Control in the coefficients with variational crimes: Application to topology optimization of Kirchhoff plates

Publication: Research - peer-reviewJournal article – Annual report year: 2012

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@article{e4dac2757c3f4cb5a8d834c1b0459c0a,
title = "Control in the coefficients with variational crimes: Application to topology optimization of Kirchhoff plates",
keywords = "Control in the coefficients, Topology optimization, Discontinuous Galerkin methods, Thin plates, Convergence analysis",
publisher = "Elsevier BV",
author = "Anton Evgrafov and Marhadi, {Kun Saptohartyadi}",
year = "2012",
doi = "10.1016/j.cma.2012.03.003",
volume = "237-240",
pages = "27--38",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",

}

RIS

TY - JOUR

T1 - Control in the coefficients with variational crimes

T2 - Application to topology optimization of Kirchhoff plates

A1 - Evgrafov,Anton

A1 - Marhadi,Kun Saptohartyadi

AU - Evgrafov,Anton

AU - Marhadi,Kun Saptohartyadi

PB - Elsevier BV

PY - 2012

Y1 - 2012

N2 - We study convergence of discontinuous Galerkin-type discretizations of the problems of control in the coefficients of uniformly elliptic partial differential equations (PDEs). As a model problem we use that of the optimal design of thin (Kirchhoff) plates, where the governing equations are of the fourth order. Methods which do not require approximation subspaces to conform to the smoothness requirements dictated by the PDE are very attractive for such problems. However, variational formulations of such methods normally contain boundary integrals whose dependence on the small, with respect to “volumetric” Lebesgue norm, changes of the coefficients is generally speaking not continuous. We utilize the lifting formulation of the discontinuous Galerkin method to deal with this issue.Our main result is that limit points of sequences of designs verifying discrete versions of stationarity can also be expected to satisfy stationarity for the limiting continuum mechanics problem. We illustrate the practical behaviour of our discretization strategy on some benchmark-type examples.

AB - We study convergence of discontinuous Galerkin-type discretizations of the problems of control in the coefficients of uniformly elliptic partial differential equations (PDEs). As a model problem we use that of the optimal design of thin (Kirchhoff) plates, where the governing equations are of the fourth order. Methods which do not require approximation subspaces to conform to the smoothness requirements dictated by the PDE are very attractive for such problems. However, variational formulations of such methods normally contain boundary integrals whose dependence on the small, with respect to “volumetric” Lebesgue norm, changes of the coefficients is generally speaking not continuous. We utilize the lifting formulation of the discontinuous Galerkin method to deal with this issue.Our main result is that limit points of sequences of designs verifying discrete versions of stationarity can also be expected to satisfy stationarity for the limiting continuum mechanics problem. We illustrate the practical behaviour of our discretization strategy on some benchmark-type examples.

KW - Control in the coefficients

KW - Topology optimization

KW - Discontinuous Galerkin methods

KW - Thin plates

KW - Convergence analysis

U2 - 10.1016/j.cma.2012.03.003

DO - 10.1016/j.cma.2012.03.003

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0045-7825

VL - 237-240

SP - 27

EP - 38

ER -