Bending response of functionally graded shallow shells under the action of non-linear thermomechanical loading considering the effects of transverse normal strain

Abstract

In this article, the bending response of single-layer functionally graded shells of double curvature is investigated under non-linear thermomechanical loadings with simply supported boundary conditions. A higher-order trigonometric shear and normal deformation theory is applied to the present study. The theory satisfies the traction-free boundary condition at the shell’s extreme top and bottom surfaces and gives a cosine distribution of transverse shear stresses through the thickness. The principle of virtual work is employed to obtain the governing differential equations. The Navier solution technique is used further to solve governing equations for the simply supported boundary conditions of the shell. The present study mainly focuses on the study of effects of transverse normal strain, shear deformation, radii of curvature, and volume fraction distributions on the bending response of shells of double curvature, such as cylindrical, spherical, hyperbolic, and elliptical. Since very little or no literatures are available on thermomechanical analysis of functionally graded shells in the open literature, the authors have formulated parabolic shear and normal deformation theory and first-order shear deformation theory to compare the present results. The numerical results of hyperbolic and elliptical shells will be a benchmark for future researchers.