Reliability-based topology optimization using the response surface method for stress-constrained problems considering load uncertainty

The objective of this work is to build a useful-response-surface-based reliability design approach for solving stress-constrained optimization problems taking into consideration load uncertainty. To this end, a reliability optimization problem of minimizing the volume fraction while satisfying a global probabilistic stress constraint is formulated, in which a Kreisselmeier-Steinhauser-function-based aggregate approach with a correction parameter is introduced to ensure accurate approximation of the maximum stress. To avoid the expensive computational cost of calculating the sensitivity of the global maximum stress with respect to random loads in reliability evaluation, a response-surface-based global stress measure is established. Finally, several typical design instances are solved to prove the performance of the presented methodology. The importance of considering load uncertainty in stress-related topology optimization is also explained by comparing the results acquired by the presented reliability-based topology optimization methodology with deterministic designs.