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Designing materials with prescribed elastic properties using polygonal cells
Author(s) -
Diaz Alejandro R.,
Bénard André
Publication year - 2003
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.677
Subject(s) - parallelogram , homogenization (climate) , planar , base (topology) , mathematics , topology (electrical circuits) , topology optimization , geometry , inverse , computer science , finite element method , mathematical analysis , combinatorics , structural engineering , computer graphics (images) , engineering , biodiversity , ecology , artificial intelligence , robot , biology
Abstract An extension of the material design problem is presented in which the base cell that characterizes the material microgeometry is polygonal. The setting is the familiar inverse homogenization problem as introduced by Sigmund. Using basic concepts in periodic planar tiling it is shown that base cells of very general geometries can be analysed within the standard topology optimization setting with little additional effort. In particular, the periodic homogenization problem defined on polygonal base cells that tile the plane can be replaced and analysed more efficiently by an equivalent problem that uses simple parallelograms as base cells. Different material layouts can be obtained by varying just two parameters that affect the geometry of the parallelogram, namely, the ratio of the lengths of the sides and the internal angle. This is an efficient way to organize the search of the design space for all possible single‐scale material arrangements and could result in solutions that may be unreachable using a square or rectangular base cell. Examples illustrate the results. Copyright © 2003 John Wiley & Sons, Ltd.