Uncertainty‐oriented thermoelastic topology optimization with stress constraint

Abstract

The material redistribution abilities of traditional deterministic topology optimization are effective in addressing stress-related design issues in thermal elastic structures. However, uncertainties are inevitable in real-world. The structural strength of a design, achieved through deterministic topology optimization, is highly susceptible to these uncertainties, which may result in failure. This article introduces a novel method for topology optimization in stress-constrained thermoelastic structures, taking into account the uncertainties associated with heat sources and loads. We employ the Kieisselmeier-Steinhauser function to aggregate the stress constraint when constructing the performance function. In order to improve optimization efficiency, the sequential optimization and reliability assessment method is used to decouple the double-layer loop reliability-based topology optimization. Initially, we derive the derivative of stress-based performance functions with respect to heat source and load uncertainty variables, thereby facilitating the use of modified chaos control for assessing structural reliability and imposing constraints. The adjoint method and chain rule are utilized to obtain the derivative information of the performance function with respect to density variables, guiding the topology updates. We present five design examples to demonstrate the effectiveness of the presented method. Monte Carlo simulations for the optimized results are performed to show that the presented method can obtain a structure that meets reliability requirements.