The Optimum Design of Spatial Frames Using the Method of Constrained Steepest Descent With State Equations

[+] Author and Article Information
D. L. Bartel

Mechanical Systems and Design, Cornell University, Ithaca, New York

E. J. Haug

U. S. Army Weapons Command, Rock Island, Illinois

Kwan Rim

Mechanics and Hydraulics, University of Iowa, Iowa City, Iowa

J. Eng. Ind 93(4), 1261-1267 (Nov 01, 1971) (7 pages) doi:10.1115/1.3428072 History: Received September 08, 1970; Online July 15, 2010


This paper considers the design of a class of spatial frames which occur frequently in mechanical systems: plane frames with out-of-plane loads. The design objective is to minimize the weight subject to constraints on stress and geometry. The method of constrained steepest descent with state equations is introduced to solve the resulting mathematical programming problem. This method differs from the usual methods of nonlinear programming in that the state variables and the state equations are used explicitly in the formulation. This results in a natural matching of the essential features of the design problem and the method used to obtain its solution. The method is effective and general in that it can be readily applied to a wide variety of design problems which occur in mechanical design.

Copyright © 1971 by ASME
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