ON A TWO-SCALE PHASEFIELD MODEL FOR TOPOLOGY OPTIMIZATION

被引：0
|
作者：
Ebeling-Rump, Moritz [1 ]
Hoemberg, Dietmar [2 ,3 ,4 ]
Lasarzik, Robert [2 ,5 ]
机构：
[1] Endless Ind GmbH, Berlin, Germany
[2] Weierstrass Inst Berlin, Berlin, Germany
[3] NTNU, Dept Math Sci, Trondheim, Norway
[4] Tech Univ Berlin, Berlin, Germany
[5] Free Univ Berlin, Berlin, Germany
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2024年 / 17卷 / 01期
关键词：
Topology optimization; linear elasticity; phase field method; Allen- Cahn equation; existence; weak solutions; DESIGN; FIELD;
D O I：
10.3934/dcdss.2023206
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article, we consider a gradient flow stemming from a problem in two-scale topology optimization. We use the phase-field method, where a Ginzburg-Landau term with obstacle potential is added to the cost functional, which contains the usual compliance but also an additional contribution including a local volume constraint in a penalty term. The minimization of such an energy by its gradient-flow is analyzed in this paper. We use an regularization and discretization of the associated state-variable to show the existence of weak solutions to the considered system.
引用
收藏
页码：326 / 361
页数：36
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