ETH Zurich - D-BAUG - IBK (Faber) - Seminar on the Finite Element Method and the Analysis of Systems with Uncertain Properties

Bathe, K.J., Finite Element Procedures, Prentice Hall, 1996.
Halder, A. and Mahadevan, S. Reliability Assessment Using Stochastic Finite Element Analysis, Wiley, 2000.

Mode

The seminar will be conducted as a study group under the responsibility of Prof. Faber and Dr. Mojsilović. All participants will in turn be responsible for presenting a part of the material and for developing the examples.

Software

The aim is to use Matlab for the exercises developed during the seminar.

Agenda

Date	Topic	Presentations	Exercises
01.11.06	Introduction and description of course material; Introduction to the use of finite elements - Physical problem, mathematical modelling and finite element solutions - Finite elements as a tool for computer supported design and assessment - Basic mathematical tools (vectors, tensors and matrix calculus)	Presentation Lecture 1
01.11.06	Basic concepts of engineering analysis - Solution of mathematical models of discrete and continuous systems	Presentation Lecture 2
08.11.06	Formulation of the method of finite elements - Formulation of the displacement based finite element method and (general) convergence of results	Presentation Lecture 3
15.11.06	Formulation and calculation of isoparametric finite element matrixes - Truss element - Continuum elements – triangular elements	Presentation Lecture 4
22.11.06	Formulation and calculation of isoparametric finite element matrixes - Continuum elements – square elements - (Detailed) Convergence considerations	Presentation Lecture 5	Exercise 1 Exercise 1-Identity Strong Form and Weak Form
29.11.06	Formulation and calculation of isoparametric finite element matrixes - Element matrixes in global coordinates - Displacement /pressure related elements for incompressible media	Presentation Lecture 6
06.12.06	Formulation and calculation of isoparametric finite element matrixes - Formulation of structural elements (beam elements and axial-symmetrical shell elements)	Presentation Lecture 7
13.12.06	Formulation and calculation of isoparametric finite element matrixes - Formulation of structural elements (plate and general shell elements)	Presentation Lecture 8	Exercise 2 Exercise 2 Figures Beam_2D_Matlab Beam_2D_Shear_Lock_Matlab Zip file Exercise 2
20.12.06	Formulation and calculation of isoparametric finite element matrixes - Numerical integration and implementation of a finite element computer code	Presentation Lecture 9
10.01.07	Solution of static finite element problems - The LDL- solution	Presentation Lecture 10	Exercise 10 Exercise 10 Matlab Code
17.01.07	Introduction to reliability analysis	Structural reliability analysis Presentation Lecture 11
24.01.07	Implicit performance functions and introduction to stochastic FEM (SFEM)	Presentation 12
31.01.07	SFEM for linear static problems	Presentation 13
07.02.07	SFEM for spatial variability problems	Presentation 14	Example 3 Example 3 Matlab Example 3 FEM Matlab

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