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EIGENVALUES OF ELEMENT STIFFNESS MATRICES. PART I: 2‐D PLANE ELEMENTS

D.J. KIDGER (Department of Engineering, University of Manchester, Simon Building, Oxford Road, Manchester M13 9PL, UK)
I.M. SMITH (Department of Engineering, University of Manchester, Simon Building, Oxford Road, Manchester M13 9PL, UK)

Engineering Computations

ISSN: 0264-4401

Publication date: 1 March 1992

Abstract

The eigenvalues of element stiffness matrices K and the eigenvalues of the generalized problem Kx = λMx, where M is the element's mass matrix, are of fundamental importance in finite element analysis. For instance, they may indicate the presence of ‘zero energy modes’, or control the critical timestep applicable in temporal integration of dynamic problems. Recently explicit formulae for the eigenvalues of the stiffness matrix of a plane, 4‐node rectangular element have been given, and the authors have extended this approach to deal with 8‐node solid brick elements as well. In the present paper, explicit eigenvalues are given for plane triangular elements and techniques for eigenmode visualization are applied to well‐known triangular and quadrilateral elements. In the companion paper (Part II), the stiffness matrices of solid tetrahedra and bricks are similarly treated.

Citation

KIDGER, D.J. and SMITH, I.M. (1992), "EIGENVALUES OF ELEMENT STIFFNESS MATRICES. PART I: 2‐D PLANE ELEMENTS", Engineering Computations, Vol. 9 No. 3, pp. 307-316. https://doi.org/10.1108/eb023868

Publisher

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MCB UP Ltd

Copyright © 1992, MCB UP Limited