正交异性复合材料J积分的研究

本文推导了正交异性复合材料板Ⅰ型裂纹Ｊ积分与位移导数的关系式，同时给出了应力强度因子Ｋ＿Ⅰ与位移的关系式，采用贴片云纹干涉法对三点弯曲粱进行了测试。由云纹图的位移场求出了Ｊ与Ｋ＿Ⅰ值，进而验证了正交异性复合材料板Ｊ与Ｋ＿Ⅰ的关系式的正确性。     

全息、散斑与云纹干涉的量程分析

本文以Fourier分析与光学统计为基础,以全息干涉的量程分析为主线,给出了全息干涉、散斑干涉与云纹干涉的最大可测位移表达式。首先由频谱分析给出了三种干涉间的相互关系,再由互相关分析得到了全息干涉法可测位移量与散斑平均尺寸间的关系式。散斑干涉与云纹干涉则作为全息干涉记录的两种特殊情况给出了其量程的上限。     

基于相位偏移干涉术的薄膜厚度测量方法

为解决薄膜厚度的高精度测量问题,提出一种基于相位偏移干涉术的薄膜厚度测量新方法,利用该方法对一个实际SiO₂薄膜样片进行测试,通过对所获取的干涉图进行相位解包及数据分析处理,实现对薄膜样片厚度的精确测试。结果表明：该方法具有非接触和测量精度高等优点,所测薄膜厚度的峰谷值为0.162μm,均方根值为0.043μm,为薄膜工艺的进一步研究提供了检测方法上的技术保障。     

微蜂窝环境中无线接收信号的特性分析

以微蜂窝系统为背景,研究了以测试射线法和虚拟源射线跟踪法为代表的射线跟踪技术,并用这两种方法对射线跟踪进行建模,分析比较两种模型的优缺点.利用这两种模型对实际情况进行计算,精确地找出所有给定情况的传播路径并可视化;对多波干涉的振幅进行了统计学分析,对宽带多波干涉现象进行了数学建模,并分析了合成波的包络统计特性.     

基于光子结构猜想的波动性现象建模仿真研究

综合龚祖同院士的光子类氢原子结构论和北大俎栋林教授的光子电磁场结构论,提出了两种结构相统一的理论猜想.基于猜想对单缝衍射、双缝干涉以及多缝干涉中光强与光子尺度、细缝宽度等参数的关系进行建模,并以双缝干涉为例进行了仿真实验.通过实验结果与经典波动光学中光强分布的对比,验证了模型的合理性.     

加性二值噪声激励下Duffing系统的随机分岔

研究了Duffing系统在加性二值噪声作用下的随机分岔现象.首先,根据二值噪声的统计特性,推导得到二值噪声状态间的跃迁概率,据此对二值噪声进行了数值模拟.其次,利用四阶Runge-Kutta(龙格-库塔)数值算法得到该系统位移和速率的稳态联合概率密度及位移的稳态概率密度.然后,通过对位移稳态概率密度单双峰结构变化的研究,发现加性二值噪声的状态和强度能够诱导系统产生随机分岔现象.最后,观察到随着系统非对称参数的逐渐变化,系统同样产生了随机分岔现象.     

构造容许位移的转换边界法

本文提出了在复杂边界条件下构造容许位移的转换边界法.所谓转换边界法,就是首先根据叠加原理将实际系统转换为基本系统及附加边界力和附加边界位移,然后应用变分原理于基本系统,最后应用级数转换的办法求得实际系统的容许位移.本文还给出了边界条件变化的混合能量原理.这边界条件变化的混合能量原理和边界条件变化的势能原理和余能原理都是转换边界法的主要理论基础.应用转换边界法我们构造了复杂边界条件平面应力问题和弯曲问题矩形板的容许位移.由于转换边界法构造容许位移是遵循着变分原理和确定的程序进行的,因而克服了Rayleigh-Ritz法猜测、拼凑容许位移的困难.     

一端固支一端简支变厚度梁的弹性力学解

研究了一端固支另一端简支连续变厚度梁在静力荷载作用下的应力和位移分布.通过引入单位脉冲函数和Dirae函数,将固支边等效为简支边与未知水平反力的叠加,利用平面应力问题的基本方程,导出满足控制微分方程及左右两端边界条件的位移函数的一般解,对上下表面的边界方程作Fourier级数展开,结合固支边位移为O的条件确定待定系数,得到的解是高精度的.数值结果与商业有限元软件ANSYS进行了比较,显示出很好的精度.     

一般组合弹性结构的有限元分析

提出一个求解一般组合弹性结构问题的有限元方法:对体件的位移、 板件的纵向位移和杆件的纵向位移用线性协调元离散, 对杆件的纵向转角用二次协调元离散, 对板件的横向位移和杆件的横向位移分别用Morley元和三次Hermite元离散. 在相应的非协调元空间上建立了广义Korn不等式, 进而证得有限元方法的唯一可解性. 最后导出方法在能量模意义下的最优误差估计.     

指数型体积分数功能梯度材料的薄壁圆柱壳振动

研究了指数型体积分数对功能梯度薄圆柱壳振动频率的影响.壳体厚度方向上的材料特性呈指数律变化.由Love薄壳理论,得到应变-位移及曲率-位移关系表达式.利用Rayleigh-Ritz方法,导出壳体的固有频率方程.假定轴向形态关系是典型的梁函数.壳体的固有频率取决于组合材料的体积分数.所得结果与已有文献的结果进行对比分析,说明本方法是正确的.     

拟协调元的位移函数及节点误差

直接从拟协调元的应变关系式出发,构造具有明确物理意义的幂级数形式的位移函数,从而得出拟协调元的常应变和线性应变系数是唯一确定的,它只能收敛到常应变的结论;刚性位移项可采用多种构造方法,不同的方法得出的节点参数与单元的本身的节点参数存在不同阶次的误差,这与常规位移法有限元不同。     

Finite-element formulations of shear localization in granular materials

Displacement and mixed finite element formulations of shear localization in granular materials are presented. The formulations are based on hypoplastic constitutive laws for soils and the mixed-enhanced treatment involving displacement, strain and stress rates as independently varied fields. Included in these formulations are the standard displacement method, the three-field mixed formulation, the method of incompatible modes, the enhanced assumed strain method and the mixed enhanced strain method. Several numerical examples demonstrating the capability and performance of the different finite element formulations are presented. The numerical results are compared with available experimental data of Hostun RF sand and numerical results of Karlsruhe sand on biaxial tests. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Generalized thermoelastic infinite medium with spherical cavity subjected to moving heat source

This paper deals with a problem of thermoelastic interactions in an isotropic unbounded medium with spherical cavity due to the presence of moving heat sources in the context of the linear theory of generalized thermoelasticity with one relaxation time. The governing equations are expressed in the Laplace transform domain and solved in that domain. The inversion of the Laplace transform is done numerically using the Riemann-sum approximation method. The numerical estimates of the displacement, temperature, stress, and strain are obtained for a hypothetical material. The results obtained are presented graphically to show the effect of the heat source velocity and the relaxation time parameters on displacement, temperature, stress, and strain.     

壳体的非线性应变分量

壳体的非线性应变分量是非线性壳体力学的基础,在壳体的稳定以及各种大变形问题中须要用到它们.由于壳体几何复杂,在现有文献中,还未见到较全面地表示此种非线性应变分量的一般公式,现在导出六个用正交曲线坐标表示的包括线性与非线性部分的壳体应变分量的公式,其中三个为拉伸应变分量,另三个为剪切应变分量.     

Functions of a complex variable in problems in the theory of elasticity with mass forces

The general equations of the theory of elasticity are reduced to an inhomogeneous fourth-order equation assuming that there is a linear dependence of the third component of the displacement vector on the third coordinate and that a mass force potential exists. The solution of this equation is presented, in particular, using two complex Kolosov–Muskhelishvili potentials. A third complex potential is introduced in addition to these. Using the three complex potentials, expressions are obtained for the components of the displacement vector and the stress and strain tensors that take account of mass forces. The application of the three potentials is analysed in problems in the theory of elasticity, and analytical solutions of several plane strain problems are presented.     

Résolution mathématique d'équations décrivant l'évolution d'une surface d'un matériau contraint

We consider a cristal structure, constituted by an elastic substrate and a film with a small thickness. The lattice parameters between the film and the substrate are not the same; consequently, a strain appears in the structure. This strain generates morphologies(see [1,2]).The difficulty consists in finding the profile of the film-vapor surface at any time, which depends on the elastic displacement of the structure. To this end, a physical model, detailed in [2], consists in solving a coupled system of partial derivative equations. The unknowns are the elastic displacement of the structure and the profile of the evolution surface. The elastic displacement solves the linearized elasticity equations posed over the domain occupied by the structure. The boundary of this domain depends on the evolution surface. The second equation is the evolution equation, depending on the elastic displacement by a term of the surface energy. This model is greatly simplified in order to obtain a decoupled two-dimensional model: the map of the film-vapor surface solves a non-linear partial derivatives equation, which is independent of the displacement of the structure.In this Note, we give some results of the existence and uniqueness of a solution for this model under some assumptions about the first derivative of the map.     

Finite element analysis of arches undergoing large rotations - I: Theoretical comparison

In this two part paper, the first part deals with five different nonlinear theories applicable to the analysis of arches in the context of solving the large displacement and the large rotation problem. These theories include, classical theory, first-order shear deformation theory, third-order shear deformation theory, modified classical theory and the Donnell-type theory. All the theories are developed using the Total Lagrangian approach. Simplifications and assumptions used in each of the theory are discussed. Explicit strain displacement gradient relations and element independent equilibrium equations in terms of displacement gradients are given for all the theories. Limitations of each of theory are discussed. In the second part of this paper, application of these theories for the classification of arch geometries is considered.     

论连续体有限变形的位移协调条件

有限变形的协凋条件在文献中常以Riemann-Christoffel张量等于零表达.水文应用Cesaro方法和作者的非线性应变-转动张量分解定理证明上述条件仅是必要的,尚不充分保证位移场的单值性与连续;文中导出新的一般有限变形的位移协调条件.当应变与转动微小时,它化为Saint-Venant方程.     

An analytical solution for displacements due to reservoir compaction under arbitrary pressure changes

Production of fluids in reservoirs, such as oil, gas and water, leads to changes in the stress and strain fields, generating compaction in the reservoir and subsidence of the ground surface. Some of the severe consequences of these displacements are rock fracture, induced seismicity, fault reactivation, wellbore failure, and reduction in the storage capacity of aquifer systems. Analytic methods based on the nucleus of strain approach with simplifying assumptions can be useful to estimate compaction and subsidence, and to indicate when more detailed analyses are required. However, these methods may present problems by the evaluation of the displacement response inside and in the vicinity of the reservoir due to the presence of singularities in the solution. In this work, an analytical displacement solution is obtained for reservoirs of arbitrary shape in a linear elastic semi-infinite medium under arbitrary distribution of pressure changes. For this, the reservoir is discretized in parallelepiped cells. A three-dimensional integration of the solution is carried out over each cell for an infinitesimal reservoir based on the nucleus of strain approach. The final displacement field is given by the superposition of the solutions of individual cells. The three-dimensional integration eliminates the singularities and allows the evaluation of displacements throughout the entire model, including the reservoir. The solutions presented can be easily implemented in a computational procedure, maintaining the low effort of similar methods. Finite element models are employed to verify the accuracy of the proposed solution.     

Generalized Korn's inequality and conformal Killing vectors

Korn's inequality plays an important role in linear elasticity theory. This inequality bounds the norm of the derivatives of the displacement vector by the norm of the linearized strain tensor. The kernel of the linearized strain tensor are the infinitesimal rigid-body translations and rotations (Killing vectors). We generalize this inequality by replacing the linearized strain tensor by its trace free part. That is, we obtain a stronger inequality in which the kernel of the relevant operator are the conformal Killing vectors. The new inequality has applications in General Relativity.