On a Saddle-Point Theorem in Minimum Compliance Design

J. J. Telega , Tomasz Lewiński

Abstract

This note deals with the displacement-based relaxed formulation of the minimum compliance layout problem of the optimal distribution of two isotropic materials within a given three-dimensional domain. In 1994, Lipton (Ref. 1) proved that minimization over elasticity tensors can be interchanged with maximization over displacements. This proof was based on the theory of Young measures. The aim of this contribution is to provide a new and straightforward proof of the Lipton saddle-point theorem by using a duality technique, thus bypassing the Young measure theory.
Author J. J. Telega - [Institute of Fundamental Technological Research of the Polish Academy of Sciences]
J. J. Telega,,
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, Tomasz Lewiński (FCE / ICE)
Tomasz Lewiński,,
- The Institute of Civil Engineering
Journal seriesJournal of Optimization Theory and Applications, ISSN 0022-3239
Issue year2000
Vol106
No2
Pages441-450
Publication size in sheets0.5
Keywords in EnglishApplications of Mathematics, Calculus of Variations and Optimal Control, duality, Engineering, general, minimization of compliance, Operation Research/Decision Theory, optimization, saddle points, Theory of Computation
ASJC Classification2604 Applied Mathematics; 1803 Management Science and Operations Research; 2606 Control and Optimization
DOIDOI:10.1023/A:1004667901231
URL http://link.springer.com/article/10.1023/A%3A1004667901231
Languageen angielski
File
lewinski14.pdf 165.87 KB
Score (nominal)30
Score sourcejournalList
Publication indicators WoS Citations = 2; Scopus Citations = 1; GS Citations = 4.0; Scopus SNIP (Source Normalised Impact per Paper): 2000 = 1.041; WoS Impact Factor: 2006 = 0.633 (2) - 2007=1.063 (5)
Citation count*5 (2020-09-08)
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