| This paper presents a thermoelastic coupled multi-objective topology optimization model for integrated design of spatially non-uniform lattice structures with load-bearing and heat transfer functionalities to fulfil the specific requirements of lightweight, high load-bearing capacity, and excellent thermal conductivity for aerospace engineering applications. To address the need for high stiffness-to-mass ratio and high-permeability configurations, the study focuses on relative density-based distribution of Octet unit cells in a lattice structure. First, the relationships between the equivalent stiffness, heat conductivity of Octet lattice cells and their geometric design parameters are established through homogenization and polynomial regression. Then, with the resulting property prediction models of the equivalent properties, the topology optimization problem of non-uniform lattice structures is formulated and solved with a gradient-based mathematical programing algorithm for determining the design variables in the unit cell level and the macro-structure level. Therein, the structural stiffness under mechanical and thermal loads, and the heat conduction performance, are simultaneously optimized. Further, a geometric post-processing approach is introduced to tackle the modeling issues related to abrupt local geometric changes in the optimized non-uniform lattice structures. The postprocess comprises of two steps: a volume-preserving equal-diameter transformation of shared rods of adjacent lattice unit cell, and a node sphere smoothing at shared nodes. Several numerical examples are presented to demonstrate the effectiveness of the optimization design method and the feasibility of additive manufacturing in realizing these intricate structures. |
