Higher-Order Plate Theory with Ideal Finite Element Suitability.

摘要

A variationally consistent tenth-order displacement theory of stretching and bending of orthotropic elastic plates is proposed which leads itself perfectly to finite element formulations based upon C and C-continuous displacement approximations. The deformations due to all strain and stress components are accounted. The theory is derived from three-dimensional elasticity via the principle of virtual work by expanding the displacement components with respect to the thickness coordinate by means of Legendre polynomials, where the transverse displacement is of a special parabolic form while the inplane displacements are linear. The issues of thickness-expansion related inconsistencies in the transverse shear strains and the transverse normal stress are resolved in a rational fashion. The resulting parabolic shear strains incorporate Reissner's shear correction factor, while the transverse normal stain varies cubically across the plate thickness. The variational principle yields seven equations of motion and exclusively Poisson-type edge boundary conditions. A qualitative assessment of the theory is carried out for the problem of static equilibrium involving an infinite plate under a sinusoidal normal pressure. Pertinent issues on the particular suitability of the theory for the development of efficient displacement plate elements are discussed. (rrh)