Shear deformation plate and shell theories: From Stavsky to present

In this paper, a review of the shear deformation plate and shell theories is presented and a consistent third-order theory for composite shells is proposed. The discussion of plate and shell theories from Stavsky to the present is largely a review of various theories for modeling laminated shells, including shear effects and some analytical studies. Following this discussion, a finite element formulation of the proposed theory is developed. The formulation has seven displacement functions satisfying the tangential traction-free conditions on the inner and outer surfaces of the shell. Exact computations of stress resultants are carried out through numerical integration of material stiffness coefficients of the laminate. Numerical examples are presented for typical benchmark problems involving isotropic and composite plates, and cylindrical and spherical shells.

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