Transverse effects in a thick plane anisotropic plate

Abstract

A plate theory is developed for the plane anisotropic plate using Kozik's linear exact displacement formulation to identify the transverse strain contributions and develop the strain-displacement equations required by the matrix-displacement finite element method of solution. Approximations are made for the transverse shear strains and transverse normal strains using a Taylor series expansion. Considerations are given for the relaxation of the Kirchhoff assumptions resulting in four theories of plate flexure. These include: (1) transverse shear, (2) transverse normal strain and stress, (3) bending-plane stress, and (4) bending-plane strain. Boundary conditions are given for simply-supported and clamped plates. Finite element stiffness matrices and force vectors are developed in symbol form using a fifth order displacement function of x and y. The results show that the displacement vector is linear in the transverse coordinate only if the transverse strains identically are zero. Results for simply-supported plates are in good agreement with those of Salerno and Goldberg for transverse shear theory. Results for clamped square plates indicate that transverse shear effects are of primary importance, and transverse normal strain and stress of secondary importance for thickness to width ratios of less than 0.1. However, at a clamped boundary a large increase in the in-plane stress and strain is indicated for transverse normal strain and stress theory and transverse normal stress may be almost as large as in-plane stress due to Poisson's effect.