非稳定流的有限单元法中承压水析奇与潜水逐步析奇的一个方法(Ⅰ、Ⅱ)

本文研究的是地下水的水位予报及反求水文地质参数的有限单元法。由二部分组成:第一部分,用有限单元法预报承压水的水位。我们构造了一个函数,它可将井口的奇点析出,把井点附近水头变化极快的情形转变为缓慢,把有开采井的问题转化成没有开采井的等价问题,然后用通常的有限单元法求解,这对于提高水位预报的精度及消除反求水文地质参数的不适定性是有重要意义的。我们以“泰斯解”和“鸠布衣解”为例说明了这种析奇点方法的有效性;第二部分,研究了潜水不稳定流的有限单元法。我们提出了逐步线性化析奇点的方法,把潜水问题转化为类似承压水问题来处理因而可用有限单元法求得比较精确的解答。第三部分,在奇点析出的基础上,用有限元技术讨论了反求水文地质参数问题。     

改进"BT"法在平原区潜水系统水位预报中的应用研究

针对潜水系统水位预报有限单元计算方法--"BT"法存在的问题,提出了改进方法--改进"BT"法,该法是在第一类边界水位的修正中,考虑水位下降与潜水蒸发减少的相互作用;该方法的关键是计算潜水蒸发减少引起的第一类边界水位下降减少值Se.用数值离散及解析公式相结合计算Se值的方法、原理、过程,并给出了"BT"法、改进"BT"法的计算实例及结果对比.     

地下水位动态的灰色预测

将地下水已知信息和未知信息,看作为灰色系统,然后利用灰色系统预测理论,分述了预测水位中所涉及的数列处理、求参、建模、精度检验、模型修正、水位预报等各工序的具体细节,最后进行了实例说明。结果证明,用该法预测的结果与实际值较为接近。     

试用有限单元法评价深层地下卤水资源量

用有限单元法评价浅层地下水资源量,是人们十分熟悉的。但对深层地下卤水资源量的评价,尚无完善的方法。本文对某储卤构造深层储卤层进行概化,用有限单元法模拟卤水生产过程并作出预报,提供了相应的结果。     

应用趋势分析灰色模块—均差插值法预报近期地下水情

用不同方法和程序对大连地区进行地下水情预报，通过实测资料的验证，趋势分析灰色模块－均差插值法，明显优于其它方法。该方法只需水位（水质）的序列资料，不需任何其他水文地质参数，即可对地下水位、水质进行近期预报。     

应用趋势分析灰色模块─均差插值法预报近期地下水情

用不同方法和程序对大连地区进行地下水情预报，通过实测资料的验证，趋势分析灰色模块－均差插值法，明显优于其它方法．该方法只需水位（水质）的序列资料，不需任何其他水文地质参数，即可对地下水位、水质进行近期预报．     

山东淄博市地下水资源评价及其合理开发利用研究

本文采用有限单元法进行地下水资源评价以解决评价区供水面积大、精度要求高的矛盾。首先根据实际的开采量和长期观测孔的水位资料,校正数学模型,反求有关参数;然后给定开采方案进行未来水头的预测;最后研究地下水资源的合理开发利用问题。利用有限单元法进行水源地或单一含水层的地下水资源评价已被证明是先进的、有效的。本文是对水文地质条件非常复杂的大面积的区域,用有限单元法进行地下水资源评价的一种尝试,可供类似地区参考。     

金龙水库补给、调蓄及排泄模拟研究

用数学模拟方法研究广西龙州县金龙水库的水量补给、调蓄及排泄。研究中分别将水库、岩溶管道、大气降水视作系统的储存单元、输送单元、补给单元,拟合水库的实时水位及地下河水的出水流量,最后给出在不同降水条件下的水位预报结果      

上海市地震滑坡的预测研究

本文选用八个工程地质类比因素,根据灰色聚类分析与模糊聚类分析预测了上海地区的地震滑坡,并用毕肖甫条分法与有限单元法对不稳定地区作了重点验证。     

前郭-扶余地区地下水流数值模拟

研究区位于松辽盆地中西部，含水层主要为第四纪地层，采用迦辽金有限单元法对区内开采层进行了数值模拟和预报，为区内小城镇发展的供水问题提供了开采方案。由于边界条件及源汇项等都是经过分析推测的，所以随着预报时间的增长，预报的可靠性也将降低。     

Three-dimensional finite element analysis of the direct simple shear test

This paper investigates two aspect of the direct simple shear (DSS) using three-dimensional finite element analysis. Firstly, the different total stress paths followed by DDS devices that impose constant cross-sectional area using a stiff external boundary, and those that use a constant total stress lateral boundary condition are explored. This is done by conducting finite element analysis of a single cubic element. It is shown that this element may be subjected to perfect simple shear using four different boundary condition types. Each boundary condition type results in the same effective stress path, but different total stress paths and excess pore pressures. The boundary condition types are related to DSS devices in use. The second aspect investigated is the fact that no DSS device can impose true simple shear conditions, as they are unable to generate the required complementary shear stress on the vertical boundaries. Full three-dimensional finite element analysis of a UWA/Berkeley type simple shear device, which has a constant total stress lateral boundary, is then presented. The results are compared to the ideal solution and effects of stress non-homogeneity on the friction angle and undrained shear strength, deduced from a standard interpretation, are established.     

Finite element modeling of wave propagation problems in multilayered soils resting on a rigid base

A new finite element scheme is proposed, in this paper, for solving two-dimensional wave propagation problems in multilayered soils resting on a rigid base. The multilayered soils are treated as multiple horizontal layers of lateral infinite extension in geometry. Since these horizontal layers can be truncated by two artificially truncated vertical boundaries, two high-order artificial boundary conditions are applied for propagating the incoming waves from the interior domain into the far field of the system. Both the semi-analytical method and the truncated boundary migration procedure are used to derive the high-order artificial boundary conditions, which are comprised of a physically meaningful dashpot and a generalized energy absorber. The main advantage of using the proposed finite element scheme is that the derived artificial boundary condition can be straightforwardly implemented in the finite element analysis, without violating the band/sparse structure of the conventional finite element equation. The related numerical examples have demonstrated that the proposed finite element scheme is of high accuracy in dealing with wave propagation problems in multiple horizontal layers.     

非稳定温度场的三维p型有限元方法研究

非稳定温度场的边界往往是温度梯度较大的区域,需要划分较密的网格。但在三维温度应力的计算中太密的网格往往使得计算成本很高。将p型阶谱有限元方法引入温度场的计算,则可以开拓一条解决这类问题的有效途径。研究了p型有限元中的温度边界条件和初值,编制了有关程序,对同一个算例,采用不同网格密度的常规有限元法和p型有限元法进行了温度场计算分析和对比。研究结果表明,用p型有限元进行非稳定温度场计算,在网格稀疏的条件下能够达到较高的精度。     

岩体材料物理网格对流形元覆盖系统形成的影响

流形元的数学覆盖与物理网格相对独立,使流形元覆盖系统的形成比有限元单元网格的形成有更大的灵活性和方便性,但在形成流形元覆盖系统时对物理网格也有一定的依赖。笔者讨论了使用规则网格作为数学覆盖时,岩体材料普遍存在的裂隙和岩层界面这两种物理网格对流形元覆盖系统形成的影响,指出数学覆盖的构造要与岩体裂隙和岩层界面相适应,并提出了相应的流形元覆盖系统的形成方法,有利于流形元法应用于大型岩体工程问题。     

水动力质量实效施加方法及地基-筒型基础-塔筒体系的地震敏感性研究

针对海上风电结构在有限元计算中水动附加质量的施加问题,提出了一种在ABAQUS软件中简便有效易于实现的方法,可以提高有限元分析的前处理效率;建立有限元模型,分析有、无考虑水动附加质量和不同边界条件对海上风电结构自振特性的影响,并从力学角度进行分析;利用有限元模拟地震动作用下的海上风电结构塔筒响应,并对水动附加质量和边界条件进行敏感性分析。通过数值计算并结合理论分析表明：提出的水动附加质量施加方法是合理实用的;水动附加质量的施加使得结构固有频率减小,且随着阶数增大,固有频率减小的绝对值增大;边界条件对体系的模态参数影响比水动附加质量更显著,黏弹性透射边界条件下计算得到结构体系的各阶频率较固定边界均有比较明显的减小;黏弹性透射边界模型在地震动作用下的位移响应比固定边界模型大。分析结果对此类海上风电工程具有借鉴意义。     

A mixed solution for two-dimensional unsteady flow in fractured porous media

A mixed finite element–boundary element solution for the analysis of two-dimensional flow in porous media composed of rock blocks and discrete fractures is described. The rock blocks are modelled implicitly by using boundary elements whereas finite elements are adopted to model the discrete fractures. The computational procedure has been implemented in a hybrid code which has been validated first by comparing the numerical results with the closed-form solution for flow in a porous aquifer intercepted by a vertical fracture only. Then, a more complex problem has been solved where a pervious, homogeneous and isotropic matrix containing a net of fractures is considered. The results obtained are shown to describe satisfactorily the main features of the flow problem under study. © 1997 by John Wiley & Sons, Ltd.     

Non-linear analysis of geomechanical problems using coupled finite and infinite elements

In modeling of many geomechanics problems such as underground openings, soil-foundation structure interaction problems, and in wave propagation problems through semi-infinite soil medium the soil is represented as a region of either infinite or semi-infinite extent. Numerical modeling of such problems using conventional finite elements involves a truncation of the far field in which the infinite boundary is terminated at a finite distance. In these problems, appropriate boundary conditions are introduced to approximate the solution of the infinite or semi-infinite boundaries as closely as possible. However, the task of positioning the finite boundary in conventional finite element discretization and the definition of the boundary and its conditions is very delicate and depends on the modeller's skill and intuition. Moreover, such a choice is influenced by the size of the domain to be discretized. Consequently, the dimensions of the global matrices and the time required for solution of the problem will increase considerably and also selection of the arbitrary location of truncated boundary may lead to erroneous result. In order to over come these problems, mapped infinite elements have been developed by earlier researchers (Simoni and Schrefier, 1987). In the present work the applicability of infinite element technique is examined for different geomechanics problems. A computer program INFEMEP is developed based on the conventional finite element and mapped infinite element technique. It is then validated using selected problems such as strip footing and circular footing. CPU time taken to obtain solutions using finite element approach and infinite element approach was estimated and presented to show the capability of coupled modeling in improving the computational efficiency. Mesh configurations of different sizes were used to explore the enhancement of both computational economy and solution accuracy achieved by incorporation of infinite elements to solve elastic and elasto-plastic problems in semi-infinite/finite domain as applied to geotechnical engineering. © Rapid Science Ltd. 1998     

Semi‐analytical far field model for three‐dimensional finite‐element analysis

A challenging computational problem arises when a discrete structure (e.g. foundation) interacts with an unbounded medium (e.g. deep soil deposit), particularly if general loading conditions and non‐linear material behaviour is assumed. In this paper, a novel method for dealing with such a problem is formulated by combining conventional three‐dimensional finite‐elements with the recently developed scaled boundary finite‐element method. The scaled boundary finite‐element method is a semi‐analytical technique based on finite‐elements that obtains a symmetric stiffness matrix with respect to degrees of freedom on a discretized boundary. The method is particularly well suited to modelling unbounded domains as analytical solutions are found in a radial co‐ordinate direction, but, unlike the boundary‐element method, no complex fundamental solution is required. A technique for coupling the stiffness matrix of bounded three‐dimensional finite‐element domain with the stiffness matrix of the unbounded scaled boundary finite‐element domain, which uses a Fourier series to model the variation of displacement in the circumferential direction of the cylindrical co‐ordinate system, is described. The accuracy and computational efficiency of the new formulation is demonstrated through the linear elastic analysis of rigid circular and square footings. Copyright © 2004 John Wiley & Sons, Ltd.     

基于二次插值的线源可控源有限元数值模拟

在准静态近似条件下,采用矩形网格单元和双二次函数插值就频率域二维线源边值问题进行了有限元数值模拟。在二维地电条件下,给出了边值问题和变分问题,并通过有限单元法对模型进行单元剖分、插值、积分和整体合成,最后通过求解复系数方程组得到了地表视电阻率响应。引入伪delta函数模拟线源,消弱了源带来的奇异性。通过与均匀大地以及层状介质模型的解析解对比,平均相对误差分别为0.71%和1.12%。建立了两个异常体模型,数值模拟表明异常响应比较明显,为进一步实现三维可控源电磁法有限元数值模拟提供了基础。