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RESEARCH PAPERS

Differentiation of Mass and Stiffness Matrices for High Order Sensitivity Calculations in Finite Element-Based Equilibrium Problems

[+] Author and Article Information
J. E. Bernard

Department of Mechanical Engineering

S. K. Kwon

Samsung Shipbuilding and Heavy Industries Co., Ltd., Changwan, Korea

J. A. Wilson

Department of Mathematics, Iowa State University, Ames, IA 50011

J. Mech. Des 115(4), 829-832 (Dec 01, 1993) (4 pages) doi:10.1115/1.2919275 History: Received September 01, 1990; Revised July 01, 1991; Online June 02, 2008

Abstract

Extension of sensitivity methods to include higher order terms depends on the ability to compute higher order derivatives of the mass and stiffness matrices. This paper presents a method based on the use of cubic polynomials to fit mass and stiffness matrices across a range of interest of the design variable. The method is illustrated through an example which uses Padé approximants to expand the solution to a statics problem. The design variable is the thickness of one part of a plate with fixed boundaries. The solution gives a very good approximation over fivefold change in the value of the design variable.

Copyright © 1993 by The American Society of Mechanical Engineers
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