Nonlinear topology optimization on thin shells using a reduced-order elastic shell model

Abstract

We present a novel numerical algorithm to perform nonlinear topology optimization on elastic thin shells. The main component of our method is a differentiable thin-shell simulator based on discrete differential geometry (DDG) discretization and the projected Newton method to solve geometrically nonlinear elasticity and its derivatives on a triangle mesh. We build a density-based topology optimization algorithm, enhanced by a density filter and a Heaviside projection scheme, to emerge and optimize topologically complex shell structures on curved surfaces. We validate our approach using standard test cases for nonlinear topology optimization and demonstrate the efficacy of our method by tackling highly nonlinear topology optimization problems by producing complex and high-resolution shell structural designs under various load conditions.