Structural parameter optimization of linear elastic systems

Pages: 1517 - 1536, Volume 10, Issue 5, September 2011

doi:10.3934/cpaa.2011.10.1517       Abstract        References        Full Text (548.9K)       Related Articles

David Russell - 418 McBryde Hall, Department of Mathematics, Virginia Tech, Blacksburg, VA 24061-0123, United States (email)

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.

Keywords:  Structural optimization, linear elastic systems, convex programming.
Mathematics Subject Classification:  Primary: 74C05, 74K10, 74K20; Secondary: 90C25.

Received: July 2009;      Revised: May 2010;      Published: April 2011.

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