A stress-based formulation of the free material design problem with the trace constraint and single loading condition

Bulletin of the Polish Academy of Sciences. Technical Sciences

T. Lewi?skiDepartment of Structural Mechanics and Computer Aided Engineering, Faculty of Civil Engineering, Warsaw University of Technology, 16 Armii Ludowej St., 00-637 Warszawa, PolandOther articles by this author:De Gruyter OnlineGoogle Scholar¹  S. CzarneckiDepartment of Structural Mechanics and Computer Aided Engineering, Faculty of Civil Engineering, Warsaw University of Technology, 16 Armii Ludowej St., 00-637 Warszawa, PolandOther articles by this author:De Gruyter OnlineGoogle Scholar¹ 

[1] Department of Structural Mechanics and Computer Aided Engineering, Faculty of Civil Engineering, Warsaw University of Technology, 16 Armii Ludowej St., 00-637 Warszawa, Poland

关键词: Keywords: : free material design;    anisotropic elasticity;    compliance minimization.;   

DOI  :  10.2478/v10175-012-0026-5

学科分类：工程和技术（综合）

来源: Polska Akademia Nauk * Centrum Upowszechniania Nauki / Polish Academy of Sciences, Center for the Advancement of Science

【 摘 要 】

The problem to find an optimal distribution of elastic moduli within a given plane domain to make the compliance minimal under the condition of a prescribed value of the integral of the trace of the elastic moduli tensor is called the free material design with the trace constraint. The present paper shows that this problem can be reduced to a new problem of minimization of the integral of the stress tensor norm over stresses being statically admissible. The eigenstates and Kelvin’s moduli of the optimal Hooke tensor are determined by the stress state being the minimizer of this problem. This new problem can be directly treated numerically by using the Singular Value Decomposition (SVD) method to represent the statically admissible stress fields, along with any unconstrained optimization tool, e.g.: Conjugate Gradient (CG) or Variable Metric (VM) method in multidimensions.

【 授权许可】

Unknown