Challenges and advances in system reliability-based optimization of structural topology

Recently, the authors have been making research efforts to overcome technical challenges in applying design/topology optimization techniques to large-scale structural systems with uncertainties. First, in order to evaluate the probability of a system failure event and its parameter sensitivities accurately and efficiently during reliability-based design optimization, a system reliability-based design optimization (SRBDO) approach using the matrix-based system reliability (MSR) method was developed. In this approach, the MSR method utilizes matrix calculations to evaluate the system failure probability and its parameter sensitivities. The SRBDO/MSR approach is applicable to general systems including series, parallel, cut-set and link-set systems consisting of statistically dependent component events. Second, the material distribution method used for topology optimization often requires a large number of design variables, especially in three-dimensional applications. A multiresolution topology optimization (MTOP) scheme is thus developed to obtain high resolution optimal topologies with relatively low computational cost. These technical advances enable system reliability-based optimization of large-scale structural topology with low computational cost. This paper presents the SRBDO/MSR approach and MTOP scheme, respectively, and demonstrates these technological advances through numerical examples of system reliability-based optimization of structural topology.