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Analysis of the effect of Pasternak’s elastic foundation parameters on the bending and free vibration of functionally graded double curved shells subjected to uniform and sinusoidal loads is the purpose of this paper in which the novelty is to develop a new formulated 2D and quasi-3D HSDT shell theories with considering the effect of transverse shear and shell thickness stretching. Numerical results are reported for different geometries including plates, cylindrical and spherical shells using a five-variable displacement field in terms of undetermined integrals by employing a trigonometric-exponential hybrid function. The impact of geometrical parameters, volume fraction and foundation stiffness on the static and vibratory behaviors is extensively discussed. Convergence studies and error analysis are carried out to validate the present approach. The proposed theory proves to be simple and useful in the analysis of double-curved FGM shells.
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