Crack Propagation Path in Two-Directionally Graded Composites Subjected to Mixed-Mode Ⅰ+Ⅱ Loading

Crack propagation path in two-directionally graded composites was investigated by the finite element method.A graded extended finite element method(XFEM)was employed to calculate displacement and stress fields in cracked graded structures.And a post-processing subroutine of interaction energy integral was implemented to extract the mixed-mode stress intensity factors(SIFs).The maximum hoop stress(MHS)criterion was adopted to predict crack growth direction based on the assumption of local homogenization of asymptotic crack-tip fields in graded materials.Effects of material nonhomogeneous parameters on crack propagation paths were also discussed in detail.It is shown that the present method can provide relatively accurate predictions of crack paths in two-directionally graded composites.Crack propagates in the decreasing direction of effective Young′s modulus.The shape and steepness of property gradient perpendicular to the crack surface have great influences on crack paths.Through redesigning material property reasonably,crack growth in graded material can be changed to improve mechanical behaviours of cracked structures.

A Theoretical Analysis of Functionally Graded Beam under Thermal Loading

Modeling of the behavior for Functionally Graded Beam (FGB) under thermal loading is introduced in the present work. The material properties are assumed to vary according to power function along the thickness of the beam. The effects of several parameters such as thermal expansion parameter, thermal conductivity and modulus of elasticity on the resultant axial stress of the FG beam have been studied. For thermal loading the steady state of heat conduction with power and exponentially variations through the thickness of FGB, is considered. The results obtained show that temperature distribution plays very important parameter controlling thermal resultant distribution of stresses and strains.

Analytical solution for functionally graded anisotropic cantilever beam subjected to linearly distributed load

The bending problem of a functionally graded anisotropic cantilever beam subjected to a linearly distributed load is investigated. The analysis is based on the exact elasticity equations for the plane stress problem. The stress function is introduced and assumed in the form of a polynomial of the longitudinal coordinate. The expressions for stress components are then educed from the stress function by simple differentiation. The stress function is determined from the compatibility equation as well as the boundary conditions by a skilful deduction. The analytical solution is compared with FEM calculation, indicating a good agreement.

Study and Commercial Application of Graded Optimization of Catalysts for Fixed Bed Residue Upgrading Unit

The SHIFT-G technology of inverse catalyst loading is used to optimize the catalyst grading in the residue hydrotreating unit. The results, taken from pilot tests and commercial units, have showed that the optimized catalyst grading system can reasonably distribute the reaction load, effectively improve the prop- erties of hydrotreated products, prolong the operating cycle and promote economic benefits.

Geometrically Nonlinear Bending Analysis of Metal-Ceramic Composite Beams under Thermomechanical Loading

A new method is developed to derive equilibrium equations of Metal-Ceramic beams based on first order shear deformation plate theory which is named first order shear deformation beam theory2(FSDBT2). Equilibrium equations obtained from conventional method (FSDBT1) is compared with FSDBT2 and the case of cylindrical bending of Metal-Ceramic composite plates for non-linear thermomechanical deformations and various loadings and boundary conditions. These equations are solved by using three different methods (analytical, perturbation technique and finite element solution). The through-thickness variation of the volume fraction of the ceramic phase in a Metal-Ceramic beam is assumed to be given by a power-law type function. The non-linear strain-displacement relations in the von-Kármán sense are used to study the effect of geometric non-linearity. Also, four other representative averaging estimation methods, the linear rule, Mori-Tanaka, Self-Consistent and Wakashima-Tsukamoto schemes, by comparing with the power-law type function are also investigated. Temperature distribution through the thickness of the beams in thermal loadings is obtained by solving the one-dimensional heat transfer equation. Finally it is concluded that for Metal-Ceramic composites, these two theories result in identical static responses. Also the displacement field and equilibrium equations in the case of cylindrical bending of Metal-Ceramic plates are the same as those supposed in FSDBT2.

High heat loading performance of actively cooled W/Cu FGM-based components

A functionally graded material-based actively water-cooled tungsten-copper mockup with a dimension of 30 mm×30 mm×25 mm was designed and fabricated by infiltration-brazing method.The thicknesses of the pure W layer and W/Cu graded layer were 2 and 3 mm,respectively.High heat flux tests were performed on the mockup using an e-beam device.There is no damage occurring on the joint after heat loading at 5 MW/m2.The temperature on the pure W surface is less than 500°C after irradiation for 100 s at 5 MW/m2,while the temperature on the brazing seam/copper surface is around 200°C.

Sound radiation of a functionally graded material cylindrical shell in water by mobility method

Based on the fundamental dynamic equations of functionally graded material (FGM) cylindrical shell, this paper investigates the sound radiation of vibrational FGM shell in water by mobility method. This model takes into account the exterior fluid loading due to the sound press radiated by the FGM shell. The FGM cylindrical shell was excited by a harmonic line radial force uniformly distributing along the generator. The FGM shell equations of motion, the Helmholtz equation in the exterior fluid medium and the continuity equation at fluid-shell interface are used in this vibroacoustic problem. The expressions of sound radiation efficiency and sound field of the FGM shell have been derived by mobility method. Radiation efficiency, modal mobility and the directivity pattern of the sound field are solved numerically. In particular, radiation efficiency and directivity pattern with various power law index are analyzed.

SWN: An SDN Based Framework for Carrier Grade WiFi Networks

With the rapid growth of mobile data traffic and vast traffic offloaded from cellular network, Wi-Fi has been considered as an essential component to cope with the tremendous growth of mobile data traffic. Although operators have deployed a lot of carrier grade Wi-Fi networks, but there are still a multitude of arrears for nowadays Wi-Fi networks, such as supporting seamless handover between APs, automatic network access and unified authentication, etc. In this paper, we propose an SDN based carrier grade Wi-Fi network framework, namely SWN. The key conceptual contribution of SWN is a principled refactoring of Wi-Fi networks into control and data planes. The control plane has a centralized global view of the whole network, can perceive the underlying network state by network situation awareness(NAS) technique, and bundles the perceived information and network management operations into northbound Application Programming Interface(API) for upper applications. In the data plane, we construct software access point(SAP) to abstract the connection between user equipment(UE) and access point(AP). Network operators can design network applications by utilizing these APIs and the SAP abstraction to configure and manage the whole network, which makes carrier grade Wi-Fi networks more flexible, user-friendly, and scalable.

不同螺栓等级下共享铁塔挂载连接件承载性能研究

为研究螺栓等级对挂载连接件承载性能的影响,选取了4.8级普通螺栓(KL-4.8)与8.8级摩擦型高强螺栓(KL-8.8)连接的挂载连接件进行静力试验研究。采用ABAQUS有限元分析软件对其受力性能进行模拟,使用可靠的数值模型系统分析螺栓等级和螺栓直径对连接件承载性能的影响。结果表明:在水平荷载作用下,两种不同螺栓等级连接的挂载连接件节点处均未出现滑移;两种连接件的破坏模式基本一致,左右两侧方钢管底部及右侧方钢管顶部均出现断裂;KL-8.8的整体刚度、极限承载能力以及变形能力均高于KL-4.8;当采用4.8级普通螺栓连接且承载力低于74.13 kN时,螺栓直径不宜小于18 mm,否则螺栓杆会发生剪切变形;当采用8.8级和10.9级高强螺栓连接时,双板件连接处节点偏于刚性连接,挂载连接件的整体刚度和极限荷载主要取决于方刚管、挂载铁杆等其他部件;挂载连接件在承载过程中通过双板件与主材之间的摩擦力和螺栓抗剪来抵抗外载,实际工程中应根据挂载重量合理选择螺栓参数。

THERMO-ELASTIC-PLASTIC RESPONSE AND OPTIMUM DESIGN OF CERAMIC-METAL FGMS-CYCLIC THERML LOADING PROBLEM

The materials are made with a graded composition and microstructure in the thickness direction from the ceramic side to the metal side. The cyclic thermal loading and high temperasure gradient environment are simulated by heating the ceramic surface with a cyclic hear flux input and cooling the metal surface with a flowing liquid niterogen. The thermal and themo-elastic-plastic response of the materials is calculated using the isotropic hardening model and kinetic hardening model. Emphasis is placed on the response analysis under the different graded compositional distributions. Through the response analysis, the optimum design process of the graded composition under the dynamic case is established, which is bused on a unified viewpoint of the heat insulation property, thermal stress relaxation property and stress history feature.

Thermo-magnetic analysis of thick-walled spherical pressure vessels made of functionally graded materials

This study presents an analytical solution of thermal and mechanical displacements, strains, and stresses for a thick-walled rotating spherical pressure vessel made of functionally graded materials (FGMs). The pressure vessel is subject to axisymmetric mechanical and thermal loadings within a uniform magnetic field. The material properties of the FGM are considered as the power-law distribution along the thickness. Navier’s equation, which is a second-order ordinary differential equation, is derived from the mechanical equilibrium equation with the consideration of the thermal stresses and the Lorentz force resulting from the magnetic field. The distributions of the displacement, strains, and stresses are determined by the exact solution to Navier’s equation. Numerical results clarify the influence of the thermal loading, magnetic field, non-homogeneity constant, internal pressure, and angular velocity on the magneto-thermo-elastic response of the functionally graded spherical vessel. It is observed that these parameters have remarkable effects on the distributions of radial displacement, radial and circumferential strains, and radial and circumferential stresses.

分级加载下不同骨料粒径的混凝土声发射波速分析

目前利用声发射技术对混凝土结构进行损伤定位时,采用固定表面波速进行损伤定位,没有考虑混凝土声发射信号是从混凝土内部传播出来以及混凝土材料在不同的阶段产生的损伤对声发射波速的影响,导致检测结果与实际产生一定的偏差。以3种不同类型的弹性波速变化将混凝土的损伤化为5个阶段。利用波速的变化结合经典材料损伤力学从而进行材料损伤的定量分析。通过试验结果分析得出:当水灰比一定时,随混凝土粗骨料粒径的增大弹性波波速呈上升的趋势,但波速上升的趋势随粒径的增大而相对减小。随着应力的增加,波速降低时,波速与应力阶段存在一定的线性关系。采用不同加载阶段波速的不同进行变波速定位,定位精度更接近实际损伤位置,可有效提高定位精度。试验得出的结果为混凝土桥梁结构无损检测提供了新的思路方向为其安全检测提供了参考价值。

海陆交互相软土固结抗剪强度指标变化规律研究

以珠三角地区海陆交互相淤泥质软土为研究对象,通过室内直剪试验探究不同固结压力和固结度下抗剪强度及抗剪强度指标的变化规律,提出抗剪强度及对应指标-固结度-固结压力三维Logistic数学模型。研究结果表明,当固结压力P≥200 kPa、固结度U≥40%时,软土黏聚力(c)和内摩擦角(φ)增长较为明显;当U=100%时,各级固结压力作用下的软土抗剪强度(τ)相较于初始状态分别提高了7.89、12.73、13.50、18.20、22.38 kPa;所给出的三维数学模型可直接计算出某一固结压力和固结度下的抗剪强度指标c、φ、τ。研究成果能够更为准确地评价该地区软土地基逐级加载过程中的整体稳定性。

Identifying the temperature effect on the vibrations of functionally graded cylindrical shells with porosities

The free thermal vibration of functionally graded material(FGM) cylindrical shells containing porosities is investigated. Both even distribution and uneven distribution are taken into account. In addition, three thermal load types, i.e., uniform temperature rise(UTR), nonlinear temperature rise(NLTR), and linear temperature rise(LTR), are researched to explore their effects on the vibration characteristics of porous FGM cylindrical shells. A modified power-law formulation is used to describe the material properties of FGM shells in the thickness direction. Love’s shell theory is used to formulate the straindisplacement equations, and the Rayleigh-Ritz method is utilized to calculate the natural frequencies of the system. The results show that the natural frequencies are affected by the porosity volume fraction, constituent volume fraction, and thermal load. Moreover,the natural frequencies obtained from the LTR have insignificant differences compared with those from the NLTR. Due to the calculation complexity of the NLTR, we propose that it is reasonable to replace it by its linear counterpart for the analysis of thin porous FGM cylindrical shells. The present results are verified in comparison with the published ones in the literature.

INFLUENCE OF TEMPERATURE-DEPENDENT PROPERTIES ON TEMPERATURE RESPONSE AND OPTIMUM DESIGN OF C/M FGMS UNDER THERMAL CYCLIC LOADING

The influence of temperature-dependent properties on temperature response and optimum design of newly developed ceramic-metal functionally graded materials under cyclic thermal loading and high temperature gradient environment is studied. The thermal conductivity of the material is considered to be dependent on the temperature. In this paper, the temperature response of the material is calculated using a nonlinear finite element method. Emphasis is placed on the influence of temperatue-dependent properties on the thermal response and insulation property of the material render the different graded compositional distributions and different heat flux magnitudes. Through the analysis, it is suggested that the influence of temperature-dependent properties can not be neglected in the temperature response analysis and the optimum design process of the material must be based on the temperature-dependent temperature analysis theory.

ANALYSIS OF SHAKEDOWN OF FG BREE PLATE SUBJECTED TO COUPLED THERMAL-MECHANICAL LOADINGS

The static and kinematic shakedown of a functionally graded （FG） Bree plate is analyzed. The plate is subjected to coupled constant mechanical load and cyclically varying temperature. The material is assumed linearly elastic and nonlinear isotropic hardening with elastic modulus,yield strength and the thermal expansion coeffcient varying exponentially through the thickness of the plate. The boundaries between the shakedown area and the areas of elasticity,incremental collapse and reversed plasticity are determined,respectively. The shakedown of the counterpart made of homogeneous material with average material properties is also analyzed. The comparison between the results obtained in the two cases exhibits distinct qualitative and quantitative difference,indicating the importance of shakedown analysis for FG structures. Since FG structures are usually used in the cases where severe coupled cyclic thermal and mechanical loadings are applied,the approach developed and the results obtained are significant for the analysis and design of such kind of structures.

INFLUENCE OF TEMPERATURE-DEPENDENT PROPERTIES ON THERMAL STRESSES RESPONSE AND OPTIMUM DESIGN OF C/M FGMS UNDER THERMAL CYCLIC LOADING

The influence of temperature-dependent properties on thermal stresses response and optimum design of newly developed ceramic-metal functionally graded materials under cyclic thermal loaning and high temperature gradient environment is studied. The thermal conductivity of material is considered to be dependent on the temperature. In this paper, the thermal stresses response of the material is calculated rising a nonlinear finite element method. Emphasis is placed on the influence of temperature-dependent properties on the thermal stresses response characteristics, the thermal stresses relaxation property and the thermal stresses history under the different graded compositional distributions and different heat flux magnitudes. Through tile analysis. it is suggested that the influence of temperature-dependent properties can not be neglected In the thermal stresses response analysis and the optimum design process of the material must be based on the temperature-dependent thermo-elastic-plastic theory.

梯度多孔金属材料梁的屈曲和屈曲基础上的振动

为研究梯度多孔金属材料梁的屈曲以及屈曲附近的振动特性,首先建立了随从分布压力下梯度多孔材料梁的动力学控制方程,得到了描述后屈曲的静态控制微分方程和描述屈曲前后振动响应的控制方程。通过打靶法数值求解两组强非线性方程,获得了简支-固支梯度多孔梁的屈曲临界载荷以及屈曲前后振动频率与载荷之间的关系曲线。分析了孔隙率系数和孔隙分布方式对屈曲临界载荷和屈曲前后振动频率的影响。结果表明,随着孔隙率系数e 0的增加,发生屈曲时的临界载荷减小;各阶固有频率也减小。屈曲前,各阶振动频率随载荷增大而减小,屈曲后,除三阶频率外,一阶和二阶频率随载荷增大而增大。

On asymmetric bending of functionally graded solid circular plates

Based on the three-dimensional elasticity equations, this paper studies the elastic bending response of a transversely isotropic functionally graded solid circular plate subject to transverse biharmonic forces applied on its top surface. The material prop- erties can continuously and arbitrarily vary along the thickness direction. By virtue of the generalized England＇s method, the problem can be solved by determining the expres- sions of four analytic functions. Expanding the transverse loarl in Fourier series along the circumferential direction eases the theoretical construction of the four analytic functions for a series of important biharmonic loads. Certain boundary conditions are then used to determine the unknown constants that are involved in the four constructed analytic functions. Numerical examples are presented to validate the proposed method. Then, we scrutinize the asymmetric bending behavior of a transversely isotropic functionally graded solid circular plate with different geometric and material parameters.

不同冲击载荷下典型路面结构的动态弯沉响应

为研究不同冲击载荷下典型路面结构的动态弯沉响应数值规律,开展试验勘测等级公路信息,分析实测数据并归纳出等级公路承载能力与路面结构的相关关系,基于统计规律构建了承载力维度下的典型路面结构。建立包含塑性损伤的多层连续道路结构模型,通过比对仿真结果与试验数据验证模型的有效性,研究模型大小对不同冲击载荷作用下路面弯沉仿真结果的影响。开展不同冲击载荷下典型路面结构的弯沉响应规律研究,计算出冲击载荷作用下路面峰值沉降与残余沉降数值,揭示不同冲击载荷下典型路面结构弯沉响应内在规律。研究结果表明:包含塑性损伤的多层连续道路结构模型能够准确反映冲击载荷下路面真实动态弯沉响应;不同冲击载荷下,路面沉降中塑性沉降量占比与冲击载荷幅值满足双指数方程;百吨级范围内,路面沉降中弹性回弹部分随冲击载荷幅值增大而增大,塑性沉降部分与载荷幅值呈指数正相关关系;百吨级以上,路面沉降中弹性回弹量达到上限1.2~1.3 mm,路面塑性沉降量与载荷幅值呈线性关系。开展的不同冲击载荷下模型大小对仿真结果的影响规律研究可为有限元仿真中确定合适的仿真模型尺度提供参考。