A refined higher-order generally orthotropic C⁰ plate bending element

Abstract

A finite element formulation for flexure of a generally orthotropic plate based on a higher-order displacement model and a three-dimensional state of stress and strain is presented here. This higher-order theory incorporates linear variation of transverse normal strain/stress and parabolic variation of transverse shear strains through the thickness of the plate. The nine-noded quadrilateral from the family of two-dimensional C⁰ continuous isoparametric Lagrangian elements is then developed as a generally orthotropic higher-order element. The performance of this element is evaluated on square plates with different support conditions and under uniformly distributed and central point loads. The numerical results of the present formulation are compared with thin plate, elasticity and Mindlin/Reissner solutions. The effect of degree of orthotropy on the maximum bending moment location is examined for different loading and boundary conditions. The effect of directional orthotropy on the location of the maximum values for the various stress-resultants is also studied.