RELATING PHASE FIELD AND SHARP INTERFACE APPROACHES TO STRUCTURAL TOPOLOGY OPTIMIZATION

被引：42
作者：
Blank, Luise [1 ]
Garcke, Harald [1 ]
Farshbaf-Shaker, M. Hassan [2 ]
Styles, Vanessa [3 ]
机构：
[1] Univ Regensburg, Fak Math, D-93040 Regensburg, Germany
[2] Weierstr Inst Appl Anal & Stochast, D-10117 Berlin, Germany
[3] Univ Sussex, Dept Math, Brighton BN1 9QH, E Sussex, England
来源：
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2014年 / 20卷 / 04期
基金：
英国工程与自然科学研究理事会;
关键词：
Structural topology optimization; linear elasticity; phase-field method; first order conditions; matched asymptotic expansions; shape calculus; numerical simulations; DIFFUSION; SYSTEMS; STRESS; MOTION; TRANSITIONS; MODELS;
D O I：
10.1051/cocv/2014006
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
A phase field approach for structural topology optimization which allows for topology changes and multiple materials is analyzed. First order optimality conditions are rigorously derived and it is shown via formally matched asymptotic expansions that these conditions converge to classical first order conditions obtained in the context of shape calculus. We also discuss how to deal with triple junctions where e.g. two materials and the void meet. Finally, we present several numerical results for mean compliance problems and a cost involving the least square error to a target displacement.
引用
收藏
页码：1025 / 1058
页数：34
相关论文
共 66 条
  • [1] THERMODYNAMICALLY CONSISTENT, FRAME INDIFFERENT DIFFUSE INTERFACE MODELS FOR INCOMPRESSIBLE TWO-PHASE FLOWS WITH DIFFERENT DENSITIES
    Abels, Helmut
    Garcke, Harald
    Gruen, Guenther
    [J]. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2012, 22 (03)
  • [2] Structural optimization using sensitivity analysis and a level-set method
    Allaire, G
    Jouve, F
    Toader, AM
    [J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2004, 194 (01) : 363 - 393
  • [3] Allaire G., 2002, OPTIMIZATION HOMOGEN
  • [4] [Anonymous], 1995, ELECTRON J DIFFER EQ
  • [5] [Anonymous], 2013, Topology optimization: theory, methods, and applications
  • [6] [Anonymous], 1992, SPRINGER SER COMPUT
  • [7] [Anonymous], 2005, An introduction to the regularity theory for elliptic systems, harmonic maps and minimal graphs
  • [8] [Anonymous], STUDIES MATH APPL
  • [9] BALDO S, 1990, ANN I H POINCARE-AN, V7, P67
  • [10] ON SHARP INTERFACE LIMITS OF ALLEN-CAHN/CAHN-HILLIARD VARIATIONAL INEQUALITIES
    Barrett, John W.
    Garcke, Harald
    Nurnberg, Robert
    [J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2008, 1 (01): : 1 - 14
1234567