Surrogate model-based method for reliability-oriented buckling topology optimization under random field load uncertainty

Structures that are subjected to compressive loads may experience not only local fractures but also buckling deformations due to instability. Furthermore, the performance of the structure can also be influenced by uncertain factors. This paper develops a surrogate model-based method for reliability-oriented buckling topology optimization under random field load uncertainty. To reduce the number of reliability constraints, the compliance and buckling responses are synthesized into a hybrid response using the P-norm to construct the limit state function. The compressed load random field is characterized by Karhunen–Loéve expansion. To avoid the complexity of sensitivity analysis in reliability evaluation, the polynomial chaos expansion is employed to estimate the probabilistic constraints in the performance measure approach. The sensitivity of the limit state function with respect to design variables is derived using the chain rule and adjoint method. Three classical design examples are tested to show the effectiveness of the presented methodology. The optimized results demonstrate that the presented methodology is effective and that random field load uncertainty has a significant influence on the final design.