Application of the Monomial Method to Shape Optimization

[+] Author and Article Information
S. A. Burns

University of Illinois at Urbana-Champaign, 104 S. Mathews #117, Urbana, IL 61801

J. Mech. Des 116(4), 1013-1018 (Dec 01, 1994) (6 pages) doi:10.1115/1.2919481 History: Received August 01, 1993; Revised January 01, 1994; Online June 02, 2008


The monomial method is an alternative to Newton’s method for solving systems of nonlinear algebraic equations. It possesses several properties not shared by Newton’s method that enhance performance, yet does not require substantial computational effort beyond that required for Newton’s method. Previous work has demonstrated that the monomial method treats problems in structural design very effectively. This paper combines the monomial method with the method of generalized geometric programming to treat the problem of structural shape optimization of continuum structures modeled by finite elements.

Copyright © 1994 by The American Society of Mechanical Engineers
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