Al_2O_3-Ti系梯度功能材料残余热应力的有限元分析

采用有限元方法（ＦｉｎｉｔｅＥｌｅｍｅｎｔＭｅｔｈｏｄ）对Ａｌ２Ｏ３－Ｔｉ系梯度功能材料在制备过程中产生的残余热应力进行了线弹性分析。详细讨论了梯度层数目、梯度层厚度和成分梯度指数对应力大小和分布的影响，确定了各项最佳参数。非梯度功能材料（ＮＦＧＭ）与优化后的梯度功能材料的残余热应力对比结果显示：梯度功能材料缓和热应力的效果十分显著。     

Al2O3—Ti系梯度功能材料残余热应力有限元分析

采用有限元方法对Ａｌ２Ｏ３－Ｔｉ系梯度功能材料在制备过程中产生的残余热应力进行了线弹性分析，详细讨论了梯底层数目，梯度层厚度和成分梯度指数对应务大小和分布的影响，确定了各项最佳参数。非梯度功能材料与优化后的梯度功能材料的残余热应务对比结果显示；梯度功能材料缓和热应力的效果十分显著。     

Al3O—Ti系梯度功能材料残余热应力的有限元分析

采用有限元方法对Ａｌ２Ｏ３－Ｔｉ系梯度功能材料在制备过程中产生的残余热应力进行了线 性性分析。详细讨论了梯度层数目、梯度层厚度和成分梯度指数对应力大小和分布的影响，确定了各项最佳参数。非梯度功能材料与优化后的梯度功能材料的残余热絷力对此结果显示：梯度功能赫兹 热应力的效果十分显著。     

功能梯度材料热应力研究进展

梯度功能材料的热应力问题贯穿梯度功能材料设计、制备、性能评价及应用整个研究领域,其中,热传导问题是热应力研究基础。介绍了梯度功能材料的概念及热传导和热应力问题的研究背景,重点分析了梯度功能材料热传导和热应力问题在数学模型、物性参数模型、解析方法、数值方法等方面的国内外研究进展,并展望进一步研究方向。     

梯度功能材料的热应力研究现状与展望

回顾了近年来梯度功能材料热应力研究领域所取得的研究成果，并展望了ＦＧＭ热应力研究的发展趋势。     

功能梯度材料的发展及展望

系统地论述了功能梯度材料的概念、设计方法、制备工艺、性能评价及其应用领域。着重于相关的热应力缓解、热弹（塑）性力学、三相微观力学模型等理论的阐述和分析，并对功能梯度材料的发展及应用前景作了展望。     

TiC-Ni梯度功能材料的优化设计

对ＴｉＣ－Ｎｉ梯度功能材料在制备过程中的残余热应力进行了计算机有限元模拟,考察了梯度组成分布指数对热应力大小,最大热应力发生的位置以及纯陶瓷ＴｉＣ侧热应力状态的影响,综合分析了热应力的大小和分布,得到了缓和制备热应力的梯度组成分布指数Ｐ＝１．０的优化设计结果。     

水冷壁管梯度陶瓷涂层的设计与性能研究

针对燃煤电厂锅炉水冷壁爆管问题,研究设计了一种热膨胀系数梯度变化的涂层结构.为了提高涂层与基体的结合强度,计算了涂层及管壁的温度场及热应力场的分布.结果表明:涂层与管壁的界面处热应力最大,并且热应力与涂层的热膨胀系数成正比,通过调整涂料各成分的含量来改变各层的热膨胀系数;采用双层结构梯度涂层,理论计算表明界面处的最大热应力为1.78 MPa;而通过拉伸力学性能测试得出涂层的平均抗剪切强度为5.60 MPa,是界面处最大热应力值的3倍左右.因此,在管壁表面喷涂功能梯度涂层,能够缓和涂层与基体界面间的热应力.     

对流换热边界下梯度功能材料板瞬态热传导有限元分析

用有限元法与有限差分法相结合的方法，对处在对流换热边界条件下的梯度功能材料板的瞬态热传导问题进行了分析，并且通过对ZrO2和Ti－6Al-4V组成的梯度功能材料板对本方法的正确性进行了检验，最后给出了对流换热边界下的瞬态温度场分布。数值计算结果表明：材料组成的分布形状系数M、环境介质温度和对流换热系数的变化对梯度功能材料板的瞬态温度场分布有明显的影响。本文结果为梯度功能材料的优化设计和进一步的热应力分析提供了理论计算依据。     

SiO2/环氧(E44)热膨胀性渐变的梯度功能材料(FGM)设计中的数学模型极其热应力分析

以基体树脂环氧(E44)为连续相，SiO2颗粒为分散相，设计了一种新型的热膨胀性渐变的梯度功能材料(FGM)，通过实验测定结合理论分析，确定了FGM材料组成与弹性模量、热膨胀系数及导热系数之间的关系式。应用经典层合板理论和热弹性力学理论分析了SiO2／环氧E44叠合层在稳态温度场内温度分布和热应力分布。结果表明，在稳态温度场内，FGM板的热应力分布依赖于体系的组成分布，当组成分布指数k=1时，最大热应力具有最小值。在该组成分布下，FGM板的热膨胀系数等各项性质都呈线性渐变。     

Design optimization of functionally graded dental implant for bone remodeling

Despite a great success, one of the key issues facing in dental implantation clinic is a mismatch of mechanical properties between engineered and native biomaterials, which makes osseointegration and bone remodeling problematical. Functionally Graded Material (FGM) has been proposed as a potential upgrade to some conventional implant materials like titanium for selection in prosthetic dentistry. The idea of FGM dental implant is that the property would vary in a certain pattern to match the biomechanical characteristics required at different regions in the hosting bone. However, mating properties do not necessarily guarantee the best osseointegration and bone remodeling. No existing report has been available to develop an optimal design of FGM dental implant for promoting a long-term success. This paper aims to explore this critical issue by using the computational bone remodeling and design optimization. A buccal–lingual sectional model, which consists of a single unit implant and four other adjacent teeth, was constructed from computerized tomography (CT) scan images. Bone remodeling induced by use of various FGM dental implants is calculated over the period of 4 years. Based upon remodeling results, response surface method (RSM) is adopted to develop a multi-objective optimal design for FGM implantation FGM designs.     

Dynamics of a functionally graded material axial bar: Spectral element modeling and analysis

Functionally graded material (FGM) bars in axial motion (hereafter called “FGM axial bars”) have great potential for applications in many engineering fields. Therefore, it is important to develop a reliable mathematical model that can provide very accurate dynamic and wave propagation characteristics in FGM axial bars, especially at high frequencies. As an extension of our previous work, we present a spectral element model for a modified FGM axial bar model wherein nonuniform lateral contraction in the thickness direction is taken into account. We assume that material properties of the modified FGM axial bar model vary in the radial direction according to the power law. The performance of the proposed spectral element model is validated through comparison with solutions from a conventional finite element model, and with the results from the previous FGM axial bar model. In addition, the effects of lateral contraction on the dynamic and wave propagation characteristics in example FGM axial bars are numerically investigated.     

Effect of anisotropy on steady state creep in functionally graded cylinder

The steady state creep in transversely isotropic functionally graded cylinder, operating under internal and external pressures, has been investigated. The cylinder is composed of functionally graded material (FGM) containing silicon carbide whiskers in a matrix of 6061Al. The creep behavior of the FGM has been described by a threshold stress based creep law. The effect of anisotropy on creep stresses and creep rates in the FGM cylinder has been analysed and compared with an isotropic FGM cylinder. The anisotropy is represented by a parameter α, defined as the ratio of radial (or axial) and tangential yield strength. The study reveals that in an anisotropic FGM cylinder i.e. when α deviates from unity, radial and tangential stresses are marginally affected whereas axial and effective stresses are significantly affected as compared to those in an isotropic FGM cylinder. The strain rates as well as inhomogeneity in strain rates in the FGM cylinder decrease significantly when α reduces from 1.3 to 0.7. The magnitude of stresses, strain rates and inhomogenity in strain rates in the FGM cylinder, subjected to internal pressure alone, could be significantly reduced by subjecting it to both internal and external pressures though the stress inhomogenity in the FGM cylinder increases.     

On the accuracy of the Haar wavelet discretization method

Current study contains adaption of Haar wavelet discretization method (HWDM) for FG beams and its accuracy estimates. The convergence analysis is performed for differential equations covering a wide class of composite and nanostructures. Corresponding error bound has been derived. It has been shown that the order of convergence of the HWDM can be increased from two to four by applying Richardson extrapolation method. The theoretical estimates are validated by numerical samples considering FGM beam as a model problem. The results obtained by applying HWDM are compared with the results of finite difference method (FDM).     

Thermo-elastic Stresses in a Functional Graded Material Under Thermal Loading,Pure Bending and Thermo-mechanical Coupling

Analytical expressions have been derived for the through thickness stresses of a Functional graded materials (FGMs) thin plate subjected to thermal loading, pure bending and thermo-mechanical coupling, respectively. The structure is comprised of a metallic layer, a ceramic layer and a functional graded layer. Continuous gradation of the volume fraction in the FGM layer is modeled in the form of an "m" power polynomial of the coordinate axis in thickness direction of the plate. Numerical scheme of discretizing the continuous FGM layer with different graded distributions such as linear (m=1), quadratic (m=2) and square root (m=0.5) has been developed by the averaging technique of composites. Solutions for the stress distributions have been derived for the system under thermal loading, pure bending and thermo-mechanical coupling, respectively.     

Transient analysis of FGM and laminated composite structures using a refined 8-node ANS shell element

In this paper, we investigate the vibration analysis of functionally graded material (FGM) and laminated composite structures, using a refined 8-node shell element that allows for the effects of transverse shear deformation and rotary inertia. The properties of FGM vary continuously through the thickness direction according to the volume fraction of constituents defined by sigmoid function, but in this method, their Poisson’s ratios of the FGM plates and shells are assumed to be constant. The finite element, based on a first-order shear deformation theory, is further improved by the combined use of assumed natural strains and different sets of collocation points for interpolation the different strain components. We analyze the influence of the shell element with the various location and number of enhanced membrane and shear interpolation. Using the assumed natural strain method with proper interpolation functions the present shell element generates neither membrane nor shear locking behavior even when full integration is used in the formulation. The natural frequencies of plates and shells are presented, and the forced vibration analysis of FGM and laminated composite plates and shells subjected to arbitrary loading is carried out. In order to overcome membrane and shear locking phenomena, the assumed natural strain method is used. To validate and compare the finite element numerical solutions, the reference solutions of plates based on the Navier’s method, the series solutions of sigmoid FGM (S-FGM) plates are obtained. Results of the present theory show good agreement with the reference solutions. In addition the effect of damping is investigated on the forced vibration analysis of FGM plates and shells.     

A multi-scale model for coupled heat conduction and deformations of viscoelastic functionally graded materials

An integrated micromechanical-structural framework is presented to analyze coupled heat conduction and deformations of functionally graded materials (FGM) having temperature and stress dependent viscoelastic constituents. A through-thickness continuous variation of the thermal and mechanical properties of the FGM is approximated as an assembly of homogeneous layers. Average thermo-mechanical properties in each homogeneous medium are computed using a simplified micromechanical model for particle reinforced composites. This micromechanical model consists of two isotropic constituents. The mechanical properties of each constituent are time–stress–temperature dependent. The thermal properties (coefficient of thermal expansion and thermal conductivity) of each constituent are allowed to vary with temperature. Sequentially coupled heat transfer and displacement analyses are performed, which allow analyzing stress/strain behaviors of FGM having time and temperature dependent material properties. The thermo-mechanical responses of the homogenized FGM obtained from micromechanical model are compared with experimental data and the results obtained from finite element (FE) analysis of FGMs having microstructural details. The present micromechanical-modeling approach is computationally efficient and shows good agreement with experiments in predicting time-dependent responses of FGMs. Our analysis forecasts a better design for creep resistant materials using particulate FGM composites.     

Dynamic stability analysis of functionally graded higher-order shear deformable microshells based on the modified couple stress elasticity theory

Size-dependent dynamic stability response of higher-order shear deformable cylindrical microshells made of functionally graded materials (FGMs) and subjected to simply supported end supports is investigated. Material properties of the microshells vary in the thickness direction according to the Mori–Tanaka scheme. The modified couple stress elasticity theory in conjunction with the classical higher-order shear deformation shell theory is utilized to develop non-classical shell model containing additional internal length scale parameter to interpret size effect. The differential equations of motion and boundary conditions are derived by using Hamilton’s principle. The governing equations are then written in the form of Mathieu–Hill equations and then Bolotin’s method is employed to determine the instability regions. Selected numerical results are given to indicate the influences of internal length scale parameter, material property gradient index, static load factor and axial wave number on the dynamic stability behavior of FGM microshells. It is found that the width of the instability region for an FGM microshell increases with the decrease of the value of dimensionless length scale parameter. Moreover, it is shown that the classical shell model has an overestimated prediction for the width of instability region corresponding to the FGM microshells especially with lower values of material property gradient index.     

The effect of notch depth on J-integral and critical fracture load in plates made of functionally graded aluminum–silicone carbide composite with U-notches under bending

The present paper deals with the effect of notch depth on J-integral and critical fracture load in a plate made of functionally graded aluminum–silicone carbide composite (Al–SiC) with U-notch under bending. The weight fraction of SiC particles varies from 0% to 20% through the specimen width. Using three criteria namely mean stress (MS), point stress (PS), and averaged strain-energy density (ASED), the critical fracture load has been predicted and its variation with respect to the notch depth has been studied. A comparison of the J-integral between functionally graded and homogeneous Al–SiC composite were made, where the notch tip in the functionally graded material is situated in a layer with same mechanical properties as the homogeneous composite. The results indicated that in the case where the notch scene is toward brittleness increment the critical J-integral in functionally graded material (FGM) is larger than that of in homogeneous material with the same mechanical properties at the notch tip. Therefore, FGM is more convenient than homogeneous material against fracture.     

Thermal stability analysis of circular functionally graded sandwich plates of variable thickness using pseudo-spectral method

In the present study, the thermal stability of laminated functionally graded (FGM) circular plates of variable thickness subjected to uniform temperature rise based on the first-order shear deformation plate theory is presented. Furthermore, two models for FGM plates with variable thickness, corresponding with two manufacturing methods, are proposed. The laminated FGM plate with variable thickness is considered as a sandwich plate constituted of a homogeneous core of variable thickness and two constant thickness FGM face sheets whose material properties are assumed to be graded in the thickness direction according to a simple power law. In order to determine the distribution of the prebuckling thermal load along the radius, the membrane equation is solved using the shooting method. Subsequently, employing the pseudo-spectral method that makes use of Chebyshev polynomials, the stability equations are solved numerically to evaluate the critical temperature rise. The results demonstrate that the thermal stability is significantly influenced by the thickness variation profile, aspect ratio, the volume fraction index, and the core-to-face sheet thickness ratio.