A single variable stress-based multi-material topology optimization method with three-dimensional unstructured meshes

Stress-minimization topology optimization with multi-phase materials is still an academic challenge, especially for three-dimensional (3D) problems. This paper proposes a novel stress-based multi-material topology optimization method to achieve a 3D stress-minimization design involving unstructured meshes. A comprehensive stair form interpolation model is introduced to address both stiff penalization and stress relaxation issues. In this model, only one type of nodal design variable is introduced to represent the multi-material density field, which is projected to the physical parameter field using smooth Heaviside functions with varied threshold settings. To minimize the global measure of stress, the P-norm stress aggregation function is established and a multi-material topology optimization problem with an arbitrary number of volume constraints is formulated. Additionally, the adjoint sensitivity analysis is performed and the provided interpolation model adaptively updates the interpolation parameters. Finally, the presented methodology is validated by several three-dimensional design examples, including a supported beam, bridge, and airplane bearing bracket.