A regularization scheme for explicit level-set XFEM topology optimization

Abstract

Regularization of the level-set (LS) field is a critical part of LS-based topology optimization (TO) approaches. Traditionally this is achieved by advancing the LS field through the solution of a Hamilton-Jacobi equation combined with a reinitialization scheme. This approach, however, may limit the maximum step size and introduces discontinuities in the design process. Alternatively, energy functionals and intermediate LS value penalizations have been proposed. This paper introduces a novel LS regularization approach based on a signed distance field (SDF) which is applicable to explicit LS-based TO. The SDF is obtained using the heat method (HM) and is reconstructed for every design in the optimization process. The governing equations of the HM, as well as the ones describing the physical response of the system of interest, are discretized by the extended finite element method (XFEM). Numerical examples for problems modeled by linear elasticity, nonlinear hyperelasticity and the incompressible Navier-Stokes equations in two and three dimensions are presented to show the applicability of the proposed scheme to a broad range of design optimization problems.

Keywords

level-set regularization / explicit level-sets / XFEM / CutFEM / topology optimization / heat method / signed distance field / nonlinear structural mechanics / fluid mechanics

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Acknowledgements

The first, second and fourth authors acknowledge the support of the United States National Science Foundation (CMMI-1463287). The third author acknowledge the support of the SUTD Digital Manufacturing and Design (DManD) Centre supported by the National Research Foundation of Singapore. The fourth author acknowledges the support of the Air Force Office of Scientific Research (Grant No. FA9550-16-1-0169) and from the Defense Advanced Research Projects Agency (DARPA) under the TRADES program (agreement HR0011-17-2-0022). The opinions and conclusions presented in this paper are those of the authors and do not necessarily reflect the views of the sponsoring organizations.

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