Frontiers of Mechanical Engineering
>> 2019,
Volume 14,
Issue 2
doi:
10.1007/s11465-019-0533-2
RESEARCH ARTICLE
A regularization scheme for explicit level-set XFEM topology optimization
. Ann and H.J. Smead Department of Aerospace Engineering Sciences, University of Colorado at Boulder, Boulder, CO 80309-0429, USA.. Singapore University of Technology and Design, SUTD Digital Manufacturing and Design Centre, Singapore 487372, Singapore
Accepted: 2019-01-14
Available online: 2019-01-14
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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.
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