An efficient standard plate theory

Abstract

A new standard plate theory, that accounts for cosine shear stress distribution and free boundary conditions for shear stress upon the top and bottom surfaces of the plate, is presented. The theory is of the same order of complexity as the first order shear deformation theory, but does not use shear correction factors, and is more efficient than the first order shear deformation theory and some refined plate theories. The theory is based on the kinematical approach in which the shear is represented by a certain sinusoidal function. The boundary value problem is deduced from the virtual power principle. In order to assess the accuracy of the proposed theory, several significant problems are investigated: bending, free undamped vibration and buckling of a three-layered (sandwich and laminated), symmetric cross-ply, rectangular or square plate simply supported along all edges; wave propagation; torsion of a rectangular plate; edge effect on the stress distribution at the edge of a circular hole in a large rectangular bent plate. For purposes of comparison, numerical results from the exact three-dimensional elasticity theory and several well known approximated theories are also presented. It is found that the proposed approach, which is very simple, is also very efficient for analysing the above problems which are significant for global responses to thick multilayered plates and edge effects. The present theory is therefore a real standard tool. Finally, some indications are given for extending the theory to shells and for obtaining refinements when necessary.