Transverse Vibration of Mindlin Plates on Two-Parameter Foundations by Analytical Trapezoidal -Elements
Publication: Journal of Engineering Mechanics
Volume 131, Issue 11
Abstract
An analytical trapezoidal hierarchical element for the transverse vibration of Mindlin plates resting on two-parameter foundations is presented. Legendre orthogonal polynomials are used as enriching shape functions to avoid the shear-locking problem and to improve considerably the computational efficiency. Element matrices are integrated in closed form eliminating the numerical integration errors conventionally found. With the continuity requirement, the element can be used to analyze any triangular and polygonal plates without difficulty, while the Kirchhoff -version elements requiring continuity are not as versatile. The computed natural frequencies for rectangular, skew, trapezoidal, triangular, annular, and polygonal plates on two-parameter foundations show that the convergence of the proposed element is very fast compared to the conventional linear finite elements with respect to the number of degrees of freedom used. Many numerical examples are given.
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Acknowledgment
The research is supported by the Hong Kong Research Grant Council Grant No. UNSPECIFIEDCityU 1009/02E.
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Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 131 • Issue 11 • November 2005
Pages: 1140 - 1145
Copyright
© 2005 ASCE.
History
Received: Jul 29, 2003
Accepted: Feb 22, 2005
Published online: Nov 1, 2005
Published in print: Nov 2005
Notes
Note. Associate Editor: Stein Sture
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