Stochastic optimization for mechanical structures

The Stochastic Optimization Problem is well known in mathematics and operations research. Due to increasing demands for performance improvement together with reduced weight and costs the introduction of uncertainties into optimization problems in mechanical engineering is also necessary. In a number of papers this Stochastic Structural Optimization Problem is formulated and solved only within certain limiting assumptions. This paper presents a general definition of the Stochastic Structural Optimization Problem. Furthermore one solution technique based on reliability calculation is presented. With this technique the use of an augmented optimization loop based on Mathematical Programming is possible. The use of the developed tool for reliability calculations and optimization is demonstrated for complex mechanical structures.