F. Tornabene and E. Viola, “Free Vibrations of Four-Parameter Functionally Graded Parabolic Panels and Shell of Revolution,” European Journal of Mechanics—A/Solids, Vol. 28, No. 5, 2009, pp. 991-1013. doi10.1016/j.euromechsol.2009.04.005 - References

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F. Tornabene and E. Viola, “Free Vibrations of Four-Parameter Functionally Graded Parabolic Panels and Shell of Revolution,” European Journal of Mechanics—A/Solids, Vol. 28, No. 5, 2009, pp. 991-1013. doi:10.1016/j.euromechsol.2009.04.005

has been cited by the following article:

TITLE: Free-Form Laminated Doubly-Curved Shells and Panels of Revolution Resting on Winkler-Pasternak Elastic Foundations: A 2-D GDQ Solution for Static and Free Vibration Analysis

AUTHORS: Francesco Tornabene, Alessandro Ceruti

KEYWORDS: Doubly-Curved Shells of Revolution; Rational Bézier Curves; Laminated Composite Shells; Winkler-Pasternak Foundation; First-Order Shear Deformation Theory; Generalized Differential Quadrature Method

JOURNAL NAME: World Journal of Mechanics, Vol.3 No.1, February 7, 2013

ABSTRACT: This work presents the static and dynamic analyses of laminated doubly-curved shells and panels of revolution resting on Winkler-Pasternak elastic foundations using the Generalized Differential Quadrature (GDQ) method. The analyses are worked out considering the First-order Shear Deformation Theory (FSDT) for the above mentioned moderately thick structural elements. The effect of the shell curvatures is included from the beginning of the theory formulation in the kinematic model. The solutions are given in terms of generalized displacement components of points lying on the middle surface of the shell. Simple Rational Bézier curves are used to define the meridian curve of the revolution structures. The discretization of the 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. Comparisons between the present formulation and the Reissner-Mindlin theory are presented. Furthermore, GDQ results are compared with those obtained by using commercial programs. Very good agreement is observed. Finally, new results are presented in order to investtigate the effects of the Winkler modulus, the Pasternak modulus and the inertia of the elastic foundation on the behavior of laminated shells of revolution.