A state of stress and displacement of elastic plates using simple and mixed shear deformation theories

Abstract

This paper presents accurate two-dimensional solutions for bending response of four types of single-layer orthotropic rectangular plates. The plates considered are of the type having two opposite sides simply-supported, and two other sides having combinations of simply-supported, clamped, and free-boundary conditions. Analytical solutions for deflections and stresses of rectangular plates are developed by means of the simple (SFPT) and mixed (MFPT) first-order shear deformable plate theories. The present MFPT not only shows improvement on predicting frequencies, critical buckling loads, deflections and in-plane stresses, but also accounts for variable transverse shear stress distributions through the thickness. This puts into evidence the important role played by MFPT in the modeling of homogeneous plate theories, which in contrast to SFPT does not require the incorporation of a shear-correction factor. For illustrative purposes, sample free vibration, stability, and bending problems for simply supported orthotropic plates are considered and comparisons of the obtained results are made with the exact and higher-order shear deformation theory results given in the literature.