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Solution of clamped rectangular plate problems

Robert L. TaylorDepartment of Civil and Environmental Engineering, Structural Engineering, Mechanics, and Materials, University of California, Berkeley, CA, U.S.ASanjay GovindjeeDepartment of Civil and Environmental Engineering, Structural Engineering, Mechanics, and Materials, University of California, Berkeley, CA, U.S.A

2004en

ABI

Annotatsiya

Abstract In this brief note, we present an efficient scheme for determining very accurate solutions to the clamped rectangular plate problem. The method is based upon the classical double cosine series expansion and an exploitation of the Sherman–Morrison–Woodbury formula. If the cosine expansion involves M terms and N terms in the two plate axes directions, then the classical method for this problem involves solving a system of ( MN ) × ( MN ) equations. Our proposal reduces the problem down to a system of well‐conditioned N × N equations (or M × M when M < N ). Numerical solutions for rectangular plates with various side ratios are presented and compared to the solution generated via Hencky's method. Corrections to classical results and additional digits for use in finite‐element convergence studies are given. As an application example, these are used to show the rate of convergence for thin plate finite‐element solutions computed using the Bogner–Fox–Schmit element. Copyright © 2004 John Wiley & Sons, Ltd.

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Identifikatorlar

DOI: 10.1002/cnm.652

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