A deflection theory for anisotropic plates in which coupling between lateral deflection and in-plane displacement is present and the effect of coupling on the buckling load

Abstract

The first purpose of the present paper is to provide an elastic theory from which problems involving coupling may be approached. Potential energy and equilibrium expressions will be derived for these are the components of the theory which are lacking. The potential energy expression may be used either in small- or large-deflection analysis. Equations of equilibrium are presented for both small- and large-deflection theory.

The second purpose of the present paper is to determine the effect of coupling on deflections and buckling of a simple supported anisotropic plate in compression. A small deflection analysis of this problem is made using the theory presented herein. No large deflection analysis is attempted; however, an estimation of the large deflection effect of coupling is made.

The electric theory presented herein forms a basis from which problems involving coupling may be treated. The significance of coupling is most apparent in problems which would involve stability considerations in the absence of coupling. The presence of deflections due to coupling prior to reaching the uncoupled buckling load forces the problem to be treated asa one of deflections rather than stability. Coupling has a general detrimental effect upon this type of problem in that it lowers the load at which deflections grow rapidly (that is, buckling in the uncoupled case).

The effect of coupling on the buckling of plates of equal bending stiffnesses in their two orthogonal directions becomes negligible as the aspect ratio of the plate becomes large. Some lateral deflection prior to buckling will occur, however, even for large aspect ratios.

The general anisotropic plate is considered in the small-deflections solution to the differential equation of equilibrium. Computations were made for cases in which the bending stiffness were equal. The equations and methods are applicable to cases in which the bending stiffness are not equal.