In this study, free vibrations of isotropic cylindrical-spherical shell panels connected to each other were investigated. Shells and panels are created by a curve around the central symmetry axis, with a rotation of 360 degrees or less. Equations were extracted using the first-order shear deformation theory, which models the effects of shear deformation and rotational inertia well. Then, assuming Donnell kinematic and Hamilton's principle, the equations of motion for the panels were extracted. The equations were discretized in both x, θ and φ, θ directions, which correspond to cylindrical and spherical sections, respectively, using the extended differential squares method. After equating the derivatives in the equations with a polynomial expansion using the method described, the differential equations were transformed into algebraic equations. In the next step, the natural frequencies of the combined cylindrical-spherical shell panels with different boundary conditions were obtained, and the accuracy of the extracted solutions was verified using Abaqus software and reputable articles. Finally, the effects of parameters such as thickness, length of the cylindrical section, and radius of the spherical section on the natural frequencies of the desired model were investigated.

In this paper, buckling of orthotropic rectangular plates under different loadings was investigated. For this reason, governing buckling equations for an isotropic plate were modified by applying constitutive equations of orthotropic materials. After obtaining the equations of orthotropic plates, Generalized Differential Quadrature method (GDQM) was applied on buckling equations and thus a set of Eigen value equations resulted. In order to solve this Eigen value problem, a computer program was developed using MATLAB software in a way that the influence of different parameters such as length to width ratio (aspect ratio), the number of layers, the angle of layers arrangement, material of layers, kind of loading and boundary conditions were included. A buckling load factor was calculated for simply supported and clamped supported plates. The results of GDQ method were compared with reported results from Rayleigh – Ritz method and with results from solving the Finite element using ANSYS 8.0 software. The comparison showed the accuracy of obtained result clearly.

In this paper, governing equations of transverse vibration of single-layer graphene sheet with different boundary conditions under 2D in-plane magnetic field action, considering its consequent forces and moments, are investigated for the first time using differential quadrature method (DQM). Governing equations of motion are obtained using non-local theory and considering Lorentz's force. The partial differential equations of system are changed to the ordinary differential equations using separation of variables method. Using differential quadrature method, the obtained governing equations are solved for different boundary conditions. The effects of elastic foundation stiffness, non-local parameter, plate aspect ratio and 2D magnetic field effects on the natural frequency of graphene sheet are evaluated. The results show that increase of foundation stiffness, non-local parameter and aspect ratio result in increase of fundamental frequency, in all boundary conditions. But, action of in-plane magnetic field results in decrease of fundamental frequency, because of decreasing flexural stiffness and increasing in-plane pressure loading.

In this research, the free vibration of the joint of two hybrid cylindrical-conical shells have been studied, considering the continuity conditions in the joint of the two shells, based on the first order shear deformation shell theory. The equations of the joint of two shells have been extracted using the Hamilton’s principle, and solved by applying the generalized differential quadrature method under different boundary conditions. Also, hybrid shells are composed of composite layers in the core and two layers of aluminum metal at the top and bottom of the shells. In this study, the Carbon-Epoxy, Glass-Epoxy and Aramid-Epoxy composite materials are used. The results obtained in this research are compared with previous studies, and there is a very good agreement between the results. Also, the effects of cone angle of the conical shell, boundary conditions, volume fraction, circumferential mode, composite materials, variation of length to shell radius and variation of thickness to shell radius, on the natural frequency have been investigated. The results have shown that, with the increase of the cone angle of the conical shell, the dimensionless natural frequency of the joint of two cylindrical-conical shells increased. Also, with increase of the circumferential mode, the non-dimensional frequency of the structure of two joined hybrid shells, first decreased and then increased.

In this paper thermal buckling of a thin cylindrical panel made of piezo-magnetic two dimensional functionally graded materials (2D-PFGM) subjected to magnetic field have been investigated. The material properties of structure assumed varying by exponential functions of volume fraction in longitudinal and circumferential directions. In order to solving the problem at the first, the equilibrium equations have been derived by the first order shear deformation theory by concerning the nonlinear terms from the strain-displacement relations. In the next step, by giving the incremental changes on the displacement components and calculating the resultant forces and moments, using Lagrang, s equations on the second functional of potential energy the stability equations have been derived. After solution the mentioned equations by generalized differential quadrature method based on the simply supported boundary conditions the critical buckling temperature has been determined. By solving the numerical example in special cases and comparing the obtained results we confident from the method of analysis. At the end, effect of geometrical features, applied voltage on the external surface of panel, and changing the material properties on the critical buckling load have been investigated.

In this paper the generalized differential quadrature method (GDQM) is presented for easy and effective bending analysis of composite sandwich plates with symmetric angle-ply face sheets under static loading based on the first order shear deformation theory (FSDT). The bending behavior of composite sandwich plates with various combinations of boundary conditions is studied. The effects of fiber orientation, ratio of thickness to length of the plate, the ratio of thickness of core to thickness of the face sheet are studied on the transverse displacement rotation about mid-plane and moment resultants. Comparisons are made with the existing solutions. The obtained graphs give very good results due to optimum design of sandwich plates. It has been found that a fast convergent rate can be achieved by the GDQM with non-uniform grids and very accurate results are obtained.

In this paper, vibration analysis of thick functionally graded beam with simply supported boundary condition under constant axial load is studied. The beam has a uniform cross-sectional area and the mechanical properties of the fungtionally graded beam are assumed to be vary through the thickness of the beam. Fundamental relations, the equilibrium and stability equations based on the displacement components are derived using the two-dimensional elasticity theory and hamilton's principle. Generalized differential quadrature (GDQ) method is used to solve the system of coupled differential equations at equilibrium and moving condition. In this paper, the influences of axial loads, dimensionless geometric parameter, functionally graded index and ratio of thickness to length on the vibration of beam is presented. To study the accuracy of the present analysis, a compression is carried out between the present results and published results and also results obtained from ABAQUSE program. Results showed that the generalized differential quadrature method is quite good. Based on the results obtained by increasing the volume fraction of fibers in the functional graded beam, the natural frequency of the beam increases and for high volume fraction, it is not possible to see much change in the natural frequency. Also, by increasing the ratio of thickness to length in the absence of the critical load the natural frequency decreased.

The following article investigates buckling of moderately thick circular Nano plates with an orthotropic property under uniform radial compressive in-plane mechanical load. Taking into account nonlocal elasticity theory (Eringen), principle of virtual work, first order shear deformation plate theory (FSDT) and nonlinear Von-Karman strains, the governing equations are obtained based on the displacements. The stability equations are derived from the neighbor equilibrium state. The differential quadrature method (DQM) as a numerical procedure is applied to discretize the derivatives of equations with a non-uniform mesh point distribution (Chebyshev-Gauss-Lobatto). The accuracy of the present results is validated by comparing the solutions with those reported in the available literatures. The effect of nonlocal parameter, thickness and radius are investigated on non-dimension of buckling loads. From results, it is possible to see that the non-dimension of buckling load of Graphene sheets increases by decreasing flexibility of boundary condition and increasing the rate of nonlocal parameter. It is possible to observe that by increasing the non-dimensional thickness of the plate, the non-dimension of buckling load reduces.