Nonlinear stability of FGM shallow spherical shells including the effects of transverse shear deformation using analytical approach

This paper represents the nonlinear response of Functionally Graded shallow spherical shells under external uniform distributed transverse loads incorporating shear deformation effects by using modified interaction method to solve the boundary value problem. Material properties are continuously distributed along the thickness and symmetric related to middle surface of the spherical shell according to power-law distribution in terms of volume fractions of constituents. All of the equations for shallow spherical shells are derived by using the first-order shear deformation of the shell theory and specialized for axisymmetric deformation with geometrical non- linearity are taken into consideration. Stability analysis for a clamped spherical shell shows the effects of material and geometric parameters, edge restraint. The closed-form formula represents the equilibrium path, yields to helpful results. Comparison of equilibrium paths using classical and first-order shear deformation theories shows that the increasing of the instability (i.e. difference of upper and lower buckling loads) yields to more considerable effects of the transverse shear deformation. Parametric studies showed that the increasing of the proportional thickness yields decreasing of the instability but for the proportional depth it is invers. The same results obtained for effect of the different values for power law index (k) of functionally graded material (FGM). Increasing the index k results more instability.