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The main purpose of this study is to investigate nonlinear bending and buckling analysis of radially functionally graded annular plates subjected to uniform in-plane compressive loads by Dynamic Relaxation method. The mechanical properties of plates assumed to vary continuously along the radial direction by the Mori–Tanaka distribution. The nonlinear formulations are based on first order shear deformation theory (FSDT) and large deflection von Karman equations. The dynamic relaxation (DR) method combined with the finite difference discretization technique is employed to solve the equilibrium equations. Due to the lack of similar research for the bending and buckling of functionally graded annular plates with material variation in the radial direction, some results are compared with the ones obtained by the Abaqus finite element software. Furthermore, some comparison study is carried out to compare the current solution with the results reported in the literature for annular isotropic plates. The achieved good agreements between the results indicate the accuracy of the present numerical method. Finally, numerical results for the maximum displacement and critical buckling load for various boundary conditions, effects of grading index, thickness-to-radius ratio and inner radius -to-outer radius ratio are presented.

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In this paper, the governing equations for a vibratory beam with moderately large deflection are derived using the first order shear deformation theory. These equations which are a system of nonlinear partial differential equations with constant coefficients are solved analytically with the perturbation technique and the natural frequencies and the buckling load of the system are determined. A parametric study is performed and the effects of the geometrical and material properties on the natural frequency and buckling load are investigated and the effect of normal transverse strain and axial load on natural frequency are examined. Some results based on the first order shear deformation theory are consistent with classic theories of beams and some yield different results. Formulation presented to calculate the transverse frequency, determines the axial frequency too. Also, the natural frequencies and buckling load are calculated with the finite elements method by applying one and three-dimensional elements and the results are compared with the analytical solution.

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In this paper, the buckling of rectangular plates subjected to non-uniform in-plane loading is investigated. At first the equilibrium equations of plate based on the first order shear deformation theory have been extracted. The kinematic relations have been assumed based on the von-Karman model and the Hook’s law has been considered as the constitutive equations. The adjacent equilibrium method has been used for deriving the stability equations. The equilibrium equations which are related to the prebuckling stress distribution, have been solved using the differential equations theory. To determine the buckling load of a simply supported plate, the Galerkin method has been used for solving the stability equations which are a system of differential equations with variable coefficients. In this paper, four types of in-plane loading, including the uniform, parabolic, cosine and triangular loading, have been considered and the effects of the plate aspect ratio and thickness on the buckling load has been investigated and the results have been compared with the finite element method and the classical plate theory. The comparison of the results show that for all loading cases, the buckling load computed by the classical plate theory is higher than the value obtained based on first order shear deformation theory.

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In this paper, free vibration of two-dimensional functionally graded (2D-FG) annular sectorial plate surrounded by Winkler-Pasternak elastic foundation has been investigated. It is assumed that the plate properties vary continuously through its both circumference and thickness according to power law distribution of the volume fraction. Primarily, we calculate the forces and resultant moments and then the total potential energy of system. Then, by applying the Hamilton’s principal any by regarding the first order shear deformation plate theory (FSDT) the governing differential equations have been derived. The numerical differential quadrature method, (DQM), has been employed for solving the motion equations. Two different boundary conditions such as simply supported and clamp-simply supported are considered. Initially, the obtained results were verified against those given in the literature and by ANSYS software and we confident from the obtain results. The effects of geometrical and elastic foundation parameters along with FG power indices effects on the natural frequencies have been studied. The study of results shows that, elastic foundation and FG parameters have significant effects on natural frequencies. By doing this research for 2D-FG materials the characteristic vibration of structure can be controlled by more parameters than 1D-FG materials.

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The objective of this investigation is to present a semi-analytical method for studying the buckling of the moderately thick composite conical shells under axial compressive load. In order to derive the equilibrium equations of the conical shell, first order shear deformation shell theory is used. The equilibrium equations are derived by applying the principle of minimum potential energy to the energy function that they are in the type of partial differential equations. In the following, the partial differential equations are transformed to algebraic type by using Galerkin and differential quadrature methods and then the standard eigenvalue equation is formed and critical buckling load is calculated. Also, to validate the results obtained in this study, comparisons are made with outcomes of previous literatures and the results of Abaqus finite element software. Analyzing the results, shows the convergence speed and good accuracy of differential quadrature method and desired precision of Galerkin method in calculating the critical buckling load. Finally, the effect of cone angle, fiber orientation, boundary conditions, ratios of thickness to radius and length to radius of the critical buckling load are studied.

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In this research, analytical and numerical investigation of the ceramic- metal FGM beam under low velocity impact is carried out by first order shear deformation beam theory. The mass and stiffness matrixes are proposed by combination of Energy method, Ritz and Lagrange method. Also, simulating of low velocity impact on the ceramic- metal FGM beam is carried out by ABAQUS software that the beam is divided about 30 layers in thickness direction in ABAQUS software to create a functionally graded beam. Maximum contact force between impactor and beam in analytical model and ABAQUS software are 1062 and 1039 N with 2.21 percent difference and maximum impactor displacement in analytical model and ABAQUS software are 0.0104 and 0.0108 mm with 3.85 percent difference. Finally, the effect of FGM function types include the combination of exponential and polynomial functions, impactor velocity 1, 2 and 3 m/s, impactor radius 8, 12.7 and 16 mm and simply and clamped supported boundary condition are investigated on the contact force and indentation histories. The maximum and minimum contact forces are belonging to first and third order polynomial function and maximum and minimum indentations are belonging to third and first order polynomial function.