Perforated discs have many applications in different parts of industry. By making such disks of functionally graded materials, more capabilities can be obtained from them. Vibration analysis of these kinds of disks can help us make them more efficient. In this paper, modeling and evaluation of disk vibration of functionally graded materials with regard to thickness were carried out using Abaqus software. Since no certain element has been defined regarding functionally graded materials for the design and analysis of a particular element in Abaqus software, molding of such materials has been used in this application. In order to verify the results, the results obtained from ABAQUS analysis have been compared with those available in the literature. The obtained results show that by defining more layers with regard to changes in properties, the obtained results approach the exact solutions.

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.

In this paper, the thermal buckling behavior of circular plates with variable thicknesses made of bimorph functionally graded materials, under uniform thermal loading circumstances, considering the first-order shear deformation plate theory and also assumptions of von Karman has been studied. The material characteristics are symmetric to the middle surface of the plate and, based on the power law, vary along with thickness; where the middle surface is intended pure metal, and the sides are pure ceramic. In order to determine the distribution of pre-buckling force in the radial direction, the membrane equation is solved using the shooting method. And the stability equations are solved numerically, with the help of pseudo-spectral method by choosing Chebyshev functions as basic functions. The numerical results in clamped and simply supported boundary conditions and the linear and parabolic thickness variations are presented. And the influence of various parameters like volume fraction index, the thickness profile and side ratio on the buckling behavior of these plates has been evaluated.

In the present paper, the buckling problem of rectangular functionally graded (FG) plate with arbitrary edge supports is investigated. The present analysis is based on the classical plate theory (CPT) and large deformation is assumed for deriving stability equations. The plate is subjected to bi-axial compression loading. Mechanical properties of FG plate are assumed to vary continuously along the thickness of the plate according to different volume of fraction functions of constituents. These functions are assumed to have power law distributions. The displacement function is assumed to have the form of double Fourier series, of which derivatives are legitimized using Stokes’ transformation method. The advantage of using this method is the capability of considering effect of any possible combination of boundary conditions on the buckling loads. The out-plane displacement distribution is assumed using Fourier Sinus Series. This results in a general eigenvalue problem which can be used for evaluating the buckling load under different edge conditions, plate aspect ratios and various volume fraction functions. For generality of problem, plate is elastically restrained using some rotational and translational springs at four edges. Some numerical examples are presented and compared the to numerical results of finite element method using ABAQUS and other researchers’ results to validate the proposed method. It has been shown that there is good agreement between them.

Rotating discs are the vital part of many kinds of machineries. Usually they are operating at a relatively high angular velocity and temperature conditions. Accordingly in practice, the creep analysis is an essential necessity in the study of rotating discs. More recently the application of Functionally Graded Materials (FGMs) in the construction of rotating discs is the subject of many researches. These newly developed heterogeneous compounds enable the designer to manage the distribution of material properties and benefit their superior thermo-mechanical capacities. Apart from the patterns of material distribution, the shape of a disc is another factor which controls the stress field and consequently the deformation and life expectations. To study the effects of cross sectional profile, three different Aluminum-Silicon Carbide FGM discs with uniform, convergent and divergent cross section profiles are selected as the case studies. It is seen that there is a definite speed in which creep relaxation reduces considerably at the entirety of the disc. This important rotational speed is named the creep limit speed. Some case studies are represented to show the effects of disc profile upon the disc creep limit speeds.

Owing to efficiency, rising stability of structures, reduction in structural weight and cost, and the improvements in fabrication process, tapered beams are extensively adopted in civil and mechanical structures. Furthermore, the use of functionally graded (FG) materials has been increasing in many mechanical components due to their conspicuous characteristics such as high strength, thermal resistance and optimal distribution of weight. In the present paper, a numerical model combining the power series expansions and the energy method is adopted for stability and free vibration analyses of axially functionally graded (FG) columns with exponentially varying cross-section. The main purpose of this paper is also calculating the critical buckling loads and natural frequencies concurrently for AFG members with exponentially-varying geometrical properties. For this, a mixed power series expansions and the principle of stationary total potential energy as a first endeavor is presented. In this study, the material properties of the non-prismatic beam including Young’ s modulus of elasticity and density of material are assumed to be graded smoothly along the beam axis by a power-law distribution of volume fractions of metal and ceramic. Moreover, the cross-sectional area and moment of inertia vary exponentially over the member’ s length. In this regard, the power series approximation is applied to solve the fourth order differential equation of motion, since in the presence of variable cross-section and axially non-homogeneous material, stiffness quantities are not constant. All geometrical and material properties and displacement component are developed based on power series of an identified degree. The natural frequencies of the AFG beam with variable cross-section are derived by imposing the boundary conditions and solving the eigenvalue problem. The explicit expression of vibrational shape function is then derived based on this rigorous numerical method. The vibrational mode shapes of an elastic member are similar to the buckling ones. Therefore, the obtained deflected shapes of the considered non-prismatic beams can be used as deformation shape of member for the linear buckling analysis. The critical buckling load of exponentially tapered beam made of AFGMs can be then estimated by adopting the principle of stationary total potential energy. According to the steps mentioned above, for measuring the accuracy and competency of the proposed numerical procedure, two numerical examples including axially non-homogeneous and homogeneous column with non-uniform section are represented. Numerical results of the critical buckling loads and natural frequencies for various boundary conditions, different gradient index and cross-section variation are represented. Due to lack of similar research for the stability and free vibration analyses of elastic AFG beams with exponential variation of the cross-sectional area and moment of inertia, outcomes of homogeneous members are compared with the results presented in other available numerical and analytical references and those related to tapered beams with material variation are then reported. The accuracy of the method is then remarked. This method has many positive points consisting of efficiency, accuracy and simplicity contrasted with more complex numerical methods. It has to be noticed that the present novel numerical technique can be applied to determine the critical buckling loads and natural frequencies of axially functionally graded (FG) prismatic beams as well as non-prismatic ones.

Vibration of the structures in contact with fluid is a phenomenon that a structure has the interaction between the fluid. Hydroelastic characteristics of plates in contact with fluid are important in various engineering applications such as in nuclear engineering, liquid storage tanks, reactor internal components, and solar plates and offshore, naval or marine structures. Fluid-coupled vibrations may be caused the structural fatigue and failure. So, the control and debilitation of the hydoelastic characteristics are important in the safety positions. This study is focused on the hydroelastic vibration of FG circular plate in contact with the bounded fluid with clamped boundary conditions. The natural frequencies of the plate coupled with fluid are calculated by finite element software ANSYS. The software method is verified by comparing the results with the results obtained by experimental tests in case homogeneous plate (Aluminum). Finally, the effects of some parameters such as fluid density, fluid height and volume fraction index on natural frequencies are discussed in details.

One of the most important analyses in the design of various structures, especially pressure vessels and their safety is the fracture mechanics. One of the important parameters in fracture mechanics is the study of the stress intensity factor of cracks in the tank wall. In the present study, the behavior of a semi-elliptical crack in a spherical pressure vessel made of functionally graded materials has been studied using Abaqus finite element software. The effects of parameters such as crack geometry, simultaneous internal and external cracks, pressure distribution, thermal load distribution, changes in the properties of the functionally graded material, and support conditions on the value of the stress intensity factor have been investigated. To model and analyze the stress intensity factor in this type of tank, various power, exponential, and linear functions have been used in the form of MATLAB code as well as a subroutine code. Crack geometry is also an important factor that has a significant effect on the stress intensity factor. So with an increase in the a/c value, the stress intensity factor also increases. Also, the examination of the support conditions shows that with the increase in the number of foundations, the stress intensity factor also increases.