A REFINED FIRST-ORDER SHEAR-DEFORMATION THEORY AND ITS JUSTIFICATION BY PLANE-STRAIN BENDING PROBLEM OF LAMINATED PLATES

A refined first-order shear-deformation theory is proposed and used to solve the plane-strain bending problem of both homogeneous plates and symmetric cross-ply laminated plates. In Reissner-Mindlin's tradition al first-order shear-deformation theory (FSDT), the displacement field assumptions include a linear inplane displacement component and a con stant transverse deflection through the thickness. These assumptions a re retained in the present refined theory. However, the associated tra nsverse shear strain derived from these displacement assumptions, whic h is still independent of the thickness coordinate, is endowed with ne w meaning-the stress-weighted average shear strain through the thickne ss. The variable distribution of transverse shear strain is assumed in such a way that it agrees with the shear stress distribution derived from the integration of equilibrium equation. This paper introduces th e effective transverse shear stiffness of plates by assuming that the normalized distribution of through-the-thickness transverse shear stre ss remains unchanged regardless of geometrical configuration (span-to- thickness ratio) for plane-strain bending problem, which is justified by the exact elasticity solution. Without losing the simplicity of the displacement field assumptions of Reissner-Mindlin's FSDT, the presen t refined first-order theory not only shows improvement on predicting deflections but also accounts for a Variable transverse shear strain d istribution through the thickness. In addition, all the boundary condi tions, equilibrium equations, and constitutive relations are satisfied pointwise. Comparisons of deflection, transverse shear strain? and tr ansverse shear stress obtained using the present theory are made with the exact results given by Pagano.