The Updated Properties Model (UPM): A topology optimization algorithm for the creation of macro–micro optimized structures with variable stiffness

Abstract

The design and manufacturing of high value industrial components is suffering a change of paradigm with 3D printing, where a macro–micro structural optimization of architected metamaterials is pursued to endow the material and the component of customized mechanical properties. Topology optimization techniques facilitate the design of both the microstructures and the overall component topology. However, current techniques do not operate directly with the mechanical properties of the material, but through density intermediates. We propose a novel topology optimization algorithm that aims to homogenize the strain level by minimizing its standard deviation across the domain with no other constraint than the imposed limits on the design space, deriving in an iterative update formula for the stiffness. Despite that the pursued objectives are different, we show that the proposed methodology can reach similar results as the current techniques, but without imposing constraints and reducing the number of external parameters, thus increasing the easy of use and its robustness. Working directly with moduli, the proposed technique is specially suitable for two-level concurrent material-component design using functionally graded metamaterials, and can be extended to materials other than linear isotropic.