Derivatives of Buckling Loads and Vibration Frequencies With Respect to Stiffness and Initial Strain Parameters

[+] Author and Article Information
Raphael T. Haftka

Virginia Polytechnic Institute and State University, Blacksburg, VA 24061

Gerald A. Cohen

Structures Research Associates, Laguna Beach, CA 92651

Zenon Mróz

Institute of Fundamental Technological Research, Warsaw, Poland

J. Appl. Mech 57(1), 18-24 (Mar 01, 1990) (7 pages) doi:10.1115/1.2888302 History: Received May 18, 1988; Revised March 20, 1989; Online March 31, 2008


A uniform variational approach to sensitivity analysis of vibration frequencies and bifurcation loads of nonlinear structures is developed. Two methods of calculating the sensitivities of bifurcation buckling loads and vibration frequencies of nonlinear structures, with respect to stiffness and initial strain parameters, are presented. A direct method requires calculation of derivatives of the prebuckling state with respect to these parameters. An adjoint method bypasses the need for these derivatives by using instead the strain field associated with the second-order post-buckling state. An operator notation is used and the derivation is based on the principle of virtual work. The derivative computations are easily implemented in structural analysis programs. This is demonstrated by examples using a general purpose, finite element program and a shell-of-revolution program.

Copyright © 1990 by The American Society of Mechanical Engineers
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