The paper focuses on a bi-dimensional (2D) formulation for the dynamic and static analysis of arbitrary shaped laminated doubly-curved shells enforced with general boundary conditions via the Generalized Differential Quadrature (GDQ). Following the Equivalent Single Layer approach, a 2D theory based on a miscel laneous assessment of the displacement field variable is provided, accounting for different higher order theories. The geometry of the structure is described with a set of principal coordinates. The fundamental equations are derived from the Hamil tonian principle, together with the natural boundary conditions. Unconventional constraints are assessed by means of in-plane and out-of-plane sets of linear elastic springs distributed along the shell edges. The accuracy of the formulation is out lined by means of a series of validating examples. Doubly-curved shells of variable thickness and different curvatures enforced with non-conventional boundary con ditions are investigated. In particular, mode frequencies and shapes, as well as the static three-dimensional deflection of the structure, have been calculated employ ing different kinematic assumptions. The results have been successfully compared to predictions by high-computationally demanding Finite Element simulations. The methodology outlined in this chapter well predicts with a reduced computational effort both the static and the dynamic response of generally anisotropic laminated structures embedding all the effects that are usually depicted by 3D formulations.
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