A three variable refined shear deformation theory for porous functionally graded doubly curved shell analysis

This study develops a three variable refined shear deformation theory to analyze the free vibration and bending behavior of porous functionally graded doubly curved shallow shells subjected to uniform and sinusoidal pressure. Shell displacements are assumed to be caused by extensional, bending, and shear effects. The in-plane displacements produced by bending effects are considered taking the form of the classical plate theory. The in-plane displacements produced by shear effects satisfy the stress-free and strain-free condition at the top and bottom surfaces, eliminating the usage of the shear correction factor in the present study. Two porosity types influence material properties and structure behaviors in different aspects. Hamilton's principle is used to derive Euler-Lagrange equations. Spatial solutions for the differential equation are assumed satisfying boundary conditions and their time-dependent amplitude equations are obtained by applying the Bubnov-Galerkin technique. Natural frequencies and transverse deflections of the shell in different geometry configurations and different porosity types and degrees are obtained and compared. The proposed theory is proved feasible to be applied in the analysis of functionally graded plates and shells with porosity. (C) 2019 Elsevier Masson SAS. All rights reserved.