN 2D AND 3D.
4. VARIATIONAL FORMULATION FOR LINEAR ELASTICITY B.V.P.
5. PLANE STRESS/STRAIN PROBLEMS USING CONSTANT STRAIN TRIANGLES.
6. ISOPARAMETRIC ELEMENTS FOR 2D PROBLEMS.
7. NUMERICAL INTEGRATION, GENERALIZATION TO 3D PROBLEMS.
8. HIGHER ORDER GRADIENT ENERGIES: BEAMS (1D) AND PLATES (2D).
9. LOCKING PHENOMENA AND SOLUTION PROCEDURES.
10. TIME-DEPENDENT ANALYSES, EIGENMODES
11.  OTHER PHYSICS PROBLEMS (ELECTROSTATICS, HEAT TRANSFER) - time permitting.
12. EXTENSION TO NON-LINEAR PROBLEMS (INCREMENTAL NEWTON-RAPHSON)- time permitting.

Prerequisites (Niveau requis) : Continuum Mechanics (MEC 431)

Grading Policy (Modalités d'évaluation) : 50% homework & attendance (strictly expected!), 50% final exam

Langue du cours : Anglais

Credits ECTS : 4

updated on September 14, 2016