Nonlinear theory for plates and shells including the effects of transverse shearing

Abstract

Nonlinear strain displacement relations for three-dimensional elasticity are determined in orthogonal curvilinear coordinates. To develop a two-dimensiona l theory, the displacements are expressed by trigonometric series representation through the thickness. The nonlinear strain-displacement relations are expanded into a series that contains all first- and second-degree terms. In the series for the displacements only the first few terms are retained. Insertion of the expansions into the three-dimensional virtual work expression leads to nonlinear equations of equilibrium for laminated and thick plates and shells that include the effects of transverse shearing. Equations of equilibrium and buckling equations are derived for flat plates and cylindrical shells. The shell equations reduce to conventional transverse shearing shell equations when the effects of the trigonometric terms are omitted and to classical shell equations when the trigonometric terms are omitted and the shell is assumed to be thin. Numerical results are presented for the buckling of a thick simply supported flat rectangular plate in longitudinal compression.