A HIGHER-ORDER PLATE-THEORY WITH IDEAL FINITE-ELEMENT SUITABILITY

A variational tenth-order theory for stretching and bending of orthotropic elastic plates is proposed which lends itself perfectly to finite element formulations based upon C-0 and C-1-continuous displacement approximations. The deformations due to all strain and stress components are accounted. The theory is derived from three-dimensional elasticity via a modified virtual work statement based upon independent displacement and transverse strain expansions through the thickness. The transverse displacement employs a special parabolic form while the in-plane displacements are taken to be linear. The issues of thickness-expansion related inconsistencies in the transverse shear strains and the transverse normal stress are resolved by the enforcement of physical stress boundary conditions and variationally consistent 'weak' transverse strain compatibility. The resulting transverse shear strains are parabolic, while the transverse normal strain 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. A simple three-node plate element is then developed comparable in computational efficiency to its Mindlin-theory counterpart but which enables accurate computation of all displacement, strain and stress components for a wide range of the plate span-to-thickness ratio.