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Compliance Minimization of Two-Material Elastic Structures

  • Grzegorz Dzierżanowski
  • Tomasz Lewiński
Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 549)

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 wellknown 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.

Keywords

Topology Optimization Shape Optimization Sandwich Plate Stress Energy Layout Optimization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© CISM, Udine 2014

Authors and Affiliations

  • Grzegorz Dzierżanowski
    • 1
  • Tomasz Lewiński
    • 1
  1. 1.Faculty of Civil EngineeringWarsaw University of TechnologyWarsawPoland

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