Static and free vibration analysis of doubly-curved functionally graded material shells

Static and free vibration analysis of doubly-curved (cylindrical, spherical, hyperbolic paraboloid, and elliptical paraboloid) functionally graded material (FGM) shells is presented here using various equivalent single-layer shell theories considering the shear deformation and rotary inertia effects. The kinematics of the various shell theories are presented using a generalized shell theory in which the displacement field is independent of the selection of transverse shear strain function which results in a theoretical unification of various equivalent single-layer shell theories. The present generalized formulation yields traction free boundary conditions on the top and bottom surfaces of the shell using constitutive relations. Equations of motion are derived by using Hamilton's principle which are further solved analytically using the Navier's technique of assuming unknown variables in the double trigonometric series. Displacements, stresses, and frequencies are presented for functionally graded cylindrical, spherical, hyperbolic paraboloid, and elliptical paraboloid shells. The present results are compared with previously published results wherever possible to verify the accuracy and efficiency of the present generalized shell theory. Also, this study contributes many new numerical results which can be useful for future researchers.