Meshfree investigation of the vibrational behavior of pre-stressed laminated composite plates based on a variationally consistent plate model

Abstract

The vibrational behavior of pre-stressed laminated composite plates is numerically investigated based on a variationally consistent shear deformation plate theory. The numerical analyses are performed by the use of meshfree radial point interpolation method (RPIM). The plate model utilized in this investigation is the Wang and Shi's [1] plate theory which accounts for continuity of interlaminar transverse shearing stresses and zigzag variation of displacement field through the plate's thickness. Firstly, the governing equations for the free vibration of pre-stressed laminated and sandwich plates based on the Wang and Shi's model are derived through the Hamilton's principle. Subsequently, the weak-form of the governing equations is obtained, and the meshfree RPIM is utilized for construction of the discretized system of equations. Several numerical examples with different Young's modulus ratios, side to thickness ratios, boundary conditions, and lamination schemes are presented in order to illustrate the accuracy of the plate theory adopted in this paper. These examples are also analyzed using the first order shear deformation theory (FSDT), the third order shear deformation theory (TSDT), and also the Shi's [2] plate theory in order to investigate the effect of different factors of plate theories on the accuracy of results in various situations.