Limit and shakedown analysis with uncertain data. (English) Zbl 1001.90024

Marti, Kurt (ed.), Stochastic optimization techniques. Numerical methods and technical applications. Selected papers of the 4th GAMM/IFIP workshop, Federal Armed Forces Univ. Munich, Neubiberg/ Munich, June 27-29, 2000. Berlin: Springer. Lect. Notes Econ. Math. Syst. 513, 253-267 (2002).
Summary: The structural reliability with respect to plastic collapse or to inadaptation is formulated on the basis of the lower bound limit and shakedown theorems. A direct definition of the limit state function is achieved. The suggested approach which combines the FE method with first order reliability methods leads to a better understanding of the influences on the structural behaviour. The theorems are implemented into a general purpose FEM program in a way capable of large-scale analysis. The limit state function and its gradient are obtained from a mathematical optimization problem. This direct approach reduces considerably the necessary knowledge of uncertain technological input data, the computing time, and the numerical error, leading to highly effective and precise reliability analyses.
For the entire collection see [Zbl 0977.00044].


90B25 Reliability, availability, maintenance, inspection in operations research
90C15 Stochastic programming