Layout optimization design method for thermo-elastic thin-walled structures with lattices and stiffeners

This work proposes a layout optimization design method for thermo-elastic thin-walled structures with lattices and stiffeners in the framework of multi-material topology optimization, in which both the steady-state temperature field and mechanical loads are considered. Firstly, taking into account the design requirements, suitable lattice unit cells are chosen and their equivalent mechanical properties are obtained by the homogenization method. Thus, the candidate lattice unit cells are represented as corresponding virtual homogeneous materials. Meanwhile, the stiffeners are modelled with solid material. Afterwards, a multi-material thermo-elastic structural optimization formulation is established and solved iteratively through gradient-driven optimization algorithms to obtain the optimized layouts of the lattices and stiffeners. In addition, the maximum size constraint and the overall volume constraint with a lower bound are introduced. The former ensures that the solid material takes the form of 'ribs' in the optimization results and the latter could meet the requirement that the design space is filled with lattice or solid material. Finally, numerical tests are conducted to demonstrate the detailed application process and validate the effectiveness of the proposed design method. This work provides an effective design tool for the application of additively manufactured lattice structures in thermo-elastic coupled load-bearing structures.