Compliance Minimization of Two-Material Elastic Structures

Grzegorz Michał Dzierżanowski , Tomasz Denis Lewiński

Abstract

Minimum compliance problem set for a structure made of two elastic, isotropic materials is tackled in this paper. The relaxation by homogenization technique is used for obtaining its mathematically well-posed formulation. The problem is first discussed in general two-material context. Derivation of main results is recalled and supplemented with some explanations and remarks. Next, an important topic of one-material layout optimization (or shape optimization) is addressed. It is hampered by the non-smoothness of formula for relaxed stress energy hence its approximation is proposed which in turn makes the FEM easier to apply in solving the equilibrium problem. Shape optimization is then linked to a well-known Michell problem of the lightest, fully stressed structures. Possible extension of the relaxation by homogenization method to other structures like thin or moderately thick plates in bending as well as thin plates or shells submerged to simultaneous in-plane and bending load are also commented.
Author Grzegorz Michał Dzierżanowski (FCE / ICE)
Grzegorz Michał Dzierżanowski,,
- The Institute of Civil Engineering
, Tomasz Denis Lewiński (FCE / ICE)
Tomasz Denis Lewiński,,
- The Institute of Civil Engineering
Pages175-212
Publication size in sheets1.85
Book Rozvany G.I., Lewiński Tomasz Denis (eds.): Topology Optimization in Structural and Continuum Mechanics , CISM International Centre for Mechanical Sciences, vol. 549, 2014, Spinger-Verlag, ISBN 978-3-7091-1643-2, [978-3-7091-1642-5], 472 p., DOI:10.1007/978-3-7091-1643-2
Keywords in EnglishTOPOLOGY OPTIMIZATION; HOMOGENIZATION METHOD; SANDWICH PLATES; OPTIMAL-DESIGN; COMPOSITE; FILTERS; ENERGY
DOIDOI:10.1007/978-3-7091-1643-2_8
Languageen angielski
File
compliance.pdf 156.16 KB
Score (nominal)10
ScoreMinisterial score = 10.0, 23-10-2019, MonographChapterAuthor
Publication indicators WoS Citations = 0; Scopus Citations = 1
Citation count*2 (2020-04-01)
Cite
Share Share

Get link to the record


* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.
Back
Confirmation
Are you sure?