Nonlinear Theory for Flexural Motions of Thin Elastic Plate—Part 1: Higher-Order Theory

Abstract

This paper develops a comprehensive higher-order theory for flexural motions of a thin elastic plate, in which the effect of finite thickness of the plate and that of small but finite deformation are taken into account. Based on the theory of nonlinear elasticity for a homogeneous and isotropic solid, the nonlinear equations for the flexural motions coupled with the extensional motions are systematically derived by the moment asymptotic expansion method. Denoting by ε the ratio of the thickness of the plate to a characteristic wavelength of flexural motions, an order of characteristic deflection is assumed to be ε2 and that of a characteristic strain ε3 . The displacement and stress components are sought consistently up to the next higher-order terms than those in the classical theory.