类桁架夹层板的等效弹性常数研究

从应变能等效出发,将具有周期性分布的夹层板的类桁架夹芯与各向异性连续材料等效,给出了相应的宏观等效弹性常数,进而用有限元方法计算了实际夹层板和等效夹层板的结构响应,用一个算例证明了该文方法的有效性.通过对类桁架夹芯的等效弹性常数的计算,结果表明该文方法可以得到较为准确的等效弹性常数,且较其它类型的均匀化方法大大降低了计算量.     

层级褶皱结构夹层板的等效弹性常数

针对二级层级褶皱结构夹层板,通过变形协调研究了其等效弹性常数。首先对一级层级褶皱结构进行正交各向异性等效,得到一级等效弹性常数;将二级层级褶皱结构看成是由正交各向异性材料组成的三角形桁架夹心,将二级层级褶皱结构等效为均匀连续正交各向异性板,依据夹层板面板与夹心变形协调特点得到夹层板整体等效弹性常数。结合结构几何参数对等效公式的误差进行了讨论,并对等效公式做出修正。通过与数值分析结果对比,表明本文提出的等效公式具有较高精度。     

焊点/底充胶夹层等效弹性常数的简化分析

将高阶逐层离散层板模型和均匀化理论相结合,应用于具有非完全(单层内)周期性微结构的多层结构,用解析法分析了电子封装结构中由焊点和底充胶构成的非均质夹层的等效弹性常数．计算结果与已有结果进行了比较,验证了文中分析方法的有效性和简便性．     

功能梯度矩形板的三维弹性分析

将功能梯度三维矩形板的位移变量按双三角级数展开，以弹性力学的平衡方程为基础．导出位移形式的平衡方程。引入状态空间方法，以三个位移分量及位移分量的一阶导数为状态变量，建立状态方程。考虑四边简支的边界条件，由状态方程得到了功能梯度三维矩形板的静力弯曲问题和自由振动问题的精确解。由给出的均匀矩形板自由振动问题的计算结果表明．与已有的理论解以及有限元方法的计算结果相吻合。假设功能梯度三维矩形板的材料常数沿板的厚度方向按照指数函数的规律变化．进一步给出了功能梯度三维矩形板的自由振动问题和静力弯曲问题的算例分析，并讨论了材料性质的梯度变化对板的动力响应和静力响应的影响。     

基于三维弹性理论的约束阻尼结构振动阻尼特性分析

本文根据三维弹性理论建立了多层弹性－粘弹性阻尼复合板自由振动的运动方程．该方程所根据的力学模型包括了影响阻尼复合板振动的几乎全部变形因素，包括弹性层和粘弹性层的平面剪切、横向剪切、纵向拉伸以及粘弹性层在厚度方向的胀缩变形。用该方程对工程声学问题所关注的中高频域结构损耗因子进行了数值计算。此外，对“附加型”和“成品型”两种结构型式约束阻尼板损耗因子的差异，尤其是阻尼层的厚度方向胀缩变形耗能对结构损耗因子的影响，进行了计算讨论。     

考虑面层约束时蜂窝芯弹性常数的确定

本文研究了面板约束效应对蜂窝芯弹性性能的影响并基于六边形蜂窝芯夹层板的代表性体单元建立了考虑面板约束效应的蜂窝芯位移模式.根据真实蜂窝芯代表性单元与其等效材料的代表性单元在宏观均匀应变作用下的总弹性应变能相等,导出了蜂窝芯材料等效弹性常数的公式,进一步探讨了蜂窝几何参数对其弹性常数的影响规律.通过与现有理论结果、有限元结果和实验数据进行对比证实本文导出的弹性常数公式具有较好的预报精度.结果表明面板约束对蜂窝芯等效弹性常数有显著影响.     

利用松质骨理想化模型对骨小梁刚度的研究

利用结构张量的概念建立了考虑松质骨结构各向异性的理想模型，将杆型与板型两种传统模型统一起来．采用均匀化理论，通过有限单元的数值计算建立了松质骨弹性常数与结构张量、固体体积比之间的数值关系，并预测了骨小梁的弹性模量．结果表明，本文模型较好地体现了松质骨的各向异性力学性质．对骨小梁的计算结果表明，骨小梁的弹性模量在６７６ＧＰａ～１０９ＧＰａ范围内，平均意义上的结果是９２１ＧＰａ．     

失谐周期结构中弹性波与振动的局部化

基于弹性波传递矩阵方法，研究了失谐周期结构中弹性波与振动的局部化问题．给出了结构中弹性波传递矩阵的一般表达式，采用奇异值分解方法，分别计算了谐和与失谐周期结构中的局部化因子，并对其进行了分析讨论．对周期结构中波传播与振动局部化的分析方法可用于结构的优化设计．     

三角形夹芯板夹心层的等效弹性常数

推导了三角形夹芯板夹心层的等效弹性常数,为验证所推导的弹性常数的合理性,用NASTRAN有限元计算程序对两种模型进行了静力计算比较,一种是用所推导的弹性常数将夹心等效后,以层合板的形式进行计算的模型,另一种是对整个结构直接采用板单元进行计算的模型.计算结果表明:两种模型结果吻合良好.     

单边自由的固支岩板黏弹性行为分析及其应用

利用黏弹性理论对单边自由的固支岩板的黏弹性力学行为进行了分析研究，重新导出了相空间中黏弹性参数的变换关系式，并利用此式建立了单边自由的固支岩板的广义Kelvin黏弹性分析格式，将其应用于某层状岩体洞室顶板的变形特性分析．计算表明，其与实际勘察结果比较接近，可供工程实际应用参考．     

A PRECISE METHOD FOR SOLVING WAVE PROPAGATION IN HOLLOW SANDWICH CYLINDERS WITH PRISMATIC CORES

Wave propagation in infinitely long hollow sandwich cylinders with prismatic cores is analyzed by the extended Wittrick-Williams(W-W) algorithm and the precise integration method(PIM). The effective elastic constants of prismatic cellular materials are obtained by the homogenization method. By applying the variational principle and introducing the dual variables, the canonical equations of Hamiltonian system are constructed. Thereafter, the wave propagation problem is converted to an eigenvalue problem. In numerical examples, the effects of the prismatic cellular topology, the relative density, and the boundary conditions on dispersion relations,respectively, are investigated.     

用均匀化理论分析蜂窝结构的等效弹性参数

在线弹性范围内,根据均匀化理论,并结合有限元方法推导出适用于二维周期性结构的均匀化的有限元格式（Homo FEM）,计算出不同相对密度下的规则蜂窝结构的等效弹性模量Ee和泊松比νe.同时,利用蜂窝结构的代表胞元模型,用常规的有限元方法（FEM）模拟计算出相应的等效弹性参数.最后将两种数值计算结果与己有的理论公式进行了比较和分析讨论.结果表明:在考察的相对密度全场范围内（0～0.4）,HOmO FEM得到的蜂窝结构的 Ee和νe 与 FEM使用平面实体单元模拟计算得到的结果一致吻合,反映出 Homo FEM数值方法的客观准确性和可行性.而 Gibson公式和 W-K得到的等效弹性模量值 Ee只是在较小相对密度的情况下（小于0.15）与数值计算结果吻合.当结构的相对密度较大时,必须考虑胞棱附近区域由应力集中导致的复杂的应力和应变分布的影响.     

Thermoelastic characteristics of a composite solid with initial stresses

Thermoelastic problem for a composite solid with initial stresses is considered on the basis of the asymptotic homogenization method. The homogenized model is constructed by means of the two-scale asymptotic homogenization techniques. The major result of a present paper is that the effective (homogenized) thermoelastic characteristics of the composite material depend not only on local distributions of all types of material characteristics: local elastic properties, local thermoelastic properties, but also on local initial stresses. Therefore it is shown that for the inhomogeneous (composite) material local initial stresses contribute towards values of the effective characteristics of the material. This kind of interaction is not possible for the homogeneous materials. From the mathematical viewpoint, the asymptotic homogenization procedure is equivalent to the computation of G-limit of the corresponding operator. And the above noted phenomenon is based on the fact that in the considering case the G-limit of a sum is not equal to the sum of G-limits. The developed general homogenized model is illustrated in the particular case of the small initial stresses, which is common for the practical mechanical problems. The explicit formulas for the effective thermoelastic characteristics and numerical results are obtained for a laminated composite solid with the initial stresses.     

基于迭代法的非线性弹性均质化研究

微观结构对复合材料的宏观力学性能具有至关重要的影响, 通过合理设计复合材料微观结构可以得到期望的宏观性能. 均质化方法作为一种有效的设计方法, 它从微观结构的角度出发, 利用均匀化的概念, 实现了对复合材料宏观力学性能的预测和设计. 而当考虑非线性因素, 均质化的实现就非常困难. 本文利用双渐近展开方法, 将位移按照宏观位移和微观位移展开, 推导了非线性弹性均质化方程. 通过直接迭代法, 对非线性弹性均质化方程进行了求解, 并给出了具体的迭代方法和实现步骤. 本文基于迭代步骤和非线性弹性均质化方程编写MATLAB 程序, 对3种典型本构关系的周期性多孔材料平面问题进行了计算, 对比细致模型的应变能、最大位移和等效泊松比, 对程序及迭代方法的准确性进行了验证. 之后对一种三元橡胶基复合材料进行多尺度均质化, 将其分为芯丝尺度和层间尺度. 用线弹性的均质化方法得到了芯丝尺度的等效弹性参数, 并将其作为层间尺度的材料参数. 在层间尺度应用非线性弹性均质化方法对结构进行计算, 得到材料的宏观等效性能, 并以实验结果为基准进行评价.      

Homogenization of Polycrystalline¶Aggregates

The effective elastic properties of a polycrystalline material depend on the single crystal elastic constants of the crystallites comprising the polycrystal and on the manner in which the crystallites are arranged. In this paper we apply the techniques of homogenization to put the problem of determining effective elastic constants in a precise mathematical framework that permits us to derive an expression for the effective elasticity tensor. We also study how the homogenized elasticity tensor changes as the probability characterizing the ensemble changes. Under the assumption that the field of orientations of the crystallographic axes of the crystallites is an independent random field, we show that our theory is compatible with the formulation used in texture analysis. In particular, we are able to prove that the physical assumption made by [10] in his study of weakly-textured polycrystals holds true. In addition, we establish some elementary bounds on the material constants that characterize the effective elasticity tensor of weakly-textured orthorhombic aggregates of cubic crystallites. Accepted: (June 15, 1999)     

Variational asymptotic micromechanics modeling of heterogeneous porous materials

This paper presents a numerical technique to predict the effective elastic properties of heterogeneous fluid-filled porous media where the heterogeneity may result from dissimilar solid and fluid phase properties or due to mismatch in porous microstructure. The technique is based on the variational asymptotic method of homogenization where finite element method is employed for discretization. Biot’s theory of poroelasticity is used to describe porous media where both solid and fluid phase motions (u ? U formulation) are considered with associated strain measures. The method estimates the poroelastic constitutive law in single analysis which makes it very efficient compared to other finite element based homogenization techniques. The method is also general enough to compute all 28 elements of an anisotropic constitutive matrix. Other than estimating the effective properties the micro-stress/strain distribution is also obtained at no additional cost.The method is successfully applied for homogenization of porous media, fluid-filled cavity and finally for effective property estimation of bone lamella. In absence of any other direct method of porous media homogenization, the present technique is compared with classical homogenization methods with fluid approximated as solid of very high Poisson’s ratio. The suitability of this approximation and various other alternatives are also discussed. It is shown that the present homogenization method can be an efficient tool for bone property estimation where fluid-filled porous hierarchical micro-/nanostructure must be respected at all steps.     

Anisotropic effective higher-order response of heterogeneous Cauchy elastic materials

The homogenization results obtained by Bacca et al. (2013a), to identify the effective second-gradient elastic materials from heterogeneous Cauchy elastic solids, are extended here to the case of phases having non-isotropic tensors of inertia. It is shown that the nonlocal constitutive tensor for the homogenized material depends on both the inertia properties of the RVE and the difference between the effective and the matrix local elastic tensors. Results show that: (i) orthotropic nonlocal effects follow from homogenization of a dilute distribution of aligned elliptical holes and, in the limit case, of cracks; (ii) even under the dilute assumption and isotropic local effective behaviour, homogenization may lead to effective nonlocal orthotropic properties.     

复合材料周期性线弹性微结构的拓扑优化设计

提出复合材料周期性线弹性微结构拓扑优化设计的模型，模型1设计具有极值弹性特性的复合材料，模型2设计工况最刚微结构单胞。通过该模型和均匀化技术可以获得优化的微结构单胞，进而改善或者得到最优宏观特性的复合材料。为了便于制造和应用，用胞体材料而不是多相材料来得到复合材料的极值弹性特性和最大刚度。优化结果表明，该模型与数值方法相结合可以有效地实现微结构的拓扑优化设计。     

Effective elastic shear stiffness of a periodic fibrous composite with non-uniform imperfect contact between the matrix and the fibers

In this contribution, effective elastic moduli are obtained by means of the asymptotic homogenization method, for oblique two-phase fibrous periodic composites with non-uniform imperfect contact conditions at the interface. This work is an extension of previous reported results, where only the perfect contact for elastic or piezoelectric composites under imperfect spring model was considered. The constituents of the composites exhibit transversely isotropic properties. A doubly periodic parallelogram array of cylindrical inclusions under longitudinal shear is considered. The behavior of the shear elastic coefficient for different geometry arrays related to the angle of the cell is studied. As validation of the present method, some numerical examples and comparisons with theoretical results verified that the present model is efficient for the analysis of composites with presence of imperfect interface and parallelogram cell. The effect of the non uniform imperfection on the shear effective property is observed. The present method can provide benchmark results for other numerical and approximate methods.