Structural parameter optimization of linear elastic systems

David Russell

doi:10.3934/cpaa.2011.10.1517

Article Contents

2011, Volume 10, Issue 5: 1517-1536. Doi: 10.3934/cpaa.2011.10.1517

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Structural parameter optimization of linear elastic systems

David Russell^1,

1.
418 McBryde Hall, Department of Mathematics, Virginia Tech, Blacksburg, VA 24061-0123

Received: June 30, 2009

Revised: April 30, 2010

Published: August 2011

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Abstract

The design of elastic structures to optimize strength and economy of materials is a fundamental problem in structural engineering and related areas of applied mathematics. In this article we explore a finite dimensional framework for approximate solution of such design problems based on linear elasticity with a range of elastic coefficients assumed available as design parameters. Solution methods for related optimization problems based on the matrix trace norm are suggested and analyzed, providing existence and uniqueness theorems. Results of computations for sample problems are presented and compared with parallel results in the literature based on other approaches.

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Mathematics Subject Classification: Primary: 74C05, 74K10, 74K20; Secondary: 90C25.

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