Nonlinear postbuckling of imperfect doubly curved thin shallow FGM shells resting on elastic foundations and subjected to mechanical loads

The nonlinear response of buckling and posbuckling of imperfect thin functionally graded doubly curved thin shallow shells resting on elastic foundations and subjected to some mechanical loads is investigated analytically. The elastic moduli of materials, Young's modulus, and Poisson ratio are all graded in the shell thickness direction according to a simple power-law in terms of volume fractions of constituents. All formulations are based on the classical theory of shells with account of geometrical nonlinearity, an initial geometrical imperfection, and a Pasternak-type elastic foundation. By employing the Galerkin method, explicit relations for the load-deflection curves of simply supported doubly curved shallow FGM shells are determined. The effects of material and geometrical properties, foundation stiffness, and imperfection of shells on the buckling and postbuckling loadcarrying capacity of spherical and cylindrical shallow FGM shells are analyzed and discussed.