Integrated multiscale topology optimization of frame structures for minimizing compliance

Frame structures are widely used in aerospace and other engineering fields due to their efficient provision of structural stiffness with minimal material usage. Recent advances in manufacturing technologies, such as 3D printing, have made it feasible to fabricate multiscale structures with complex microstructures, enabling further weight reduction. To fully exploit the design space of multiscale frame structures while circumventing the prohibitive computational costs in conventional solid-element-based direct numerical simulations, this paper proposes an Integrated Multiscale Topology Optimization (IMTO) method for frame structures. The method aims to minimize structural compliance by simultaneously optimizing both the macroscale (topological connectivity of the frame geometry) and microscale (material distribution within Representative Volume Elements, RVEs) in a unified framework. The macro- and micro-scale design variables are simultaneously‌ embedded in the compliance formulation while the sensitivity analysis is systematically computed via the chain rule to unify the multiscale optimization into a single-scale framework. Compared to concurrent multiscale approaches, this strategy not only achieves computational efficiency with a single optimization loop, but also allows ‌adaptive volume fraction allocation‌ across RVEs. Numerical examples demonstrate the importance of considering shear deformation effects in the topology optimization of frame structures, and also validate the feasibility of the method for performing multiscale topology optimization design of large-scale frame structures in engineering applications.