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.
Highlights
During the last sixty years, two-dimensional linear theories of thin shells have been developed including important contributions by Timoshenko and Woinowsky-Krieger [1], Flügge [2], Gol’denveizer [3], Novozhilov [4], Vlasov [5], Ambartusumyan [6], Kraus [7], Leissa [8,9], Markuš [10], Ventsel and Krauthammer [11] and Soedel [12]
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 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
Summary
During the last sixty years, two-dimensional linear theories of thin shells have been developed including important contributions by Timoshenko and Woinowsky-Krieger [1], Flügge [2], Gol’denveizer [3], Novozhilov [4], Vlasov [5], Ambartusumyan [6], Kraus [7], Leissa [8,9], Markuš [10], Ventsel and Krauthammer [11] and Soedel [12]. Effect of the initial curvature in the evaluation of the stress resultants a generalization of the Reissner-Mindlin (RM) theory has been proposed in literature by Kraus [7], Qatu [16,17] and Toorani and Lakis [18,19]. In the present work their kinematic model is used in order to include the effect of the curvature from the beginning of the shell formulation In this way, the strain relationships have to change and, as a consequence, the equilibrium equations in terms of displacements have to be modified. The first is the improvement of the Reissner-Mindlin Theory using a different kinematical model In this way the effect of the curvature of the shell structure is considered from the beginning of the theory derivation. The fourth is the use of the Generalized Differential Quadrature method to solve the governing shell equations
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