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. In this change of paradigm, metamaterials have an important role because when a component is 3D-printed, it is performed from the micro level, where custom structures may be designed to endow the material and the component of special of customized mechanical properties. Topology optimization techniques facilitate the design of both the microstructures and the overall component topology, and today the component topology may be designed assuming a continuous spectrum of mechanical properties facilitated by different locally designed microstructures. However, current topology optimization techniques do not operate directly with the mechanical properties of the material, but through density intermediates, using density-based limits like a minimum or maximum density, assuming an homogeneous base material. We propose here a novel topology optimization algorithm which operates directly on the mechanical properties and energies, without employing density intermediates. The proposed approach reduces the algorithmic complexity since the optimization is performed by the direct iterative update of the mechanical properties, through information taken from its finite element analysis. We show that the proposed methodology can reach similar results as the current techniques based on a gradient descent optimization, eliminating the need for external parameters and, hence, increasing the easy of use and its robustness. The proposed technique is specially suitable for two-level concurrent material-component design using functionally graded metamaterials.