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Title: Refined plate theory and its variants
Authors: SHIMPI, RP
Issue Date: 2002
Citation: AIAA JOURNAL, 40(1), 137-146
Abstract: The development of a new refined plate theory and its two simple variants is given. The theories have strong commonality with the equations of classical plate theory (CPT). However, unlike CPT, these theories assume that lateral and axial displacements have bending and shear components such that bending components do not contribute toward shear forces and, likewise, shearing components do not contribute toward bending moments. The theory and one of its variants are variationally consistent, whereas the second variant is variationally inconsistent and uses the relationships between moments, shear forces, and loading. It should be noted that, unlike any other refined plate theory, the governing equation as well as the expressions for moments and shear forces associated with this variant are identical to those associated with the CPT, save for the appearance of a subscript. The effectiveness of the theory and its variants is demonstrated through an example. Surprisingly, the answers obtained by both the variants of the 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, first raised by Levinson, about the so called superiority of variationally consistent methods.
ISSN: 0001-1452
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