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A construction of laminates from rank-1 polygons

Published online by Cambridge University Press:  11 July 2007

Z. Iqbal
Z. Iqbal
Affiliation:
Mathematical Institute, University of Oxford, 24–29 St Giles, Oxford OX1 3LB, UK
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Abstract

We construct non-trivial laminates distributed continuously along a smooth closed ‘evolute’ curve by approximating an auxiliary (‘involute’) curve by a polygon with rank-1 sides. We give an explicit example in which the evolute has no rank-1 connections. Using these techniques, given a finite set of matrices B1,…,Br and any other matrix A, we show how to construct a laminate with positive mass at each Bi, any proportion less than 1 of its support on the Bi, and centre of mass at A.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 130 , Issue 6 , December 2000 , pp. 1311 - 1335
Copyright
Copyright © Royal Society of Edinburgh 2000

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