Topology Optimization of Thermal Structures with Stress Constraints

Abstract

It is known in topology optimization, that in the presence of thermal loading, the conventional maximum stiffness design objectives generally do not lead to maximum strength structures due to the design dependency of thermoelastic loads. In this paper we present the application of stress constraints to structural topology optimization problems with thermal loading in an effort to develop a new technique for the design of hot structures where thermal stresses are of primary concern. A modern stress-relaxation technique is employed to circumvent the singularity phenomena in the stress constraints. In addition, we utilize stress aggregation functions to reduce the number of constraints in the optimization problem. We note that pre-existing formulations for thermoelastic topology optimization and stress-constraint handling are employed, but for the first time they are combined to consider thermal stresses. Preliminary numerical results indicate that the stress-constrained problem leads to different designs with superior thermoelastic performance when compared to the minimum compliance problems. In today’s aerospace industry, a number of practical examples are evident where the capability developed in this work is desirable. These include the design of engine exhaust-washed structures (EEWS) on embedded engine aircraft and integrated thermal protection systems (TPS) on hypersonic vehicles. In both cases, structural components are subjected to an extreme combined loading environment that is characterized by elevated temperatures and design against thermal stresses is of paramount concern.