Multi-Objective Thermo-Mechanical Topology Optimization of Lightweight Structures for Structural Stiffness, Thermal Performance, and Dynamic Characteristics

Abstract This study presents a multi-objective topology optimization framework for lightweight thermo-mechanical structures subjected to simultaneous mechanical, thermal, and dynamic requirements. A two-dimensional simply supported structure is modeled using a structured quadrilateral finite element mesh comprising 4,800 Q4 elements and 4,961 nodes. The material distribution is parameterized using the Solid Isotropic Material with Penalization (SIMP) approach with a penalization factor of 3.0 and a prescribed volume fraction of 40%. Three coupled performance criteria are considered: structural compliance, total heat transfer, and fundamental natural frequency. Thermal, structural, and modal finite element analyses are sequentially performed for each candidate topology within a multi-objective evolutionary optimization procedure. The optimized configuration preserves the prescribed material volume and total mass of 31.20 kg while redistributing material toward mechanically and dynamically efficient regions. The results show a reduction in structural compliance from 8.70646×10 − 2 to 8.65559×10 − 2 , corresponding to a 0.584% improvement. The fundamental natural frequency increases from 145.63 to 148.24 Hz, representing a 1.793% improvement, while the second and third natural frequencies reach 295.03 and 555.69 Hz, respectively. Total heat transfer changes only marginally from 43.2021 to 43.2368 W, corresponding to a 0.0804% increase. The final optimized structure exhibits a maximum displacement of 4.6663×10 − 4 m, maximum von Mises stress of 1.0372×10 5 Pa, mean von Mises stress of 1.3848×10 4 Pa, and maximum heat flux of 421.08 W/m². The results demonstrate that coupled topology optimization can improve structural stiffness and dynamic performance while maintaining a fixed material budget and nearly unchanged thermal behavior. The proposed framework provides a computationally efficient basis for the design of lightweight structures requiring simultaneous mechanical, thermal, and vibration performance.