Effects of transverse normal strain on the bending response of functionally graded shells under the action of hygrothermomechanical loading

This study examined the bending behavior of functionally graded (FG) material shells with single-layer-double curvature (spherical, cylindrical, hyperbolic, and elliptical), under the action of both linear and non-linear hygrothermomechanical loads. A simply supported boundary conditions of the shell are used. The elastic properties, thermal expansion coefficient, and moisture expansion coefficients are assumed to vary along the direction of thickness following a power-law distribution of material gradation. The traction-free boundary conditions of shear stresses are satisfied at the top and bottom surfaces of the shell, resulting in a cosine distribution of transverse shear stresses. The principle of virtual work is used to obtain the governing differential equation, which is then solved using the Navier solution technique. The effect of transverse displacement is divided into thickness stretching, bending, and shear effect, which facilitates in predicting the behavior of FGM shells under hygrothermomechanical loading more accurately. The theory considers both the effects of transverse shear and normal strains, which is strongly recommended in the well-established literature. The main objective of this research is to explore how transverse normal strain (with and without), shear deformation, radii of curvature, and volume fraction distribution affect FGM shell bending response under hygrothermomechanical loading. All obtained results are presented in a non-dimensional form and validated by developing higher-order trigonometric shell theory, parabolic shell theory, and first-order shell theory. Many results are presented for the first time in this article and can be used as benchmark for future research studies.