Syllabus academic year 2007/2008
 FINITE ELEMENT METHOD FOR NON-LINEAR SYSTEMS FHL066

Higher education credits: 7,5. Grading scale: TH. Level: A (Second level). Language of instruction: The course might be given in English. Optional for: F4, F4tvb, M4, M4fo, M4mo. Course coordinator: Professor Matti Ristinmaa, Matti.Ristinmaa@solid.lth.se, Hållfasthetslära. Prerequisites: FHL064 Finite Element Method, Advanced Course or ETE110 Modelling and Simulation in Field Theory or similar course. Assessment: The course consists of a serie of seminaries. In parallel computer laborations are given the numerical implementation. Examination is based on the two project assignments, which consider both theoretical och numerical issues. The projects are graded and the final grade is based on the summed grade. Home page: http://www.solid.lth.se.

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 using 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

• 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, Div. of Structural Mechanics and Div. of Solid Mechanics, Lund Institute of Technology.
Notes, Div. of Solid Mechanics.