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 traditional first-order shear-deformation theory (FSDT), the displacement field assumptions include a linear inplane displacement component and a constant transverse deflection through the thickness. These assumptions are retained in the present refined theory. However, the associated transverse shear strain derived from these displacement assumptions, which is still independent of the thickness coordinate, is endowed with new meaning-the stress-weighted average shear strain through the thickness. 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 the effective transverse shear stiffness of plates by assuming that the normalized distribution of through-the-thickness transverse shear stress 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 present refined first-order theory not only shows improvement on predicting deflections but also accounts for a Variable transverse shear strain distribution through the thickness. In addition, all the boundary conditions, equilibrium equations, and constitutive relations are satisfied pointwise. Comparisons of deflection, transverse shear strain? and transverse shear stress obtained using the present theory are made with the exact results given by Pagano.