Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



An improved estimate for the error in the classical, linear theory of plate bending

Author: James G. Simmonds
Journal: Quart. Appl. Math. 29 (1971), 439-447
DOI: https://doi.org/10.1090/qam/99753
MathSciNet review: QAM99753
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Abstract: The relative mean square error in the three-dimensional stress field predicted by classical plate theory is shown to be $ O{\left( {h/{L_ * }} \right)^2}$, where $ h$ is the plate thickness and $ {L_ * }$ is a mean square measure of the wavelength of the midplane deformation pattern. This improves a recent result of Nordgren who obtained a relative error estimate of $ O\left( {h/{L_ * }} \right)$. The improved error estimate, which, like Nordgren's, is based on the Prager--Synge hypercircle theorem in elasticity, is obtained by constructing a kinematically admissible three-dimensional displacement field that depends on the solution of the classical plate equations but which yields an accurate, nonzero distribution of the transverse shearing strain through the thickness.

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DOI: https://doi.org/10.1090/qam/99753
Article copyright: © Copyright 1971 American Mathematical Society

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