Modified element stacking method for multi-material topology optimization with anisotropic materials

This article presents a modified element stacking method for anisotropic multi-material topology optimization. This method can transform standard multi-material topology optimization formulations into a series of equivalent single-material topology optimization ones to overcome the various limitations inherent to conventional techniques. First, typical multi-material topology optimization methods utilize material interpolation schemes that restrict the study to the isotropic domain with a constant Poisson’s ratio, limiting practical applications and solution accuracy. Additionally, in attempts to further extend these classical multi-material topology optimization methods to anisotropic materials, preparing the necessary element information matrices becomes increasingly laborious or even impossible for complex models, preventing the application of sensitivity analysis for robust gradient-based optimization methods. To directly address these limitations, the element interpolation method replaces material interpolation schemes with an element interpolation framework, where each design cell property is determined using a weighted sum of various coincident single-material elements. This paper provides a thorough description of element interpolation and presents several numerical examples demonstrating successful implementation.