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Refined plate theory and its variants

Authors: SHIMPI, RP;

Refined plate theory and its variants

Abstract

Thedevelopmentofa newree ned platetheoryand its two simplevariantsisgiven. Thetheorieshavestrongcommonality withtheequationsofclassicalplatetheory (CPT).However,unlikeCPT,thesetheoriesassumethatlateral and axial displacements have bending and shear components such that bending components do not contribute toward shearforces and, likewise, shearing components do not contribute toward bending moments. The theory and one of its variants are variationally consistent, whereasthesecond variant isvariationally inconsistent and usesthe relationships between moments, shear forces, and loading. It should be noted that, unlike any other ree ned plate theory, thegoverning equation as well as the expressions for moments and shear forces associated with thisvariant areidentical tothoseassociated withtheCPT,savefortheappearanceofasubscript. Theeffectivenessofthetheory and itsvariantsisdemonstratedthroughanexample. Surprisingly,theanswersobtained by boththevariantsofthe theory, one of which is variationally consistent and the other one is inconsistent, are same. The numerical example studied, therefore, not only brings out the effectiveness of the theories presented, but also, albeit unintentionally, supports the doubts, e rst raised by Levinson, about the so called superiority of variationally consistent methods.

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India
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
338
Top 1%
Top 1%
Average
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