Strong Formulation Finite Element Method Based on Differential Quadrature: A Survey

General higher-order shear deformation theories for the free vibration analysis of completely doubly-curved laminated shells and panels

Electro-mechanical vibration analysis of functionally graded piezoelectric porous plates in the translation state

The Generalized Differential Quadrature (GDQ) Method is applied to study four parameter functionally graded and laminated composite shells and panels of revolution. The mechanical model is based on the so-called First-order Shear Deformation Theory (FSDT), in particular on the Toorani-Lakis Theory. The solution is given in terms of generalized displacement components of points lying on the middle surface of the shell. The generalized strains and stress resultants are evaluated by applying the Differential Quadrature rule to the generalized displacements. The transverse shear and normal stress profiles through the thickness are reconstructed a posteriori by using local three-dimensional elasticity equilibrium equations. In order to verify the accuracy of the present method, GDQ results are compared with the ones obtained with semi-analytical formulations and with 3D finite element method. A parametric study is performed to illustrate the influence of the parameters on the mechanical behavior of functionally graded shell structures made of a mixture of ceramics and metal.

Static analysis of functionally graded doubly-curved shells and panels of revolution

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.

Yang Li

Papers

Free vibration of a functionally graded piezoelectric beam via state-space based differential quadrature