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Two-variable sinusoidal shear and normal deformation theory is used in this paper for elastic analysis of doubly curved nanoshells resting on elastic foundation. Thickness stretching effect is accounted based on higher-order shear and normal deformation theory. The transverse displacement is decomposed into bending and stretching components based on two-variable sinusoidal shear deformation theory. Unlike classical structural theories for plates and shells, the present theory considers an extra variable as transverse displacement along the thickness direction. 3D constitutive relations are presented based on generalized Hooke’s law. The principle of virtual work is used for derivation of governing equations and proper boundary conditions. An extensive parametric analysis is performed to present variation of in-plane and transverse displacements along the thickness direction in terms of the nonlocal parameter, opening angles and foundation characteristics. Comparison of results with and without thickness stretching effect show that the present theory improves results about 4% with respect to the structural theories without stretching effect.

Bending response of FG composite doubly curved nanoshells with thickness stretching via higher-order sinusoidal shear theory