Stochastic Finite Element Method
Uncertainties with regard to loading conditions and material properties are usually treated in a post-processing manner by safety factors. To overcome the limitations of that approach novel computational techniques for the treatment of stochastic differential have been developed.
During our stochastic finite element method module, you will be trained to go beyond deterministic mechanical predictions.
Computational aspects for stochastic analysis of structures
The following issues will be discussed:
- Motivation for stochastic computational techniques e.g. for non-linear system response
- Statistical basics and stochastic methods for the treatment of random variables, random fields and random processes
- Computational sampling techniques, e.g. Monte-Carlo methods, stochastic collocation techniques, computational aspects (e.g. parallelization, intrusive vs. non-intrusive etc
- Inverse problems, identification of parameters, experimental uncertainty analysis
- Discretization techniques for random fields and random processes
- Spectral Stochastic Finite Element Method – Theory, Implementation and Investigation
- Alternative concepts on modelling stochastic processes, e.g. Fokker-Planck-representation, computational aspects
- Model order reduction for mechanical problems with uncertainties
- Postprocessing, Quantity of Interest: Preparation and interpretation of computed results
Scheme of stochastic computation based on sampling approach
Material & Methods
Algorithms are developed and experienced based on an existing open finite element system written in Matlab language.
Students are guided by practical exercises in the computer lab.
Example of previous student project: stochastic Galerkin method
Sparse structure of the element stochastic stiffness matrix
Evaluation is based on final project reported by:
- a final report in an article template,
- an oral presentation as a seminar for all other participants.
The project topic is established in accordance with own student interests.
R.G. Ghanem and P.D. Spanos, Stochastic Finite Elements: A Spectral Approach, Springer-Verlag, 1991.
O.P. Le Maitre, O.M. Knio, Spectral Methods for Uncertainty Quantification, Springer, 2010.