Non-probabilistic reliability-based topology optimization against loading uncertainty field with a bounded field model

This paper presents a non-probabilistic reliability-based topology optimization under the distributed loading uncertainty, in which the loading uncertainty is described as the non-probability bounded field model. The reliability-based optimization model is a nested optimization process, in which the inner-loop optimization problem is to evaluate the structural reliability under the loading field uncertainty. Based on material-field series-expansion (MFSE) optimization method, the outer-loop optimization problem is expressed as determining the optimum structural topology that minimizes structural volume under the non-probability reliability index constraint. The nested optimization problem is solved via a gradient-based optimization algorithm. To reduce the computational cost of the optimization model, the concerned performance approach is employed to transform the non-probabilistic reliability-based optimization model equivalently. Three numerical examples considering uncertain loading field (including 2D and 3D structures) are given to illustrate the validity of the proposed method.