(Created 2010-07-25.)

FINITE ELEMENT METHOD FOR NON-LINEAR SYSTEMS | FHL066 |

**Aim**

The aim of the course is to provide an understanding about modelling and simulation of non-linear structural and material problems using the finite element method.

*Knowledge and understanding*

For a passing grade the student must

- understand the basic assumptions when establishing the finite element formulation for a structural non-linear problem
- understand the basic assumptions in large deformations and large strains
- utilize the finite element method in structural non-linear problems

*Skills and abilities*

For a passing grade the student must

- be able to establish a non-linear finite element formulation
- write a non-linear finite element program
- establish the weak form of different non-linear problems

*Judgement and approach*

For a passing grade the student must

- have the capacity to analyze, model and simulate structural non-linear problems using the finite element method

**Contents**

The course treats the finite element method where both geometrical and material nonlinearities are present. The fundamental equations for large deformations and strains and the various strain measures and stress measures are introduced. The corresponding strong and weak forms of the equilibrium equations are discussed, both in their spatial and material format. The nonlinear finite element formulation is derived from the general three-dimensional case. Emphasis is given to the fundamental principles in the FE-formulation. During the course, the participants are going to establish their own nonlinear FE-program.

**Literature**

Choice of:

Bonnet, J. and Wood, R.D., Nonlinear constinuum mechanics for finite element analysis, Cambridge Univ. Press.

Bathe, K-J, Finite element procedures, Prentice Hall.

Krenk, S., Non-Linear Modelling and Analysis.

CALFEM - A finite element toolbok to MATLAB, Studentlitteratur.

Notes, Div. of Solid Mechanics.

Wriggers, P., Nonlinear Finite Element Methods.