共查询到18条相似文献，搜索用时 906 毫秒
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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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无网格法是近几年来发展的一种新的基于变分原理的数值计算方法,由于在计算形函数中不需要划分网格.在力学、电磁学等领域得到了广泛的研究.基于无网格法在大地电磁勘探正演中的应用进行了研究,首先对无网格法的基本原理进行了阐述,并利用广义变分原理推导出了相应的离散方程,编制了相应的程序,最后通过两个理论模型的计算结果检验了算法的正确性. 相似文献
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无网格法在地下水水位预测中的应用 总被引：1，自引：0，他引：1
基于移动最小二乘理论的无网格法是近几年来兴起的一种新的数值计算方法,与有限元法相比,它的主要优点在于无需单元信息,只需节点信息。用无网格法构造了场函数,包括基函数和权函数的选取,形函数及其导数的计算。根据鞍山市首山区水文地质条件,建立了求解双层渗流二维平面系统的数学模型,详细推导了模型求解的无网格方程。应用已识别的参数,用无网格法对该数学模型进行了求解, 并对该区的地下水水位进行了预测,预测的水位与实际水位变化规律基本一致。 相似文献
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首先讨论了Lagrangian和Eulerian无网格近似的联系和区别,然后基于稳定节点积分和增量本构理论,建立了分析边坡静动力破坏的高效大变形无网格法,并给出了详细的计算流程。该方法采用弹塑性损伤耦合本构关系来模拟岩土类材料的破坏演化过程,其中屈服函数采用Drucker-Prager准则,损伤准则为基于应变的各项同性损伤函数。由于无网格近似和稳定节点积分具有非局部近似的特性,在保证空间离散稳定性和提高计算效率的同时,也可准确有效地模拟应变集中所形成的剪切带的发生与扩展,通过数值算例验证了方法的有效性。 相似文献
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无网格法是一类新型数值算法,具有精度高、高阶形函数构造与物性加载便利等特点,在计算力学领域应用广泛。将无网格方法（PIM、RPIM及EFGM）用于重力异常场二维正演计算:首先从重力异常二维变分问题出发,利用Galerkin法结合高斯积分公式推导了对应的无网格离散系统矩阵表达式;其次通过数值试验得出了RPIM-MQ、RPIM-exp及EFGM-exp形状参数的建议值,最后比较分析了最优形状参数下不同无网格法的计算效果。结果表明:无网格法适用于介质物性分布变化较大的重力异常二维正演,exp函数形状参数αc最优取值区间为[1.5,1.7],β建议值为0.6,MQ函数q取值区间为-4.1~1.9;EFGM较PIM及RPIM具有更高的计算精度。 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
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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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岩土工程数值计算中的无网格方法及其全自动布点技术 总被引：14，自引：3，他引：11
自然单元法采用无网格的思想全域构造插值函数,它的求解精度高,计算时间少,可准确地施加边界条件,兼具有无网格法和有限单元法的优点和特点,是一种理想的用于岩土及地下工程分析计算的数值方法。文中简要地介绍了自然单元法的基本理论,并针对岩土及地下工程问题特点,给出了一种无网格离散点的全自动布置方法。 相似文献
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A meshfree node‐based smoothed point interpolation method (NS‐PIM), which has been recently developed for solid mechanics problems, is applied to obtain certified solutions with bounds for hydraulic structure designs. In this approach, shape functions for displacements are constructed using the point interpolation method (PIM), and the shape functions possess the Kronecker delta property and permit the straightforward enforcement of essential boundary conditions. The generalized smoothed Galerkin weak form is then applied to construct discretized system equations using the node‐based smoothed strains. As a very novel and important property, the approach can obtain the upper bound solution in energy norm for hydraulic structures. A 2D gravity dam problem and a 3D arch dam problem are solved, respectively, using the NS‐PIM and the simulation results of NS‐PIM are found to be the upper bounds. Together with standard fully compatible FEM results as a lower bound, we have successfully determined the solution bounds to certify the accuracy of numerical solutions. This confirms that the NS‐PIM is very useful for producing certified solutions for the analysis of huge hydraulic structures. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
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Omid Ghaffaripour Golnaz A. Esgandani Arman Khoshghalb Babak Shahbodaghkhan 《国际地质力学数值与分析法杂志》2019,43(11):1919-1955
This paper presents the first application of an advanced meshfree method, ie, the edge-based smoothed point interpolation method (ESPIM), in simulation of the coupled hydro-mechanical behaviour of unsaturated porous media. In the proposed technique, the problem domain is spatially discretised using a triangular background mesh, and the polynomial point interpolation method combined with a simple node selection scheme is adopted for creating nodal shape functions. Smoothing domains are formed on top of the background mesh, and a constant smoothed strain, created by applying the smoothing operation over the smoothing domains, is assigned to each smoothing domain. The deformation and flow models are developed based on the equilibrium equation of the mixture, and linear momentum and mass balance equations of the fluid phases, respectively. The effective stress approach is followed to account for the coupling between the flow and deformation models. Further coupling among the phases is captured through a hysteretic soil water retention model that evolves with changes in void ratio. An advanced elastoplastic constitutive model within the context of the bounding surface plasticity theory is employed for predicting the nonlinear behaviour of soil skeleton. Time discretisation is performed by adopting a three-point discretisation method with growing time steps to avoid temporal instabilities. A modified Newton-Raphson framework is designed for dealing with nonlinearities of the discretised system of equations. The performance of the numerical model is examined through a number of numerical examples. The state-of-the-art computational scheme developed is useful for simulation of geotechnical engineering problems involving unsaturated soils. 相似文献
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An alternative approach for quasi‐static large deformation analysis of saturated porous media using meshfree method 
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下载免费PDF全文 An alternative coupled large deformation formulation combined with a meshfree approach is proposed for flow–deformation analysis of saturated porous media. The formulation proposed is based on the Updated Lagrangian (UL) approach, except that the spatial derivatives are defined with respect to the configuration of the medium at the last time step rather than the configuration at the last iteration. In this way, the Cauchy stresses are calculated directly, rendering the second Piola–Kirchhoff stress tensor not necessary for the numerical solution of the equilibrium equations. Moreover, in contrast with the UL approach, the nodal shape function derivatives are calculated once in each time step and stored for use in subsequent iterations, which reduces the computational cost of the algorithm. Stress objectivity is satisfied using the Jaumann stress rate, and the spatial discretisation of the governing equations is achieved using the standard Galerkin method. The equations of equilibrium are satisfied directly, and the nonlinear parts of the system matrix are derived independent of the stresses of the medium resulting in a stable numerical algorithm. Temporal discretisation is effected based on a three‐point approximation technique that avoids spurious ripple effects and has second‐order accuracy. The radial point interpolation method is used to construct the shape functions. The application of the formulation and the significance of large deformation effects on the numerical results are demonstrated through several numerical examples. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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提出了一种基于颗粒接触的无网格方法（PCMM）,并编制了相应的C++程序,解决了有限元等网格类方法在模拟边坡失稳滑动过程中的网格畸变问题。该方法利用颗粒离散元中的接触拓扑创建连续介质单元,通过颗粒的运动演化实现连续介质单元的自动删除及重建,通过在连续介质单元中引入考虑应变软化效应的Mohr-Coulomb模型及最大拉应力模型,实现边坡的弹塑性分析及失稳滑移过程的模拟。利用PCMM分析了均质边坡的弹塑性场、沙堆的形成过程及土质边坡的失稳过程。计算结果表明,PCMM在小变形下具有足够的精度,且在模拟材料大变形方面具有明显优势,是一种模拟边坡成灾范围的有效方法。 相似文献
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B‐bar based algorithm applied to meshfree numerical schemes to solve unconfined seepage problems through porous media 下载免费PDF全文
下载免费PDF全文 The object of this work is to establish a meshfree framework for solving coupled, steady and transient problems for unconfined seepage through porous media. The Biot's equations are formulated in displacements (or u − w) assuming an elastic solid skeleton. The free surface location and its evolution in time are obtained by interpolation of pore water pressures throughout the domain. Shape functions based on the principle of local maximum entropy are chosen for the meshfree approximation schemes. In order to avoid the locking involved in the fluid phase of the porous media, a B‐bar based algorithm is devised to compute the average volumetric strain in a patch composed of various integration points. The efficiency of such an implementation for one phase problems is shown through the Benchmark problem, Cook's membrane loaded by a distributive shear load. The proposed methodology is firstly applied to various classical examples in unconfined steady seepage problems through earth dams, then to the dynamic consolidation of a soil column. The results obtained for both problems are quite satisfactory and demonstrate the feasibility of the proposed method in solving coupled problems in porous media. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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A fully coupled meshfree algorithm is proposed for numerical analysis of Biot’s formulation. Spatial discretization of the governing equations is presented using the Radial Point Interpolation Method (RPIM). Temporal discretization is achieved based on a novel three-point approximation technique with a variable time step, which has second order accuracy and avoids spurious ripple effects observed in the conventional two-point Crank Nicolson technique. Application of the model is demonstrated using several numerical examples with analytical or semi-analytical solutions. It is shown that the model proposed is effective in simulating the coupled flow deformation behaviour in fluid saturated porous media with good accuracy and stability irrespective of the magnitude of the time step adopted. 相似文献
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With our meshfree numerical code SPARC (Soft PARticle Code), which is based on strong solutions of the equations of equilibrium, we were able to derive vortex patterns ("turbulence") in deformations hitherto believed to be homogeneous. The formation of such vortices demonstrates the nonuniqueness of the corresponding boundary value problem. We present some evidence that such vortices can be related with ptygmatic folds, which are observed in rock. 相似文献