Vol. 6, No. 4, 2018

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ISSN: 2325-3444 (e-only)
ISSN: 2326-7186 (print)
Optimal orthotropy and density distribution of two-dimensional structures

Narindra Ranaivomiarana, François-Xavier Irisarri, Dimitri Bettebghor and Boris Desmorat

Vol. 6 (2018), No. 4, 293–305
Abstract

This paper describes an optimization methodology giving simultaneously the optimal spatial material distribution and the optimal material orthotropy distribution in a two-dimensional space. The spatial material distribution is parametrized by a density variable that defines the presence or absence of material. A general orthotropic material is parametrized by the polar invariants of the elasticity tensor. The criterion is the compliance that measures the global structural stiffness. The numerical procedure iterates successively between local minimizations and finite element calculations. Thanks to the polar method, the local minimizations are solved explicitly providing analytical solutions. An optimization of a beam shows the effectiveness of the method in finding concurrently the optimal shape and the optimal material.

Keywords
topology optimization, SIMP, polar method, distributed orthotropy, material design
Mathematical Subject Classification 2010
Primary: 74P10
Milestones
Received: 12 October 2017
Revised: 7 May 2018
Accepted: 14 June 2018
Published: 1 October 2018

Communicated by Francesco dell'Isola
Authors
Narindra Ranaivomiarana
Centre de Châtillon
Office National d’Etudes et de Recherches Aérospatiales
Chatillon
France
François-Xavier Irisarri
Centre de Châtillon
Office National d’Etudes et de Recherches Aérospatiales
Chatillon
France
Dimitri Bettebghor
Centre de Châtillon
Office National d’Etudes et de Recherches Aérospatiales
Chatillon
France
Boris Desmorat
Institut Jean Le Rond d’Alembert
Sorbonne Université
Paris
France