Topology optimization of structures composed of multiple architected materials with spatially-varying relative density encased in a solid shell

We present a topology optimization formulation for design of maximally stiff structures composed of multiple architected materials with spatially-varying relative density, encased in a solid shell. A simple erosion-based strategy for defining the shell is integrated with a general multi-architected-material formulation that can handle spatial variations in the architected infill’s relative density. By exploiting the erosion-based strategy, we return to the standard density filter that is based on explicit solution of a convolution integral, rather than using a partial differential equation-based density filter that has become common for shell-infill problems. The standard density filter both simplifies the implementation and the expression of shell thickness, which can be controlled precisely using parameters of operations used to define the shell. Material existence design variables determine whether each point in the domain contains material or void and an erosion of the material existence field distinguishes the solid shell from the porous infill. Architecture selection and relative density design variable fields select from a set of candidate architectures at each design point and define their local relative densities, respectively. Homogenized properties of the candidate architected materials are precomputed and polynomial fits of their stiffness-density relationships allow for continuously-varying relative density in the porous infill region. A range of two-dimensional numerical examples demonstrates the ability to handle many architectures with spatially-varying relative density, accommodate global and local volume constraints, achieve high-quality solid shells with controlled thickness, and tune the designs using parameters of the formulation.