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紧支径向基函数能使支配方程中的刚度矩阵具有稀疏性,很适合应用于无网格方法中,其缺点是在插值计算时精度不高.点插值方法的插值函数具有Delta函数性质,可以很方便的施加本质边界条件,但在计算插值函数时矩阵易出现奇异.为了提高计算精度并避免点插值法的局限性,首先对紧支径向基函数进行完备性修正,然后用完备性修正的紧支径向基函数代替多项式来形成插值函数,建立了紧支径向基函数点插值方法.由于该方法中的形函数满足Delta函数性质,因此本质边界条件可以像传统的有限元方法一样很容易施加.然后将该方法用于二维弹性静力问题的求解,导出了其相应的离散方程.最后将该方法应用于一个悬臂梁的分析中,初步验证了该方法的有效性与合理性. 相似文献
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径向基函数点插值无网格法(radial point interpolation method,RPIM)是一种新型的无网格法,其形函数具有插值特性,且形式简单,易于施加本质边界条件。文中介绍了径向基函数点插值无网格法的基本原理,推导了三维情况下点插值无网格法的基本公式。从变分原理出发,结合比奥固结理论,建立了流-固耦合的三维点插值无网格法基本方程和数值积分方法,并开发了相应计算程序。通过三维悬臂梁和单向固结问题的数值试验,验证了该方法对三维弹性问题和流-固耦合问题的适用性和有效性 相似文献
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复杂地层建模与三维可视化 总被引：1，自引：0，他引：1
提出了一种新的复杂地层建模方法。该方法先将离散的钻孔数据点分类,而后将不同类的离散数据点用径向基函数进行拟合;所生成的拟合曲面相交、裁剪得到地层的空间范围;由离散的数据点以及拟合插值点生成地层交界面格网,再经过计算机图形处理生成地层模型的三维图形。利用该方法对复杂地层建模,自动化程度较高、效果较好。 相似文献
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介绍径向基函数插值配点法,将其应用于非均质多孔介质中的一维地下水稳定流、非稳定流问题,算例结果表明,该方法既计算效率高又有较高的精度。 相似文献
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针对线弹性断裂力学问题,提出扩展径向点插值无网格法（X-RPIM）。该方法基于单位分解思想,在传统径向点插值无网格法的位移模式中加入扩展项来描述裂纹两侧的不连续位移场和裂尖奇异场。由于其形函数具有Kronecker ? 函数性质,易于施加本质边界条件。详细描述了X-RPIM不连续位移模式的建立,支配方程的离散形式以及J积分计算混合模式裂纹的应力强度因子的实现过程,讨论了不同积分区域对应力强度因子的影响。数值算例分析证明了该方法在求解断裂问题时的可行性和有效性,同时说明扩展径向点插值无网格法在模拟裂纹扩展问题时具有良好的前景。 相似文献
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为了研究采样和网格化方法对地球物理数据成图精度的影响,为野外数据采集布设提供一定的依据,采用数值模拟确定重力异常场场值,通过不同采样间距和不同插值方法计算重力异常绝对误差均方根值和节点处的绝对误差值,对比不同插值方法的误差,得到了如下认识：1）对于同一插值方法而言,存在小间距绝对误差均方根值小于大间距绝对误差均方根值的关系。2）对不同的插值方法而言:当采样间距小于最小异常地质体尺度时,绝对误差均方根值由小到大的顺序是径向基函数法、改进的谢别德法、克里金插值法、自然邻点法、反距离加权插值法、最近邻点法、最小曲率法,并且线性插值三角网法与自然邻点法具有几乎相同的数值;当采样间距大于最小异常地质体尺度时,绝对误差均方根值由小到大的顺序是径向基函数法、改进的谢别德法、克里金插值法、自然邻点法、最小曲率法、最近邻点法、反距离加权插值法,并且线性插值三角网法和自然邻点法具有几乎相同的数值。3）从绝对误差均方值看,径向基函数方法、改进的谢别德方法和克里金方法数值较小,其中径向基函数值绝对误差均方根值最小。4）从节点处绝对误差值来看,径向基函数方法、克里金方法、改进的谢别德方法相对其他插值方法具有更小的误差,不存在局部误差较小或较大的情况,是相对较好的插值方法,并且径向基函数方法是最好的。 相似文献
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地震勘探广泛应用于油气、煤田勘探。地震波场数值模拟是整个地震勘探数据处理技术的基石。将径向基函数（RBF）引入地震声波波场数值模拟中,在空间上用径向基函数无网格法来构造二阶导数,而在时间上采用简单的二阶差分公式,并重点讨论了形状参数c对该方法精度的影响,总结c经验取值范围为2~4倍平均数据点间距。设计不同模型,利用径向基函数无网格法进行声波波场模拟,并与空间四阶时间二阶的有限差分计算结果进行对比,结果表明:同样精度下,径向基函数每个波长所取的数据点数远小于空间四阶矩形网格有限差分每个波长所取的网格点数,即径向基函数的空间采样率更低,这表明径向基函数具有更小的数值频散。 相似文献
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A new numerical tool is presented which models the two-dimensional contaminant transport through saturated porous media using a meshfree method called the radial point interpolation method (RPIM) with polynomial reproduction. In RPIM, an approximate solution is constructed entirely in terms of a set of nodes and no characterisation of the interrelationship of the nodes is needed. An advection-dispersion equation with sorption is considered to illustrate the applicability of the RPIM. The Galerkin weak form of the governing equation is formulated using two-dimensional meshfree shape functions constructed using thin plate spline radial basis functions. A computer program is developed for the implementation of the RPIM procedure. Three numerical examples are presented and the results are compared with those obtained from the analytical solution and finite element method. The experimental results are also used to validate the approach. The proposed RPIM has generated results with no oscillations and they are insensitive to Peclet constraints. 相似文献
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相较于极限平衡法,强度折减法在计算边坡稳定性系数上有许多优势,但更大的计算量在一定程度上限制了其在边坡可靠度分析中的应用。为了有效地减少可靠度分析中数值模型的计算次数,以减轻使用强度折减法所带来的计算压力,引入了基于主动学习径向基函数（ARBF）代理模型的高效分析方法：利用主动学习函数在极限状态面附近搜索训练样本更新代理模型,加快模型训练的收敛速度;采用线性核径向基插值函数简化模型参数优化过程,建立简洁、稳定的代理模型。此外,为了充分发挥主动学习代理模型的优势,提出针对土质边坡特性的初始采样策略。当得到稳定的代理模型后,结合蒙特卡罗模拟计算边坡的系统失稳概率。作为对比,基于两个典型边坡算例,测试了两种经典的可靠度方法：主动学习克里金模型（AK）和二次响应面法（QRSM）,论证了引入的主动学习径向基函数代理模型在计算效率上的高效性和计算模型上的稳定性。 相似文献
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This paper presents two test procedures for evaluating the bond stress–slip and the slip–radial dilation relationships when the prestressing force is transmitted by releasing the steel (wire or strand) in precast prestressed elements. The bond stress–slip relationship is obtained with short length specimens, to guarantee uniform bond stress, for three depths of the wire indentation (shallow, medium and deep). An analytical model for bond stress–slip relationship is proposed and compared with the experimental results. The model is also compared with the experimental results of other researchers. Since numerical models for studying bond‐splitting problems in prestressed concrete require experimental data about dilatancy angle (radial dilation), a test procedure is proposed to evaluate these parameters. The obtained values of the radial dilation are compared with the prior estimated by numerical modelling and good agreement is reached. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
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J. C. Gálvez J. M. Benítez M. J. Casati B. S. Tork D. A. Cendón 《国际地质力学数值与分析法杂志》2011,35(11):1257-1277
This paper presents a numerical procedure for bond between indented wires and concrete, and the coupled splitting process of the surrounding concrete. The bond model is an interface, non‐associative, plasticity model. It is coupled with a cohesive fracture model for concrete to take into account the splitting of such concrete. Bond between steel and concrete is fundamental for the transmission of stresses between both materials in precast prestressed concrete. Indented wires are used to improve the bond in these structural elements. The radial component of the prestressing force, increased by Poisson's effect, may split the surrounding concrete, decreasing the wire confinement and diminishing the bonding. The combined action of the bond and the splitting is studied with the proposed model. The results of the numerical model are compared with the results of a series of tests, such as those which showed splitting induced by the bond between wire and concrete. Tests with different steel indentation depths were performed. The numerical procedure accurately reproduces the experimental records and improves knowledge of this complex process. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
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This paper deals with the computational aspects of nonaqueous phase liquid (NAPL) dissolution front instability in two-dimensional
fluid-saturated porous media of finite domains. After the governing equations of an NAPL dissolution system are briefly described,
a combination of the finite element and finite difference methods is proposed to solve these equations. In the proposed numerical
procedure, the finite difference method is used to discretize time, while the finite element method is used to discretize
space. Two benchmark problems, for which either analytical results or previous solutions are available, are used to verify
the proposed numerical procedure. The related simulation results from these two benchmark problems have demonstrated that
the proposed numerical procedure is useful and applicable for simulating the morphological evolution of NAPL dissolution fronts
in two-dimensional fluid-saturated porous media of finite domains. As an application, the proposed numerical procedure has
been used to simulate morphological evolution processes for three kinds of NAPL dissolution fronts in supercritical NAPL dissolution
systems. It has been recognized that: (1) if the Zhao number of an NAPL dissolution system is in the lower range of the supercritical
Zhao numbers, the fundamental mode is predominant; (2) if the Zhao number is in the middle range of the supercritical Zhao
numbers, the (normal) fingering mode is the predominant pattern of the NAPL dissolution front; and (3) if the Zhao number
is in the higher range of the supercritical Zhao numbers, the fractal mode is predominant for the NAPL dissolution front. 相似文献
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Analytical‐numerical solution for stress distribution around tunnel reinforced by radial fully grouted rockbolts 
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下载免费PDF全文 This paper presents an analytical‐numerical approach to obtain the distribution of stresses and deformations around a reinforced tunnel. The increase in the radial stress of the reinforced tunnel, based on the performance of a bolt, is modeled by a function, which its maximum value is in the vicinity of the bolt periphery and it exponentially decreases in the far distance from the bolt. On the basis of this approach, the shear stiffness between the bolt and the rock mass and the shear stress distribution around the bolt within the rock mass are also analytically obtained. The results are compared with those obtained by the assumption of ‘uniform increase of radial stress’ method, which is made by the previous studies. The analyses show when the bolts' spacing is large, the safety factor must be increased if the ‘uniform increase of radial stress’ method is used for the design. Finally, a procedure is introduced to calculate the non‐equal deformation of the rock mass between the bolts at any radius that can be useful to compute the bending moment in shotcrete layer in New Austrian Tunnelling Method (NATM) approach. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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Piyang Liu Gary Douglas Couples Jun Yao Zhaoqin Huang Wenhui Song Jingsheng Ma 《Computational Geosciences》2018,22(5):1187-1201
The two-scale continuum model is widely used in simulating the reactive dissolution process and predicting the optimum injection rate for carbonate reservoir acidizing treatment. The numerical methods of this model are currently based on structured grids, which are not applicable for complicated geometries. In this study, a general numerical scheme for simulating a reactive flow problem on both structured and unstructured grids is presented based on the finite volume method (FVM). The convection and diffusion terms involved in the reactive flow model are discretized by using the upwind scheme and two-point flux approximation (TPFA), respectively. The location of the centroid node inside each control volume is moved by using an optimization algorithm to make the connections with the surrounding elements as orthogonal as possible, which systematically improves the accuracy of the TPFA scheme. Additionally, in order to avoid the computational complexity resulting from the discretization of the non-linear term, the mass balance equation is only discretized in the spatial domain to get a set of ordinary differential equations (ODEs). These ODEs are coupled with the reaction equations and then solved using the numerical algorithm on ODEs. The accuracy and efficiency of the proposed method are studied by comparing the results obtained from the proposed numerical method with previous experimental and numerical results. This comparison indicates that, compared with the previous methods, the proposed method predicts the wormhole structure more accurately. Finally, the presented method is used to check the effect of the domain geometry, and it is found that the geometry of the flow domain has no effect on the optimum injection velocity, but the radial domain requires a larger breakthrough volume than the linear domain when other parameters are fixed. 相似文献
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A simple parameter estimation procedure, designated as integration-based estimation (IBE), was introduced to determine the hydraulic properties of an aquifer using slug test models subjected to certain flow geometries such as radial and spherical flows. The basic idea behind the proposed IBE approach is to link an integration value at pre-defined normalized head levels for field data with that of a theoretical type curve. The IBE method removes the need for the implementation of the classical graphical matching process which would be ineffective to acquire aquifer parameters for non-ideal aquifer conditions. As the second aspect of this study, a new decision tool was suggested to determine the suitable slug test model to be utilized for the site data since diagnosing the flow character properly is of crucial importance for following a convenient analysis procedure. The estimation performance and limitation of the proposed IBE method were tested for several slug test scenarios including radial and spherical flow models with a number of synthetically generated data sets as well as a field application. Results reveal that the IBE together with the identification methodology not only is able to retrieve aquifer parameters as reliable as the existing techniques in the literature but also diagnoses the flow character precisely as demonstrated in this study. 相似文献
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A Combined Analytical and Numerical Approach for the Evaluation of Radial Loads on the Lining of Vertical Shafts 总被引：1，自引：0，他引：1
Pierpaolo Oreste Giovanni Spagnoli Luigi Lo Bianco 《Geotechnical and Geological Engineering》2016,34(4):1057-1065
The evaluation of the load acting on a shaft support is of fundamental importance for the correct dimensioning of the structure. The load acting on the support can appear somewhat complex. One approach to define the load on the lining may be to use the convergence-confinement method (CCM) normally used in the tunneling design. This process involves intersecting the convergence-confinement (CC) curve with the support reaction line. However, in order to be able to adopt this technique, it is necessary to know the radial displacement of the shaft wall at the point in which the support is to be installed. Using the equations of Vlachopoulos and Diederichs (Rock Mech Rock Eng 42:131–146, 2009) the reaction line of the support can be calculated. Numerical models developed with Flac 2D v.6.0 considering the Mohr–Coulomb criterion and an ideal elasto-plastic behavior simulating stepwise excavation and support installation were developed. The relation between applied internal stress and radial displacement of the wall shaft, obtained by the numerical simulation was compared with the CC curve obtained by the CCM and it showed a good match between the two methods. However, an iterative procedure has also been used to insert the reaction line in the CC graph. The result shows lower initial displacements (and therefore greater radial stress) when compared with the values obtained by numerical calculation with the axisymmetric model. It is therefore recommended the combined use of the CCM (analytical method) and the axisymmetric numerical model (step by step simulation) to obtain the values of the final load on the lining and the final plastic radius, necessary for the correct design of supporting structures on the shaft wall. 相似文献
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针对波浪数值模拟中基于矩形网格的数值方法在深水到浅水的网格间距选择与复杂边界处理上的缺陷,以及基于正交曲线网格和无结构网格的数值方法前处理工作复杂的问题,引入最近在计算力学中发展起来的无网格法——径向点插值法,对经典的双曲型缓坡方程进行空间离散,并在时间上采用四阶Adams-Bashforth-Moulton格式求解建立近岸波浪传播数学模型,通过椭圆形浅滩地形和环形河道的波浪传播计算验证,表明该无网格方法可较为有效地模拟近岸波浪的传播变形,且在处理复杂边界时具有较高的精度. 相似文献