http://www.igsse.tum.de/news/news-detail/article/block-course-advanced-stochastic-finite-element-methods/calendar/2016/6.html

IGSSE Alumnus Dr. Iason Papaioannou of the Engineering Risk Analysis Group offers a block course with interdisciplinary setting in the area of computational mechanics.

Finite element (FE) applications necessitate the consideration of the uncertain nature of input parameters, such as material properties, load and geometry. These uncertainties may be represented by a set of stochastic variables defined using probability distributions and spatial correlations, such that random realizations describing a possible parameter state may be produced. The FE solution may no longer be deterministic, since the stochastic variables are involved in the FE solution process. Instead, stochastic FE methods may be employed for the determination of a probability structure which relates possible solution states with corresponding probabilities of occurrence. This course introduces state-of-the-art methods for stochastic FE analysis with application to elastostatic problems with uncertain input parameters. The course is of interest for students in any discipline in applied science and engineering.

At the end of the course, participants will be able to:

• Apply efficient Monte Carlo methods for solving FE systems with uncertain input
• Apply spectral stochastic FE methods with various algorithmic settings
• Assess the sensitivity of stochastic FE systems to input random variables
• Apply stochastic FE methods to estimate the reliability of engineering systems

The course will consist of lectures (50%) and tutorials (50%). The tutorials will be carried out using Matlab. Therefore, the students are requested to bring their laptops with either Matlab or Octave installed (Octave is freeware). The exam will be a take-home project.

Participants have to register via TUMonline.

Participants should have knowledge of probability theory including random variables and random fields. Also, the course assumes basic knowledge of the linear elastic finite element method. Basic knowledge of Matlab is an advantage. Literature

A script will be distributed in electronic form. For further reading, the following are recommended:

• Xiu, D. Numerical methods for stochastic computations: A spectral method approach. Princeton; Princeton University Press; 2010
• Ghanem, RG, Spanos, PD. Stochastic finite elements: A spectral approach. New York: Springer; 1991 (reissued by Dover Publications; 2004)
• Sudret, B, Der Kiureghian, A. Stochastic finite elements and reliability: A state-of-the-art report. University of California, Berkeley, Technical Report no UCB/SEMM-2000/08; 2000