介质膜反射镜层间电场分布

本文给出了两种方法推导非四分之一波长介质膜系相邻高折射率膜层场强振幅平方公式。第一种方法是从膜系分界面两边介质膜中驻波电场强度平方比关于分界面位置及相角的解析表达式入手,分析各层的相移关系,得出所求公式。第二种方法是从多层介质膜分界面处场强复数形式的递推公式出发,通过数学变换,消去辅助参数,得出所求公式。     

材料微结构界面层损伤演化的数值分析

用计算微观力学方法,对多晶体微结构界面及损伤本构关系进行了细致构造,并拓宽了Ｇｕｒｓｏｎ体胞模型,使之计及弹塑性耦合效应;应用多域边界元数值计算方法,对微结构的界面力学行为进行了数值仿真;讨论了界面层在形变过程中空洞损伤及损伤率的变化规律,获得了与理论分析相一致的结论,见证了本文分析的合理性及可行性     

流体饱和多孔隙介质中弹性波运动方程的解—伪谱法

本文提出了一种解流体饱和多孔隙介质中波传播方程的数值方法，并详细推导了该方法的计算公式．用此公式对单界面模型中地震波的传播进行了模拟，结果与Ｂｉｏｔ理论预测的相符．     

混凝土材料的细观结构数值模拟与性能分析

在细观上将混凝土看作是由粗骨料、水泥砂浆和界面三相介质组成的复合材料,根据体视学原理并应用蒙特卡洛方法模拟出混凝土的二维圆形骨料分布;应用理论公式计算出界面厚度,并将界面看作是包围在骨料外面的一层圆环,在细观上模拟生成混凝土的三相组成;基于骨料随机模型,应用有限单元法提出了混凝土稳态氯离子扩散系数的计算方法并与试验结果进行了对比。结果表明,该模型用于计算混凝土稳定氯离子扩散系数是有效的。     

二层介质的时-深转换模型研究

在水平叠加时间剖面上,研究了两桩号处上、下层底界面对应的反射时间以推算其空间反射点位置。已往分层作图法不符合射线原理,程序扫描迭代法运算量大且不稳定,故当二层介质倾向一致或相反时,其特例公式无法适应各种情况。针对这一问题,根据平面波在二层均介质中的传播理论,当两介质层倾向一致时,用几何法推出上层底界面的入射角和下层底界面的倾角的公式,并确定角的正负,进而分析出通式;当两介质层倾角不同时,根据实例模型用解析法编程验证了通式的正确性,从而导出时－深转换的通用数学模型。在地震资料解释中便于计算机准确、高效地将地震成果转换为地质成果。     

应用改进虚拟流方法计算多介质可压缩流动

原始的虚拟流(GFM)方法在处理强激波与物质界面作用时遇到了困难,计算结果不准确.本文采用改进虚拟流方法(MGFM)对多介质可压缩流体进行了数值模拟,采用二阶TVD-WAF格式结合HLLC求解器求解Euler方程得到流场参数分布,应用五阶WENO求解level set方程捕捉物质界面.在此基础上分别计算了一维和二维数值算例.结果表明,该方法在能精确捕捉到物质界面的同时可以计算较强激波情况下的流场,并且可以捕获激波、物质界面和各类间断的相互作用.     

硬X射线梯度渐变多层膜设计

讨论了硬X射线梯度渐变多层膜的膜对材料的选择 ,介绍了分析方法、数值解析方法和分堆栈法三种用于膜系理论设计的方法,并且就这三种方法的优缺点进行了比较和分析.     

一种矩阵求逆方法

给出一种有利于机助求解大型逆矩阵的方法——按位替换求逆法．此方法采用矩阵三角分解原理,将矩阵表达为分解上、下三角阵的乘积,利用上、下三角阵的求逆结果求得原矩阵的逆阵．矩阵求逆分三步进行：第一步求约化系数,第二步求上、下三角阵的逆阵,第三步求原矩阵的逆阵．每一步计算均采用按位替换求解法,即将矩阵中不同位置的元素表达为相应位置的位置函数值,每一步计算是用新的位置函数值替换相应位置的原有位置函数值,最终将原矩阵中各位置的元素替换为其逆矩阵中相应位置的元素．求逆公式简单,利于编程,节省所需内存空间。     

非均匀介质中弹性波的传播

对弹性波在非均匀介质传播时的波幅进行了研究,用解析方法探讨了非均匀区域性质变化时对弹性波波幅的影响,将非均匀区域离散成薄层,建立了波动方程和波幅传递矩阵,通过数值计算结果与解析解的比较,为弹性波在工程中的应用提供了计算分析的依据.     

方位电阻率测井在地层界面电磁响应的研究

利用解析法计算随钻方位电阻率仪器激发的电磁场随仪器方位变化的规律,研究其在地层界面预测中的应用。通过分析电磁波在各层介质中的反射和透射规律,得出了介质层中电磁波的解析表达式,计算了电磁波电阻率随钻测量的幅度衰减和相移,分析了定向电磁测量对地层界面的灵敏性,研究了地层相对倾角和接收天线倾角对电磁测量的影响。研究表明,线圈距和目的层厚度越大,定向电磁测量的探测范围越大;随着地层相对倾角和接收天线倾角的增加,定向幅度衰减在接近地层界面时的变化越明显,对地层界面的灵敏性增强。结合方位电阻率成像和定向电磁响应说明,在常规随钻电阻率仪器的基础上,增加倾斜接收天线,可以实现地层倾向的预测和判断。     

高分辨率复杂电极系的高效数值模拟

文中讨论了一种高分辨率组合侧向电极系。利用高效的数值模式匹配方法并结合表面积分方程,对其进行了数值模拟。其结果表明,该电极系不但具有很高的纵向分辨率,而且也具有较深的径向探测深度,较好地解决了纵向分辨率与径向探测深度之间的矛盾,同时一次测量还可获得更多的地层信息。     

Modeling complex crack problems using the three-node triangular element fitted to numerical manifold method with continuous nodal stress

A three-node triangular element fitted to numerical manifold method with continuous nodal stress, called Trig3-CNS (NMM) element, was recently proposed for linear elastic continuous problems and linear elastic simple crack problems. The Trig3-CNS (NMM) element can be considered as a development of both the Trig3-CNS element and the numerical manifold method (NMM). Inheriting all the advantages of Trig3-CNS element, calculations using Trig3-CNS (NMM) element can obtain higher accuracy than Trig3 element without extra degrees of freedom (DOFs) and yield continuous nodal stress without stress smoothing. Inheriting all the advantages of NMM, Trig3-CNS (NMM) element can conveniently treat crack problems without deploying conforming mathematical mesh. In this paper, complex problems such as a crucifix crack and a star-shaped crack with many branches are studied to exhibit the advantageous features of the Trig3-CNS (NMM) element. Numerical results show that the Trig3-CNS (NMM) element is prominent in modeling complex crack problems.     

Simulation of hydraulic fracture utilizing numerical manifold method

A 2nd order numerical manifold method(NMM) based method is developed to simulate the hydraulic fractures propagating process in rock or concrete. The proposed method uses a weak coupling technique to analyze the fluid phase and solid phase. To study the seepage behavior of the fluid phase, all the fractures in solid are identified by a block cutting algorithm and form a flow network. Then the hydraulic heads at crack ends are solved. To study the deformation and destruction of solid phase, the 2-order NMM and sub-region boundary element method are combined to solve the stress-strain field. Crack growth is controlled by the well-accepted criterion, including the tension criterion or Mohr-Coulomb criterion for the initialization of cracks and the maximum circumferential stress theory for crack propagation. Once the crack growth occurs, the seepage and deformation analysis will be resolved in the next simulation step. Such weak coupling analysis will continue until the structure becomes stable or is destructed. Five examples are used to verify the new method. The results demonstrate that the method can solve the SIFs at crack tip and fluid flow in crack network precisely, and the method is effective in simulating the hydraulic facture problem. Besides, the NMM shows great convenience and is of high accuracy in simulating the crack growth problem.     

Numerical manifold method based on isogeometric analysis

In this study, numerical manifold method(NMM) coupled with non-uniform rational B-splines(NURBS) and T-splines in the context of isogeometric analysis is proposed to allow for the treatments of complex geometries and local refinement. Computational formula for a 9-node NMM based on quadratic B-splines is derived. In order to exactly represent some common free-form shapes such as circles, arcs, and ellipsoids, quadratic non-uniform rational B-splines(NURBS) are introduced into NMM. The coordinate transformation based on the basis function of NURBS is established to enable exact integration for the manifold elements containing those shapes. For the case of crack propagation problems where singular fields around crack tips exist, local refinement technique by the application of T-spline discretizations is incorporated into NMM, which facilitates a truly local refinement without extending the entire row of control points. A local refinement strategy for the 4-node mathematical cover mesh based on T-splines and Lagrange interpolation polynomial is proposed. Results from numerical examples show that the 9-node NMM based on NURBS has higher accuracies. The coordinate transformation based on the NURBS basis function improves the accuracy of NMM by exact integration. The local mesh refinement using T-splines reduces the number of degrees of freedom while maintaining calculation accuracy at the same time.     

A high order numerical manifold method and its application to linear elastic continuous and fracture problems

The numerical manifold method (NMM) is a partition of unity (PU) based method. For the purpose of obtaining better accuracy with the same mesh, high order global approximation can be adopted by increasing the order of local approximations (LAs). This, however, will cause the “linear dependence” (LD) issue, where the global matrix is rank deficient even after sufficient constraints are enforced. In this paper, through quadrilateral mesh to form the mathematical cover, a high order numerical manifold method called Quad4-COLS (NMM) is developed, where the constrained and orthonormalized least-squares method (CO-LS) is used to construct the LAs. The developed Quad4-COLS (NMM) does not need extra nodes or DOFs to construct high order global approximations, while is free from the LD issue. Nine numerical tests including five tests for linear elastic continuous problems and four tests for linear elastic fracture problems are carried out to validate the accuracy and robustness of the proposed Quad4-COLS (NMM).     

A two-scale contact model for collisions between blocks in CDEM

Contact detection between interacting blocks is of great importance to discontinuity-based numerical methods, such as DDA, DEM, and NMM. A rigorous contact theory is a prerequisite to describing the interactions of multiple blocks. Currently, the penalty method, in which mathematical springs with high stiffness values are employed, is always used to calculate the contact forces. High stiffness values may cause numerical oscillations and limit the time step. Furthermore, their values are difficult to identify. The intention of this study is to present a two-scale contact model for the calculation of forces between colliding blocks. In this new model, a calculation step taken from the moment of contact will be divided into two time stages: the free motion time stage and the contact time stage. Actually, these two time stages correspond to two real physical processes. Based on this, we present a new numerical model that is intended to be more precise and useful in calculating the contact forces without mathematical springs. The propagation of the elastic wave during collision is of a characteristic length, which determines the volume of material involved in the contact force calculation. In conventional contact models, this range is always regarded as the length of one element, which may lead to an inaccurate calculation of contact forces. In fact, the real scale of this range is smaller than the length of a single element, and subdivided elements, which are refined according to the characteristic length and are presented in the new contact model.     

数值流形方法在八结点有限元网格上的实现

数值流形方法常基于有限元法三结点或四结点单元.在八结点单元构成的网格上构建流形覆盖和权函数,采用拉格朗日乘子法施加位移约束条件,推导了分析静态问题的计算列式.无需细致网格划分即可更精确地分析具有曲线边界的区域,计算结果的误差能量模较有限元法降低超过一个量级.还提出另一套简明有效的覆盖函数,能降低求解规模近1/3.利用算例分析了这种方法两套覆盖函数的收敛率.对解答有体积闭锁的问题均有很高精度.     

An h-adaptive numerical manifold method for solid mechanics problems

The numerical manifold method(NMM) features its dual cover systems, namely the mathematical cover and physical cover,which provide a unified framework for mechanics problems involving continuum and discontinuum deformation. Uniform finite element meshes can be and are usually used to construct the mathematical cover. Though this strategy can handle different kinds of problems in a unified way, it is not economical for cases with steep deformation gradients or singularities. In this paper, using the recovery-based error estimator, an h-adaptive NMM on quadtree meshes is proposed to deal with such cases. The quadtree meshes serve as the mathematical meshes, on which the local refinement is carried out. When the quadtree meshes are refined,the corresponding mathematical cover, physical cover and manifold elements are updated accordingly. To handle the hanging nodes in the quadtree meshes, we resort to mean value coordinates. Comparing to the refinement based on manifold elements,the proposed strategy guarantees consistent structured meshes throughout the adaptive process, thus retaining the unique feature of original NMM. In contrast with polygonal finite element method, an advantage of the proposed method is that the meshes do not need to conform to the crack face and material boundary, which means the adaptive NMM is very suitable for problems with complex geometric boundary. Several representative mechanics problems, including crack problems, are analyzed to investigate the effectiveness of the proposed method. It is demonstrated that the proposed adaptive NMM has higher accuracy and better performance comparing to uniform refinement strategy.     

An <Emphasis Type="Italic">h</Emphasis>-adaptive numerical manifold method for solid mechanics problems

The numerical manifold method (NMM) features its dual cover systems, namely the mathematical cover and physical cover, which provide a unified framework for mechanics problems involving continuum and discontinuum deformation. Uniform finite element meshes can be and are usually used to construct the mathematical cover. Though this strategy can handle different kinds of problems in a unified way, it is not economical for cases with steep deformation gradients or singularities. In this paper, using the recovery-based error estimator, an h-adaptive NMM on quadtree meshes is proposed to deal with such cases. The quadtree meshes serve as the mathematical meshes, on which the local refinement is carried out. When the quadtree meshes are refined, the corresponding mathematical cover, physical cover and manifold elements are updated accordingly. To handle the hanging nodes in the quadtree meshes, we resort to mean value coordinates. Comparing to the refinement based on manifold elements, the proposed strategy guarantees consistent structured meshes throughout the adaptive process, thus retaining the unique feature of original NMM. In contrast with polygonal finite element method, an advantage of the proposed method is that the meshes do not need to conform to the crack face and material boundary, which means the adaptive NMM is very suitable for problems with complex geometric boundary. Several representative mechanics problems, including crack problems, are analyzed to investigate the effectiveness of the proposed method. It is demonstrated that the proposed adaptive NMM has higher accuracy and better performance comparing to uniform refinement strategy.     

Two-dimensional numerical manifold method with multilayer covers

In order to reach the best numerical properties with the numerical manifold method (NMM), uniform finite element meshes are always favorite while constructing mathematical covers, where all the elements are congruent. In the presence of steep gradients or strong singularities, in principle, the locally-defined special functions can be added into the NMM space by means of the partition of unity, but they are not available to those complex problems with heterogeneity or nonlinearity, necessitating local refinement on uniform meshes. This is believed to be one of the most important open issues in NMM. In this study multilayer covers are proposed to solve this issue. In addition to the first layer cover which is the global cover and covers the whole problem domain, the second and higher layer covers with smaller elements, called local covers, are used to cover those local regions with steep gradients or strong singularities. The global cover and the local covers have their own partition of unity, and they all participate in the approximation to the solution. Being advantageous over the existing procedures, the proposed approach is easy to deal with any arbitrary-layer hanging nodes with no need to construct super-elements with variable number of edge nodes or introduce the Lagrange multipliers to enforce the continuity between small and big elements. With no limitation to cover layers, meanwhile, the creation of an even error distribution over the whole problem domain is significantly facilitated. Some typical examples with steep gradients or strong singularities are analyzed to demonstrate the capacity of the proposed approach.