Dynamic analysis of stiffened bi-directional functionally graded plates with porosities under a moving load by dynamic relaxation method with kinetic damping

Abstract

The principal purpose of this study is investigating the dynamic analysis of porous bi-directional functionally graded (FG) plates reinforced by eccentrically outside stiffeners and subjected to a moving load with a constant velocity. The materials are assumed to be graded in two directions and their effective properties are computed by the rule of mixtures. The FG plates are assumed to have both even and uneven distribution of porosities over the plate cross-section. Using appropriate kinematic relations, the displacements of the plate mid-plane are compatible with those of the stiffeners. The governing differential equations of porous bi-directional FG plates are derived through Hamilton's principle based on the first order shear deformation theory (FSDT) and Von Karman relations for large deflections. Moreover, dynamic relaxation method with kinetic damping (K-DR) coupled with Newmark integration technique are used to solve the plate's time-varying nonlinear equations. The effects of some numerical aspect ratios such as volume fraction, boundary conditions, porosity coefficients and distribution patterns and the existence of stiffeners on dynamic behaviors are investigated. The results show that the stiffness of the porous bi-directional FG plates is highly improved with the aid of eccentric stiffeners; hence, better dynamic behaviors are provided.