ABSTRACT
The preceding chapters of the book were devoted to the study of bending, buckling, and natural vibrations of rectangular plates using the classical plate theory (CPT), in which transverse normal and shear stresses are neglected. The first-order shear deformation plate theory (FSDT) extends the kinematics of the CPT by relaxing the normality restriction (see Section 3.2) and allowing for arbitrary but constant rotation of transverse normals. The third-order shear deformation plate theory (TSDT) further relaxes the kinematic hypothesis by removing the straightness assumption; i.e., straight normal to the middle plane before deformation may become cubic curves after deformation. In this chapter, the first-order and third-order shear deformation plate theories are developed and they are employed in the bending, buckling, and natural vibration analysis of rectangular plates. The most significant difference between the classical and shear deformation
theories is the effect of including transverse shear deformation on the predicted deflections, frequencies, and buckling loads. As will be seen in the sequel, the classical plate theory underpredicts deflections and overpredicts frequencies as well as buckling loads of plates with side-to-thickness ratios of the order of 20 or less (i.e., thick plates). For this reason alone it is necessary to use the first-order or third-order shear deformation plate theory in the analysis of relatively thick plates.
Under the same assumptions and restrictions as in the classical laminate theory, but relaxing the normality condition, the displacement field of the first-order theory can be expressed in the form (Figure 10.1.1)
