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RESEARCH PAPERS: Design Automation Papers

Dual Formulation of Variational Problems in Optimal Design

[+] Author and Article Information
G. I. N. Rozvany, S. R. Adidam

Monash University, Clayton, Victoria, Australia

J. Eng. Ind 94(2), 409-418 (May 01, 1972) (10 pages) doi:10.1115/1.3428170 History: Received June 15, 1971; Online July 15, 2010

Abstract

Using a dual variational formulation, criteria for bounds on the minimum cost of rigid, perfectly plastic structures are derived. The results are used to point out a duality which exists between plastic analysis and plastic optimal design. The relations between the theories of Prager, Shield, Drucker, Heyman, and Michell are discussed. The proposed theory is applied to Tresca sandwich plates and fiber-reinforced plates. Identical upper and lower bounds are used to show that the “membrane solution” gives a minimum volume for a certain class of Tresca sandwich-plates.

Copyright © 1972 by ASME
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