Thermo-elastic topology optimization for lightweight structures with temperature- and stress-dependent thermal contact resistance

Thermal contact resistance plays a crucial role in interface heat transfer in multi-layer structures such as aerospace and electronic devices. However, conventional topology optimization neglects the nonlinearity and design-dependent issues caused by thermo-elastic contact. This paper presents a novel computational framework for thermo-mechanical bidirectional coupling topology optimization that incorporates temperature- and stress-dependent thermal contact resistance, formulating a lightweight optimization model subject to constraints on the compliance and temperature. Within this framework, the discontinuous Galerkin finite element method is integrated with the continuous finite element method to solve numerical discontinuities in contact problems. Furthermore, the spatial distribution of thermal contact resistance within thermo-elastic structures is modeled using the semi-empirical model. To address both the temperature dependence of material properties and the temperature-stress dependence of thermal contact resistance, a hybrid sensitivity analysis scheme utilizing the adjoint method is developed and verified. Finally, two numerical examples demonstrate the effectiveness of the proposed framework. In addition, dynamic thermal contact resistance leverages its inherent interfacial temperature discontinuity to provide enhanced design flexibility for optimization models with dual-temperature constraints. Compared to the models of neglecting thermal contact resistance or assuming constant thermal contact resistance, the dynamic thermal contact resistance model achieves a lightweight design.