A geometrically nonlinear theory of elastic plates

Abstract

equations follow. It is shown that only five equilibrium equations can be derived in this manner, because the component of virtual rotation about the normal is not independent. These equilibrium equations contain terms which cannot be obtained without the use of a finite rotation vector which contains three nonzero components. These extra terms correspond to the difference of in-plane shear stress resultants in other theories; this difference is a reactive quantity in the present theory. Introduction This paper focuses on geometrically nonlinear analysis (i.e., small strain with possibly large deflections and rotations) of plates-solids with one small dimension and without initial curvature. We note that if all three dimensions of a flexible body are comparable, and if the body is undergoing smallstrain deformation, then the displacement field in addition to rigid-body motion must be small. If, however, one or two dimensions of the body are small relative to the other(s), then even if the strains remain small the body can undergo large deflections

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