Winkler–Pasternak foundation effect on the static and dynamic analyses of laminated doubly-curved and degenerate shells and panels

By Francesco Tornabene, Nicholas Fantuzzi, Erasmo Viola, J. Reddy. Composites Part B: Engineering, 2014

162 citations recorded by the source corpus.

Abstract This work presents the static and dynamic analyses of laminated doubly-curved shells and panels of revolution resting on the Winkler–Pasternak elastic foundation using the generalized differential quadrature (GDQ) method. The analyses are worked out considering the first-order shear deformation theory (FSDT) for the aforementioned moderately thick structural elements. The solutions are given in terms of generalized displacement components of points lying on the middle surface of the shell. Several types of shell structures such as doubly-curved and revolution shells, singly-curved and degenerate shells are considered in this paper. The main novelty of this paper is the application of the differential geometry within GDQ method to solve doubly-curved shells resting on the Winkler–Pasternak elastic foundation. The discretization of the differential system by means of the GDQ technique leads to a standard linear problem for the static analysis and to a standard linear eigenvalue problem for the dynamic analysis. In order to show the accuracy of this methodology, numerical comparisons between the present formulation and finite element solutions are presented. Very good agreement is observed. Finally, new results are presented to show effects of the Winkler modulus, the Pasternak modulus, and the inertia of the elastic foundation on the behavior of laminated doubly-curved shells.

Subfields: Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/84cd3cad265b79eecd7ea18ffc399282904faefe

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Citations in the corpus

Static analysis of functionally graded conical shells and panels using the generalized unconstrained third order theory coupled with the stress recovery (2014, methodology): “With the in-plane stress components indirectly derived from the GDQ-solution [54–92] of the fundamental system, the integration of the three dimensional indefinite equilibrium equations is carried out.”
Four-parameter functionally graded cracked plates of arbitrary shape: A GDQFEM solution for free vibrations (2016, unknown): “The accuracy, stability, and reliability of GDQ method involving laminated composite and FGM plates and shells have been already presented in the literature by many researches [22–50].”
Static analysis of doubly-curved anisotropic shells and panels using CUF approach, differential geometry and differential quadrature method (2014, background): “The main common aspect of these mesh-less techniques is that the functional approximation starts from a set of scattered points, which do not have any relationship among them [58–60,64–97].”
Strong formulation finite element method for arbitrarily shaped laminated plates - Part I. Theoretical analysis (2014, background): “It has been shown by several papers in literature that sometimes it is convenient to use a different number of grid points when the two coordinate directions have different length MN (Tornabene and Reddy 2013 and Tornabene et al. 2013b, 2014a, b).”