A refined shell theory considering the effects of transverse normal strain for the analysis of functionally graded porous shallow shells with double curvature

Abstract

In this paper, a static and free vibration analysis of functionally graded porous shallow shells with double curvature containing an even distribution of porosity is investigated using a trigonometric shear and normal deformation theory. Both the effects of transverse shear and normal strains are included in the present theory to investigate their effects on the responses of FGM porous shells. The theory satisfies zero transverse shear stress conditions at the top and bottom surfaces of the shell. Hamilton’s principle is used for obtaining governing equations and boundary conditions of the present theory for functionally graded porous shallow shells. The FGM porous shell is assumed isotropic at any point within the shell domain, with its elastic properties varying across its thickness by a power law in terms of the volume fractions of the shell constituents. The simply-supported FG porous shell is analyzed in the present study using the Navier method. The numerical results of FGM porous plates are obtained and compared with other higher-order theories available in the literature to verify the present theory. Further, the numerical results are presented for the FGM porous shells with double curvature. The effects of a/h ratios, porosity distribution factor, and radii of curvature on deflections, stresses, and fundamental frequencies are presented. The solution of hyperbolic and elliptical FGM porous shells is presented for the first time in this paper.