Applicability of the Large-deflection Theory on Thick Plates

Abstract

In recent years, composite materials including synthetic resins are widely used as structural materials for plates. For such structures, large-deflection is often allowed, so that large deformation analysis becomes necessary. To such an end, von Kármán large-deflection theory of plate bending has been mainly used. This theory is, however, based on essentially the same assumptions as those of classical Lagrange's thin plate theory for infinitesimal deformation, except that the magnitude of the deflection is permitted up to the order of the plate thickness. Thus the applicability of such a theory may be doubtful for thick plate. In this paper, we examine the applicability of the above theory to uniformly loaded clamped circular plates with various different thickness by comparing with appropriate numerical solutions. The numerical method enployed here is a three-dimensional finite element method based on the incremental finite-deformation theory formulated in convected coordinates. From the obtained numerical results, the applicability of the considered theory is confirmed if the magnitude of maximum deflection is within 4 times the plate thickness.