Finite element approach for free vibration and transient response of bi-directional functionally graded sandwich porous skew-plates with variable thickness subjected to blast load

Abstract

At the first time, the finite element method was used to model and analyze the free vibration and transient response of non-uniform thickness bi-directional functionally graded sandwich porous (BFGSP) skew plates. The whole BFGSP skew-plates is placed on a variable visco-elastic foundation (VEF) in the hygro-thermal environment and subjected to the blast load. The BFGSP skew-plate thickness is permitted to vary non-linearly over both the length and width of the skew-plate, thereby faithfully representing the real behavior of the structure itself. The analysis is based on a four-node planar quadrilateral element with eight degrees of freedom per node, which is approximated using Lagrange Q₄ shape function and C¹ level non-conforming Hermite shape function based on refined higher-order shear deformation plate theory. The forced vibration parameters of the non-uniform thickness BFGSP skew-plate are fully determined using Hamilton's principle and the Newmark-β direct integration technique. Accuracy of the calculation program is validated by comparing its numerical results with those from reputable sources. Furthermore, a thorough assessment is conducted to determine the impact of various parameters on the free and forced vibration responses of the non-uniform thickness BFGSP skew-plate. The findings of the paper may be used in the development of civil and military structures in situations that are prone to exceptional forces, such as explosions and impacts load.