Simple Formulation for the Flexure of Plates on Nonlinear Foundation
Publication: Journal of Engineering Mechanics
Volume 134, Issue 1
Abstract
Plates resting on an elastic medium are normally analyzed in a simplified way using the linear Winkler foundation approach. Nevertheless, plates resting on layered medium with vast differences in their moduli exhibit nonlinear behavior under pressure. The present technical note deals with a nonlinear finite-element procedure to analyze plates with linear strain displacement relations resting on a nonlinear elastic media. The coupled problem is formulated using the total potential energy (TPE) concept. The nonlinear foundation stiffness matrices have been derived using the Taylor expansion of the TPE at equilibrium and a symbolism of grouping the energy contributions. The nonlinear foundation stiffness matrices derived in the present technical note have been demonstrated to yield results that agree well with published results in the literature. A brief parametric study on the effects of nonlinearity of the foundation is also presented using the proposed foundation stiffness matrices.
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Acknowledgments
This technical note is published with the kind permission of the Director, Structural Engineering Research Centre, Chennai 600113, India. The writers would like to pay their homage to Professor Liviu Librescu who passed away during the Virginia Tech tragedy (2007). The writers are inspired by Professor Librescu’s work cited in this paper.
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Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 134 • Issue 1 • January 2008
Pages: 110 - 115
Copyright
© 2008 ASCE.
History
Received: Mar 27, 2003
Accepted: Mar 12, 2007
Published online: Jan 1, 2008
Published in print: Jan 2008
Notes
Note. Associate Editor: Arif Masud
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