Natural dynamic characteristics of a circular cylindrical Timoshenko tube made of three-directional functionally graded material

The natural dynamic characteristics of a circular cylindrical tube made of three-directional(3 D) functional graded material(FGM) based on the Timoshenko beam theory are investigated. Hamilton’s principle is utilized to derive the novel motion equations of the tube, considering the interactions among the longitudinal, transverse,and rotation deformations. By dint of the differential quadrature method(DQM), the governing equations are discretized to conduct the analysis of natural dynamic charact...     

A meshless collocation method for the plane problems of functionally graded material beams and plates using the DRK interpolation

A meshless collocation method is developed for the static analysis of plane problems of functionally graded (FG) elastic beams and plates under transverse mechanical loads using the differential reproducing kernel (DRK) interpolation, in which the DRK interpolant is constructed by the randomly distributed nodes. A point collocation method based on this DRK interpolation is developed for the plane stress and strain problems of homogeneous and FG elastic beams and plates. It is shown that the present DRK interpolation-based collocation method is indeed a truly meshless approach with excellent accuracy and has a fast convergence rate.     

An application of the Morgenstern family with standard two‐sided power and gamma marginal distributions to the Bayes premium in the collective risk model

The Bayes premium is a quantity of interest in the actuarial collective risk model, under which certain hypotheses are assumed. The usual assumption of independence among risk profiles is very convenient from a computational point of view but is not always realistic. Recently, several authors in the field of actuarial and operational risks have examined the incorporation of some dependence in their models. In this paper, we approach this topic by using and developing a Farlie–Gumbel–Morgenstern (FGM) family of prior distributions with specified marginals given by standard two‐sided power and gamma distributions. An alternative Poisson–Lindley distribution is also used to model the count data as the number of claims. For the model considered, closed expressions of the main quantities of interest are obtained, which permit us to investigate the behavior of the Bayes premium under the dependence structure adopted (Farlie–Gumbel–Morgenstern) when the independence case is included. Copyright © 2012 John Wiley & Sons, Ltd.     

Reliability assessment of different plate theories for elastic wave propagation analysis in functionally graded plates

The importance of elastic wave propagation problem in plates arises from the application of ultrasonic elastic waves in non-destructive evaluation of plate-like structures. However, precise study and analysis of acoustic guided waves especially in non-homogeneous waveguides such as functionally graded plates are so complicated that exact elastodynamic methods are rarely employed in practical applications. Thus, the simple approximate plate theories have attracted much interest for the calculation of wave fields in FGM plates. Therefore, in the current research, the classical plate theory (CPT), first-order shear deformation theory (FSDT) and third-order shear deformation theory (TSDT) are used to obtain the transient responses of flexural waves in FGM plates subjected to transverse impulsive loadings. Moreover, comparing the results with those based on a well recognized hybrid numerical method (HNM), we examine the accuracy of the plate theories for several plates of various thicknesses under excitations of different frequencies. The material properties of the plate are assumed to vary across the plate thickness according to a simple power-law distribution in terms of volume fractions of constituents. In all analyses, spatial Fourier transform together with modal analysis are applied to compute displacement responses of the plates. A comparison of the results demonstrates the reliability ranges of the approximate plate theories for elastic wave propagation analysis in FGM plates. Furthermore, based on various examples, it is shown that whenever the plate theories are used within the appropriate ranges of plate thickness and frequency content, solution process in wave number-time domain based on modal analysis approach is not only sufficient but also efficient for finding the transient waveforms in FGM plates.     

FGM with REDx: chemically reactive dimensionality extension

We propose a new approach to improve the accuracy of flamelet-generated manifolds (FGMs) method by extending the manifolds with additional chemically reactive degrees of freedom. Following the ideas of intrinsic low-dimensional manifold, the dimensionality of the FGM is increased by performing a local time-scale analysis of the chemical source term. A few slow characteristic directions of the reaction kinetics are used to extend the FGM, while the remaining reaction groups, characterised by fast time-scales, are assumed in steady state. The introduced method for FGM REactive Dimensionality extension is abbreviated as FGM-REDx. It is tested in one-dimensional simulations reproducing an expansion of burnt gases in an aero-engine stator. This process is characterised by a rapid change of enthalpy and pressure, altering, among others, the chemistry of pollutants CO and NO. The primary focus was on the assessment of the FGM's capability to predict the pollutants emissions. The rates of physical/thermodynamic perturbations turned out to be severe enough for the chemical species composition to go off the flamelet. The FGM extended with one additional chemically reactive dimension has been generated and successfully applied to the test cases, yielding a high accuracy gain over the standard FGM.     

热载荷下粘弹性功能梯度材料薄板的准静态响应

由热粘弹性功能梯度材料的本构方程出发,利用Laplace变换,通过引进薄板的“结构函数”和“热函数”,建立了各向同性薄板的数学模型．采用卷积双线性形式,给出了薄板准静态问题的简化Gunin型泛函．在空域上和时域上分别采用Ritz法和kgerdre插值法考察了温度变化和功能梯度对于薄板响应的影响。     

Buckling analysis of functionally graded material (FGM) sandwich truncated conical shells reinforced by FGM stiffeners filled inside by elastic foundations

An analytical solution for buckling of an eccentrically stiffened sandwich truncated conical shell is investigated. The shell consists of two functionally graded material (FGM) coating layers and a core layer which are metal or ceramic subjected to an axial compressive load and an external uniform pressure. Shells are reinforced by stringers and rings, in which the material properties of shells and stiffeners are graded in the thickness direction following a general sigmoid law distribution. Two models of coated shell-stiffener arrangements are investigated. The change of the spacing between stringers in the meridional direction is taken into account. A couple set of three-variable-coefficient partial differential equations in terms of displacement components are solved by the Galerkin method. A closed-form expression for determining the buckling load is obtained. The numerical examples are presented and compared with previous works.     

Revisiting the elastic solution for an inner-pressured functionally graded thick-walled tube within a uniform magnetic field

In this paper, the mechanical responses of a thick-walled functionally graded hollow cylinder subject to a uniform magnetic field and inner-pressurized loads are studied. Rather than directly assume the material constants as some specific function forms displayed in pre-studies, we firstly give the volume fractions of different constituents of the functionally graded material (FGM) cylinder and then determine the expressions of the material constants. With the use of the Voigt method, the corresponding analytical solutions of displacements in the radial direction, the strain and stress components, and the perturbation magnetic field vector are derived. In the numerical part, the effects of the volume fraction on the displacement, strain and stress components, and the magnetic perturbation field vector are investigated. Moreover, by some appropriate choices of the material constants, we find that the obtained results in this paper can reduce to some special cases given in the previous studies.     

功能梯度板的非线性动力分析

非线性材料功能梯度板件的动力分析是属于在数学方程上同时具有变系数、非线性、非定常特征的固体力学问题.文中首先将问题的变系数非线性偏微分方程组转化为各向异性常系数非线性常微分方程,然后用小参数法求得解析解,适用于各种形状、边界及功能梯度分布的板件非线性弹性振动分析.     

Stochastic analysis of a thermoelastic problem in functionally graded plates with uncertain material properties

The statistics (i.e., mean and variance) of temperature and thermal stress are analytically obtained in functionally graded material (FGM) plates with uncertainties in the thermal conductivity and coefficient of linear thermal expansion. These FGM plates are assumed to have arbitrary nonhomogeneous thermal and mechanical properties through the entire thickness of plate and are subjected to deterministic convective heating. The stochastic temperature and thermal stress fields are analysed by assuming the FGM plate is multilayered with distinct, random thermal conductivity and coefficient of linear thermal expansion in each layer. Vodicka’s method, which is a type of integral transform method, and a perturbation method are employed to obtain the analytical solutions for the statistics. The autocorrelation coefficients of each random property and cross-correlation coefficients between different random properties are expressed in exponential function forms as a non-homogeneous Markov random field of discrete space. Numerical calculations are performed for FGM plates composed of partially stabilised zirconia (PSZ) and austenitic stainless steel (SUS304), which have the largest dispersion of the random properties at the place where the volume fractions of the two constituent materials are both 0.5. The effects of the spatial change in material composition, thermal boundary condition and correlation coefficients on the standard deviations of the temperature and thermal stress are discussed.