A generalized exact volume constraint method for the topology optimization based on the nonlinear reaction-diffusion equation

Abstract

From a intuitive perspective, exact boundary representation emerges as the most favorable approach for topology optimization of structural systems based on the finite element method (FEM). Under exact boundary representation, the material domain can be precisely defined, granting the flexibility to impose arbitrary boundary conditions on newly generated boundaries throughout the optimization process. This newfound capability is achieved through the recently introduced exact volume constraint method, which effectively addresses the convergence challenges associated with exact boundary representation. However, one key consideration that has not yet been explored is the potential nonlinearity of the reaction-diffusion equation governing the evolution of the level set function. Consequently, the primary objective of this study is to expand upon the proposed topology optimization methodology, which incorporates exact boundary representation, to account for nonlinear aspects of the reaction-diffusion equation. Subsequently, we will conduct a comparative analysis of the results obtained using various proportional constants denoted as K in relation to the level set function ϕ.