Reliability-based topology optimization using reliability index approach

Abstract

Reliability-Based Topology Optimization (RBTO) based on the Evolutionary Structural Optimization (ESO) using Reliability Index Approach (RIA) is developed. When the uncertainties such as the elastic modulus, applied load and dimensional variation exist in design process, the optimum topology obtained from the Deterministic Topology Optimization (DTO) can not satisfy the design constraints since it is obtained without consideration of uncertainties related to the random variables. To alleviate the possible degradation of performance in design process, these uncertainties must be considered during the process of topology or design optimization. In the case that the RBTO is used, it is possible to perform the topology optimization where the uncertainties of the random variables should be considered since RBTO can deal with the probabilistic constraints in topology optimization. Reliability Index Approach (RIA) and Performance Measure Approach (PMA) calculate the reliability index as a measure of the probability of failure. In this study, the RIA, which has the probabilistic constraints that are formulated in terms of the reliability index, is adopted to evaluate the probabilistic constraints. In the RBTO based on ESO, the sensitivity number is defined as the change of the reliability index due to the removal of the each element.