Static Buckling of 2D FG Porous Plates Resting on Elastic Foundation based on Unified Shear Theories

This article develops a mathematical model to study the static stability of bi-directional functionally graded porous unified plate (BDFGPUP) resting on elastic foundation. The power function distribution is proposed for the gradation of material constituent through thickness and axial directions. Three types of porosity are selected to portray the distribution of voids and cavities through the thickness of the plate. Unified theories of plate are exploited to present the kinematic fields and satisfy the zero-shear strain/stress at the top and bottom surfaces without shear correction factor. Hamilton???s principle is employed to derive the governing equations of motions including the higher terms of force resultants. An efficient numerical method namely differential integral quadrature method (DIQM) is manipulated to discretize the structure spatial domain and transform the coupled variable coefficients partial differential equations to a system of algebraic equations. Problem validation and verification have been proven with previous works for bucking phenomenon. Parametric studies are exemplified to exhibit the significant impacts of kinematic shear relations, gradation indices, porosity type, and boundary conditions on the static stability and buckling loads of BDFGP plate. The proposed model is economical in different applications in nuclear, mechanical, aerospace, naval, dental and medical fields.