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.     

Stereology of Extremes; Bivariate Models and Computation

The extremal shape factor of spheroidal particles is studied in the stereological context using the extreme value theory. The domain of attraction is invariant with respect to the transformation between spatial characteristics and planar sections characteristics. It is shown that for the Farlie-Gumbel-Morgenstern bivariate distribution of size and shape factor one can estimate the normalizing constants of shape factor conditioned by unknown particle size. The theoretical solution is followed by a detailed simulation study which demonstrates the use of estimation techniques developed. The method is useful for engineering applications in materials science, where microstructural extremes correlate with the properties of materials.     

功能梯度中厚圆/环板轴对称弯曲问题的解析解

基于一阶剪切变形板理论，导出了热/机载荷作用下，位移形式的功能梯度 中厚圆/环板轴对称弯曲问题的控制方程，获得了问题的位移和内力的一般解析解. 作为特 例，分别研究了边缘径向固定和可动的夹紧和简支的4种实心功能梯度圆板，给出了它们的 解，并分析了热/机载荷作用下解的形态，讨论了横向剪切变形、材料梯度常数和边界条件， 对板的轴对称弯曲行为的影响.     

Thermal stress intensity factor for functionally gradient half space with an edge crack under thermal load

Summary The aim of this work is to investigate the thermal stress intensity factor of a functionally gradient half space with an edge crack under a steady heat flux. All material properties of the functionally gradient half space, except for the coefficient of linear thermal expansion, are exponentially dependent on the distance from the boundary of the plate. The coefficient of linear thermal expansion is assumed to be two-dimensionally dependent. The problem is reduced to a singular integral equation by using the Fourier transform. The thermal stress intensity factor versus the nonhomogeneous material parameters is calculated and represented in figures. The numerical results show that thermal stress intensity factor is dramatically decreased when the material nonhomogeneous parameters are appropriately selected.     

Risk concentration based on Expectiles for extreme risks under FGM copula

Risk concentration is used as a measurement of diversification benefits in the context of risk aggregation. Expectiles, which are known to possess many good properties, have attracted increasing interest in recent years. In this paper, we aim to study the asymptotic properties of risk concentration based on Expectiles. Firstly, we extend the results on the second-order asymptotics of Expectiles in Mao et al. (2015). Secondly, we investigate the second-order asymptotics of tail probabilities and then apply them to risk concentrations based on Expectiles as well as on VaR.     

基于FGM(1,1)模型的河北省高新技术产业增加值预测

高新技术产业是国民经济的战略性先导产业,在综合国力竞争中起着重要的作用.利用2014年到2018年河北省高新技术产业增加值数据,运用FGM(1,1)模型,给出了河北省高新技术产业增加值的预测模型,并进行了实证研究.预测结果显示,河北省高新技术产业增加值将保持稳定增长趋势.     

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.     

The Anti-plane Dynamic Fracture Analysis of Functionally Graded Materials with Arbitrary Spatial Variations of Material Properties

Anti-plane dynamic fracture analysis is presented for functionally graded materials (FGM) with arbitrary spatial variations of material properties. The FGM with the material properties varying continuously in an arbitrary manner is modeled as a multi-layered medium with the elastic modulus and mass density varying linearly in each sub-layer and continuous at the interfaces between two adjacent sub-layers. With this linearly inhomogeneous multi-layered model, the problem of a crack in a graded interfacial zone bonded to two homogeneous half-spaces or in a coating bonded to a homogeneous half-space subjected to the anti-plane shear impact load is investigated. Laplace and Fourier transforms and transfer matrix are applied to reduce the associated mixed boundary value problem to a Cauchy singular integral equation which is solved numerically in the Laplace transformed domain. The dynamic stress intensity factors (DSIF) are obtained by using the numerical technique of Laplace inversion.     

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.     

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.