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.