Thermoelastic topology optimization for stiffened thin-walled structures under design-dependent thermal loading problems

Abstract

Due to their high specific strength and stiffness, stiffened thin-walled structures are extensively utilized in aerospace applications to maintain a high load-bearing capacity in a complex thermo-mechanical coupled environment. Thermal deformation significantly impacts the intake and exhaust performances, aerodynamic profiles, and even structural safety, hence how to design a reasonable stiffener layout for thermal structures is necessary. Thermoelastic topology optimization is an efficient method. However, to reduce the thermal load and maintain stiffness, design-dependent thermal loading problems such as the grayscale issues and the material-less effect often result. Due to the high proportion of gray elements and a lower penalized element stiffness, thermal deformation magnitude is closely related to the grayscale issues. Therefore, the key challenge is to address the grayscale issues induced by the thermal load. To address this challenge, a thermoelastic topology optimization method via regional strain energy minimization (RSEM) is proposed in this study. The region here means the skin domain of stiffened thin-walled structures. To control the width size of stiffeners consisting of voxels, a maximum size constraint is established through the p-mean aggregation function, employing the Helmholtz-type anisotropic filter to calculate the solid ratio. This study compares three optimization formulations that minimize the compliance, global strain energy and regional strain energy as objective functions, respectively. Two numerical examples are presented to demonstrate the effectiveness of the proposed method in addressing design-dependent thermal loading problems. Compared to conventional methodologies, the proposed method can generate a clear stiffener layout and reduce the thermal deformation by 77% for an engineered thin-walled end cap structure under a thermo-mechanical coupled field.