功能梯度材料构件三维分析的细观元模型

提出一种新颖的功能梯度构件分析的细观元法,给出了方法模型、基本算式及特点与功能。细观元法对构件的常规有限单元内部设置密集细观单元以反映材料特性梯度变化,又通过协调条件将各细观元结点自由度转换为同一常规有限元自由度,再上机计算。这种细观元法既能充分反映材料功能梯度及组分变化特性,而其计算单元与自由度又与常规有限元一样,是一种针对功能梯度构件分析的有效数值方法。算例表明了细观元法对不同情况下功能梯度构件分析的适应性与精度。     

具有不同功能梯度分布函数的板件的三维分析

发展了一种新颖的功能梯度结构分析的细观元法。细观元法对结构的常规有限单元内部设置密集细观单元以反映材料特性梯度变化,又通过协调条件将各细观元结点自由度转换为同一常规有限元自由度,再上机计算。这种细观元法既能充分反映材料功能梯度变化特性;而其计算单元又和常规有限元一样,是一种针对功能梯度结构分析的有效数值方法。文中通过细观元技术进行计算、分析,给出了具有不同功能梯度分布函数板件的力学量三维分布形态。     

空隙分布对功能梯度板件宏观响应的影响

提出了一种新的功能梯度结构分析的细观元法. 细观元法对结构的常 规有限单元内部设置密集细观单元以反映材料细观构造,又通过协调条件将各细观元结点自 由度转换为同一常规有限元自由度. 此方法实现了材料细观结构到构件宏观响 应的直接过渡分析. 用细观元法来分析细观构造上空隙存在对宏观响应影响,给出了含 有不同分布与形状、位置空隙的功能梯度板件的力学量三维分布形态,实现功能梯度材料结 构宏、细观间跨尺度分析.     

中等组分网状结构局部微变对功能梯度板三维动力特性的影响

利用细观元方法根据材料实际金相图片信息进行材料参数输入,对发生局部网格变化的功能梯度板件进行三维动力特性分析,完成了材料细观结构与构件宏观响应间的跨尺度分析.细观元法在结构的常规有限元内部设置密集的细观单元来反映材料细观构造,此方法可实现材料细观结构到构件宏观响应的直接过渡分析,为具有细观结构微观变化的功能梯度板件的分析提供一种新的工具.利用细观元法对具有中等组分网状结构发生局部微变的功能梯度板进行三维动力特性分析,给出其固有频率及振型的三维分布,特别是功能梯度板应力振型的平面等值线图差异,得到较好的结果.     

功能梯度材料板件三维分析的半解析梯度有限元法

将半解析有限元与梯度有限元相结合,形成一种半解析梯度有限元来求解功能梯度材料板件问题。该方法兼有有限元法的适应性强、程序统一,半解析有限元法的节省单元与计算工作量,梯度有限元法的适应构件内部材料性能任意梯度分布等特点,并实现用一维数值计算给出构件三维分析结果。算例分析表明了方法的精度、功能与上述特点,充分揭示了功能梯度材料板件力学响应的三维形态。半解析梯度有限元法可推广应用到其他功能梯度材料面结构的各类分析中。     

反映材料微观结构效应的宏观动力特性分析

探讨了实现复合材料细观结构与构件宏观动力特性直接关联的细观元法。细观元法先进行宏观单元剖分，然后分析细观结构，将微结构力学量转化为宏观结点量计算。该方法不增加自由度，但使得微结构层次上任意铺设方式和任意微小变化均能在宏观动力特性上得到反映。     

非匀质材料板的微结构优化设计

探讨具有微结构构造的非匀质材料构件在微结构层次上的优化设计,即寻求满足构件宏观性能要求的最佳微结构材料与构造参数。文中采用细观元法确定非匀质材料构件宏观性能与材料微结构参数间定量关系,建立起微结构优化设计数学模型,具体分析了复合材料板件满足强度、刚度要求的最佳微结构参数。有关方法可适用于复合材料、功能梯度材料、智能材料等新材料构件。     

竖向裂缝对功能梯度板的热响应影响

采用条单元法分析了竖向裂缝对功能梯度板的热响应影响。功能梯度板的材料属性沿板厚方向连续线性变化,温度变化热源作用于带竖向裂缝的功能梯度板上。通过研究得出了裂缝距离热源不同位置、不同长度裂缝及不同频率温度变化热源等状态时,功能梯度板上表面的热响应情况。采用条单元法研究带竖向裂缝的功能梯度板的热响应问题,为带裂缝的功能梯度板的热研究提供了一定的指导。     

横向裂缝对功能梯度板的热响应影响

采用条单元法分析了横向裂缝对功能梯度板热响应的影响。研究了功能梯度板的材料属性沿板厚方向连续线性变化时,温度变化热源作用于带横向裂缝的功能梯度板的问题（此热源沿板厚方向连续线性变化）。通过研究不同频率温度变化热源,得到了当量纲为一的温度变化热源频率为3.14时,功能梯度板上表面出现的位移响应比较均匀;通过研究裂缝长度取H、3H、5H时出现的位移响应,得到了根据位移响应特性判断裂缝长度的方法;通过对不同深度裂缝的研究表明：裂缝越深,上表面位移响应强度越小。本研究对带横向裂缝的功能梯度板的热响应问题具有一定的指导意义。     

基于自然单元法的功能梯度板固有频率优化

对功能梯度板的固有频率优化问题进行研究.从无网格方法自然单元法出发,建立了功能梯度板的一阶剪切变形理论的自由振动分析格式.自然单元法是一种基于自然邻近插值的无网格数值方法.自然邻近插值不涉及矩阵求逆运算,也不需要任何人为的参数.较之于传统复合材料,功能梯度板材料属性沿厚度方向呈梯度连续变化,因此材料加工时产生的残余应力小很多,此外,功能梯度板具有可设计的优点.以第一阶固有频率为优化目标建立优化模型,通过单纯形法搜索较优的功能梯度板的成分分布.最后通过矩形功能梯度板在不同边界条件下的基频优化的实例,验证了整个算法的可行性和有效性.     

THREE-DIMENSIONAL STATIC ANALYSES FOR FGM PLATES WITH MEDIUM COMPONENTS AND DIFFERENT NET STRUCTURES

A new microelement method for the analyses of functionally graded structures was proposed. The key of this method is the maneuverable combination of two kinds of elements. Firstly, the macro elements are divided from the functionally graded material structures by the normal finite elements. In order to reflect the functionally graded distributions of materials and the microconstitutions in each macro-element, the microelement method sets up the dense microelements in every macro-element, and translates nodes to the same as the normal finite elements by the degrees of freedom of all microelemental the compatibility conditions. This microelement method can fully reflect the micro constitutions and different components of materials, and its computational elements are the same as the normal finite elements, so it is an effective numerical method for the analyses of the functionally graded material structures. The three-dimensional analyses of functionally graded plates with medium components and different micro net structures are given by using the microelement method in this paper. The differences of the stress contour in the plane of functionally graded plates with different net microstructures are especially given in this paper.     

Transient thermal stresses in two-dimensional functionally graded thick hollow cylinder with finite length

In this paper transient thermal stresses in a thick hollow cylinder with finite length made of two-dimensional functionally graded material (2D-FGM) based on classical theory of thermoelasticity are considered. The volume fraction distribution of materials, geometry and thermal load are assumed to be axisymmetric but not uniform along the axial direction. The finite element method with graded material properties within each element is used to model the structure. Temperature, displacements and stress distributions through the cylinder at different times are investigated. Also the effects of variation of material distribution in two radial and axial directions on the thermal stress distribution and time responses are studied. The achieved results show that using 2D-FGM leads to a more flexible design so that time responses of structure, maximum amplitude of stresses and uniformity of stress distributions can be modified to a required manner by selecting suitable material distribution profiles in two directions.     

基于金相图片识别功能梯度材料参数的梯度分布函数

功能梯度材料具有复杂的细观结构.其内部构造远比匀质材料复杂.以目前的实验条件,测量功能梯度材料参数分布函数一般是十分困难的.该文提出一种细观元方法,直接利用功能梯度材料金相图片信息,来进行功能梯度构件宏观响应的跨尺度力学分析.另在功能梯度材料结构静、动力正演分析基础上,根据正演所求得的挠度或固有频率值,采用混和罚函数法来反演识别功能梯度材料参数的宏观梯度分布函数.     

功能梯度板动力分析的光滑有限元法研究

为提高功能梯度板动响应问题求解精度,基于一阶剪切变形板理论,提出了求解功能梯度板自由振动问题的Cell-Based 光滑有限元格式．功能梯度板材料属性沿厚度方向呈梯度连续变化,计算系统刚度矩阵时在光滑域内进行光滑梯度操作,可提高求解精度．采用Cell-Based 光滑有限元法,讨论了长厚比、形状因子和边界条件对两种典型功能梯度方板无量纲频率参数的影响,并与FEM法的解和文献中的解做了对比．数值算例的结果表明,光滑梯度操作可改善有限元系统的刚度,Cell-Based 光滑有限元法的计算结果更加逼近真实解,从而为功能梯度材料的进一步应用打下基础．     

弹性地基加肋功能梯度板自由振动分析的无网格法

基于一阶剪切变形理论和移动最小二乘近似研究Winkler弹性地基上加肋功能梯度板的固有频率。假设功能梯度板的材料性质沿厚度方向按幂函数连续变化,基于物理中面和移动最小二乘近似分别推导功能梯度板和肋条的动能和势能,再通过引入位移协调条件,建立板和肋条节点参数转换关系,叠加两者的总能量,然后利用Hamilton原理推导加肋功能梯度板自由振动控制方程。采用完全转换法施加边界条件。通过将本文的计算结果与有限元以及文献的结果对比,验证方法的收敛性以及准确性。     

Transient heat conduction in two-dimensional functionally graded hollow cylinder with finite length

In this paper a thick hollow cylinder with finite length made of two dimensional functionally graded material (2D-FGM) subjected to transient thermal boundary conditions is considered. The volume fraction distribution of materials, geometry and thermal boundary conditions are assumed to be axisymmetric but not uniform along the axial direction. The finite element method with graded material properties within each element is used to model the structure and the Crank–Nicolson finite difference method is implemented to solve time dependent equations of the heat transfer problem. Two-dimensional heat conduction in the cylinder is considered and variation of temperature with time as well as temperature distribution through the cylinder are investigated. Effects of variation of material distribution in two radial and axial directions on the temperature distribution and time response are studied. The achieved results show that using two-dimensional FGM leads to a more flexible design so that transient temperature, maximum amplitude and uniformity of temperature distributions can be modified to achieve required specifications by selecting a suitable material distribution profile in two directions.     

Two-dimensional modeling of heterogeneous structures using graded finite element and boundary element methods

In the present work, graded finite element and boundary element methods capable of modeling behaviors of structures made of nonhomogeneous functionally graded materials (FGMs) composed of two constituent phases are presented. A numerical implementation of Somigliana’s identity in two-dimensional displacement fields of the isotropic nonhomogeneous problems is presented using the graded elements. Based on the constitutive and governing equations and the weighted residual technique, effective boundary element formulations are implemented for elastic nonhomogeneous isotropic solid models. Results of the finite element method are derived based on a Rayleigh–Ritz energy formulation. The heterogeneous structures are made of combined ceramic–metal materials, in which the material properties vary continuously along the in-plane or thickness directions according to a power law. To verify the present work, three numerical examples are provided in the paper.