A level set method for shape and topology optimization of both structure and support of continuum structures

Qi Xia; Michael Yu Wang; Tielin Shi

doi:10.1016/j.cma.2014.01.014

A level set method for shape and topology optimization of both structure and support of continuum structures

Qi Xia, Michael Yu Wang, Tielin Shi

Research output: Contribution to journal › Article › Research › peer-review

81 Citations (Scopus)

Abstract

We present a level set method for the shape and topology optimization of both structure and support. Two level set functions are used to implicitly represent a structure. The traction free boundary and the Dirichlet boundary are represented separately and are allowed to be continuously changed during the optimization. The optimization problem of minimum compliance is considered. The shape derivatives of both boundaries are derived by using a Lagrangian function and the adjoint method. The finite element analysis is done by modifying a fixed background mesh, and we do not use the artificial weak material. Numerical examples in two dimensions are investigated.

Original language	English
Pages (from-to)	340-353
Number of pages	14
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	272
DOIs	https://doi.org/10.1016/j.cma.2014.01.014
Publication status	Published - 15 Apr 2014
Externally published	Yes

Keywords

Dirichlet boundary
Homogeneous Neumann boundary
Level set method
Shape and topology optimization
Shape derivative

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10.1016/j.cma.2014.01.014

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title = "A level set method for shape and topology optimization of both structure and support of continuum structures",

abstract = "We present a level set method for the shape and topology optimization of both structure and support. Two level set functions are used to implicitly represent a structure. The traction free boundary and the Dirichlet boundary are represented separately and are allowed to be continuously changed during the optimization. The optimization problem of minimum compliance is considered. The shape derivatives of both boundaries are derived by using a Lagrangian function and the adjoint method. The finite element analysis is done by modifying a fixed background mesh, and we do not use the artificial weak material. Numerical examples in two dimensions are investigated.",

keywords = "Dirichlet boundary, Homogeneous Neumann boundary, Level set method, Shape and topology optimization, Shape derivative",

author = "Qi Xia and Wang, {Michael Yu} and Tielin Shi",

note = "Funding Information: This research work is partly supported by the National Natural Science Foundation of China (Grant No. 51105159 ), Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20110142120091 ). We thank Professor Gr{\'e}goire Allaire for the discussions about shape sensitivity analysis. The insightful comments of the reviewers are cordially appreciated.",

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T1 - A level set method for shape and topology optimization of both structure and support of continuum structures

AU - Xia, Qi

AU - Wang, Michael Yu

AU - Shi, Tielin

N1 - Funding Information: This research work is partly supported by the National Natural Science Foundation of China (Grant No. 51105159 ), Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20110142120091 ). We thank Professor Grégoire Allaire for the discussions about shape sensitivity analysis. The insightful comments of the reviewers are cordially appreciated.

PY - 2014/4/15

Y1 - 2014/4/15

N2 - We present a level set method for the shape and topology optimization of both structure and support. Two level set functions are used to implicitly represent a structure. The traction free boundary and the Dirichlet boundary are represented separately and are allowed to be continuously changed during the optimization. The optimization problem of minimum compliance is considered. The shape derivatives of both boundaries are derived by using a Lagrangian function and the adjoint method. The finite element analysis is done by modifying a fixed background mesh, and we do not use the artificial weak material. Numerical examples in two dimensions are investigated.

AB - We present a level set method for the shape and topology optimization of both structure and support. Two level set functions are used to implicitly represent a structure. The traction free boundary and the Dirichlet boundary are represented separately and are allowed to be continuously changed during the optimization. The optimization problem of minimum compliance is considered. The shape derivatives of both boundaries are derived by using a Lagrangian function and the adjoint method. The finite element analysis is done by modifying a fixed background mesh, and we do not use the artificial weak material. Numerical examples in two dimensions are investigated.

KW - Dirichlet boundary

KW - Homogeneous Neumann boundary

KW - Level set method

KW - Shape and topology optimization

KW - Shape derivative

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DO - 10.1016/j.cma.2014.01.014

M3 - Article

AN - SCOPUS:84893948092

SN - 0045-7825

VL - 272

SP - 340

EP - 353

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

ER -

A level set method for shape and topology optimization of both structure and support of continuum structures

Abstract

Keywords

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