Reliability-based topology optimization using a standard response surface method for three-dimensional structures

In this paper, a reliability-based topology optimization (RBTO) for 3-D structures was performed using bi-directional evolutionary structural optimization (BESO) and the standard response surface method (SRSM). In order to get a stable optimal topology, the most recently-developed filter scheme was implemented with BESO, and SRSM was used to generate an approximate limit state function. These results were compared with the recently announced results of RBTO for 2-D structures, and the differences between the results for the 3-D and 2-D structures were examined. A cantilever beam and an MBB beam were selected as the numerical examples. The comparison showed that the optimal topologies of deterministic topology optimization (DTO) and RBTO for the 2-D and 3-D MBB beams, respectively, are very different. Specifically, the two-support member on the left hand side comes into being along the width for the 3-D case, but not for the 2-D case. This shows that RBTO for 3-D structures should be performed as part of the design process.