A regularization scheme for explicit level-set XFEM topology optimization

doi:10.1007/s11465-019-0533-2

Frontiers of Mechanical Engineering

2019, Vol. 14

Issue (2): 153-170 https://doi.org/10.1007/s11465-019-0533-2

本期目录

A regularization scheme for explicit level-set XFEM topology optimization

Markus J. GEISS¹, Jorge L. BARRERA¹, Narasimha BODDETI², Kurt MAUTE¹(

)

¹. Ann and H.J. Smead Department of Aerospace Engineering Sciences, University of Colorado at Boulder, Boulder, CO 80309-0429, USA
². Singapore University of Technology and Design, SUTD Digital Manufacturing and Design Centre, Singapore 487372, Singapore

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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.

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

收稿日期: 2018-09-01 出版日期: 2019-04-22

Corresponding Author(s): Kurt MAUTE

引用本文:

. [J]. Frontiers of Mechanical Engineering, 2019, 14(2): 153-170.
Markus J. GEISS, Jorge L. BARRERA, Narasimha BODDETI, Kurt MAUTE. A regularization scheme for explicit level-set XFEM topology optimization. Front. Mech. Eng., 2019, 14(2): 153-170.

链接本文:

https://academic.hep.com.cn/fme/CN/10.1007/s11465-019-0533-2
https://academic.hep.com.cn/fme/CN/Y2019/V14/I2/153

Fig.1

Fig.2

Fig.3

Parameter	Value
Weak boundary condition penalty Eq. (15)	$γ N = 100 / h$
Ghost penalty Eq. (13)	$γ G = 0.001$
Perimeter penalty weight Eq. (3)	$w 2 = 0.01$
Lower bound of s	$s L = − 3 h$
Upper bound of s	$s U = + 3 h$
Target bound of LSF	$ϕ Bnd = 2 h$
Filter radius used in 2D	$r f = 1.6 h$
Filter radius used in 3D	$r f = 2.4 h$

Tab.1

Parameter	Value
Young’s modulus	$E = 2 × 103$
Poisson’s ratio	$ν = 0$
LS regularization weight	$w 3 = 0.01$
Element edge length	$h = 1.0$

Tab.2

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Parameter	Value
Young’s modulus	$E = 2.0 × 103$
Poisson’s ratio	$ν = 0.4$
LS regularization weight	$w 3 = 0.01$
Element edge length	$h = 1.0$

Tab.3

Fig.9

Fig.10

Fig.11

Fig.12

Fig.13

Fig.14

Parameter	Value
Reynolds number	$Re = 66.0$
Fluid density	$ρ = 1.0$
LS regularization weight	$w 3 = 0.05$
Element edge length	$h = 0.25$

Tab.4

Fig.15

Fig.16

Fig.17

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