共查询到16条相似文献,搜索用时 234 毫秒
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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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声波散射数值模拟的两种新方案 总被引:4,自引:0,他引:4
孙建国 《吉林大学学报(地球科学版)》2006,36(5):863-868
声波散射的数值模拟问题一般用网格法或积分方程法解决。当模型的尺度很大时,两种方法都会遇到计算机资源不足所造成的困难。另外,在网格法中,场源的位置和场源附近的波场奇异性逼近精度都受网格点的控制,因此难以满足实际问题所提出的要求。针对这些问题,提出了两种处理声波散射问题的新方案。一种主要针对网格法,另外一种针对积分方程法。在针对网格法的方案中,通过模型分解和波场分裂,将原始的总场计算问题转化为散射场计算问题。由于背景场是由解析公式给出的,所以可以将场源放置在数值网格的任意位置,不一定非得在网格点上。基于同样的原因,场源附近的波场奇异性可以精确地算出。在针对积分方程法的方案中,通过引入拟线性近似,使得散射场的数值求解不必再借助于代数方程组,只要进行数值积分即可。所建立的数值计算方案具有普遍的适用性,其基本思想可以直接用于解决弹性波散射的数值模拟问题并用于反演密度和速度。 相似文献
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岩土体的渗透破坏、地下工程的防渗设计等无不与渗流计算有关。针对渗流自由面问题,提出一种重心拉格朗日插值的配点型无网格方法。由于渗流自由面问题的求解区域是不规则区域,该方法通过将不规则求解区域嵌入一个正则矩形区域,在正则区域上采用重心拉格朗日插值近似未知函数,利用配点法离散渗流问题的控制方程,将重心拉格朗日插值的微分矩阵离散成代数方程表达的矩阵形式。将自由面上的边界条件通过重心拉格朗日插值离散,通过置换方程法和附加方程法施加边界条件,利用正则区域上的重心插值配点法,通过迭代确定最终自由面的位置。数值算例表明所提出的无网格方法对于求解渗流自由面问题的正确性和高精度。 相似文献
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最小二乘配点无网格法是一种新型高效的无网格法。该方法除节点外又在研究域内引入辅助点,近似函数仍然只通过节点构造,微分方程在所有节点和辅助点上满足。本文将最小二乘配点无网格法应用于非均质多孔介质中的二维地下水稳定流问题,推导了计算格式、编制了相应的计算程序。算例结果表明,最小二乘配点无网格法算法简单,有较高的精度且节省计算量。 相似文献
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提出了一种模拟裂纹扩展的水平集和无网格耦合方法。由于水平集和无网格方法都是建立在离散节点上,因而可以很自然地实现耦合。在该方法中,两个在裂尖处相互正交的水平集不仅用于描述裂纹的几何形态和裂尖位置,而且用于建立无网格伽辽金法(简称EFGM)不连续近似函数中的Heaviside跳跃项和裂尖处的Westergaard扩展项。当裂纹扩展时,则由水平集更新算法确定新裂纹的位置。水平集和无网格耦合法无需使用可视法、衍射法或透明法,克服了这些方法在裂尖处人为引入的不连续且能很好地再生 奇异场;而且节点影响域不受裂纹线切割的影响,在计算中往往使用较小的影响域,保持了整体刚度矩阵的带状、稀疏性;另外,水平集简化了扩展节点的选取和附加函数的建立,其更新过程无需求解演化方程,实现简单且易于编程。数值算例表明本文方法具有较高的计算精度,其模拟的裂纹扩展路径与试验结果吻合得很好,从而验证了本文方法的正确性和可行性。 相似文献
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自然单元法(NEM)是较近出现的一种无网格方法,其形函数兼有无网格的特点和传统有限元的优点,是一种理想的适合岩土工程问题计算的新型数值方法。介绍了自然单元法的基本原理和特性,并讨论了其在岩土工程中的具体应用。将Goodman单元引入自然单元法以实现对不连续面的模拟,研究表明,在NEM中加入节理单元的总体原则和具体的实施细节与FEM中完全相同;而在一般的无网格方法中,则稍微复杂一点。为了实现对岩土工程中常见的无限域或半无限域问题的模拟,引入了无界单元;由于自然单元法的特性,自然单元法和无界元可实现无缝“耦合”。具体的数值算例验证了上述思路。 相似文献
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In this paper, the numerical model of the transverse vibrations of a thin poroelastic plate saturated by a fluid was proposed. Two coupled dynamic equations of equilibrium related to the plate deflection and the equivalent moment were established for an isotropic porous medium with uniform porosity. The fundamental solutions for a porous plate were derived both in the Laplace transform domain and in the time domain. A meshless method was developed and demonstrated in the Laplace transform domain for solving two coupled dynamic equations. Numerical examples demonstrated the accuracy of the method of the fundamental solutions and comparisons were made with analytical solutions. The proposed meshless method was shown to be simple to implement and gave satisfactory results for a poroelastic plate dynamic analysis. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
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Alexander Bihlo Colin G. Farquharson Ronald D. Haynes J Concepción Loredo-Osti 《Computational Geosciences》2017,21(1):117-129
Probabilistic domain decomposition is proposed as a novel method for solving the two-dimensional Maxwell’s equations as used in the magnetotelluric method. The domain is split into non-overlapping sub-domains and the solution on the sub-domain boundaries is obtained by evaluating the stochastic form of the exact solution of Maxwell’s equations by a Monte-Carlo approach. These sub-domains can be naturally chosen by splitting the sub-surface domain into regions of constant (or at least continuous) conductivity. The solution over each sub-domain is obtained by solving Maxwell’s equations in the strong form. The sub-domain solver used for this purpose is a meshless method resting on radial basis function-based finite differences. The method is demonstrated by solving a number of classical magnetotelluric problems, including the quarter-space problem, the block-in-half-space problem and the triangle-in-half-space problem. 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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The method of fundamental solution for 3‐D wave scattering in a fluid‐saturated poroelastic infinite domain
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Zhongxian Liu Zhikun Wang Alexander H.D. Cheng Jianwen Liang Chuchu Wang 《国际地质力学数值与分析法杂志》2018,42(15):1866-1889
By using a complete set of poroelastodynamic spherical wave potentials (SWPs) representing a fast compressional wave PI, a slow compressional wave PII, and a shear wave S with 3 vectorial potentials (not all are independent), a solution scheme based on the method of fundamental solution (MFS) is devised to solve 3‐D wave scattering and dynamic stress concentration problems due to inhomogeneous inclusions and cavities embedded in an infinite poroelastic domain. The method is verified by comparing the result with the elastic analytical solution, which is a degenerated case, as well as with poroelastic solution obtained using other numerical methods. The accuracy and stability of the SWP‐MFS are also demonstrated. The displacement, hoop stress, and fluid pore pressure around spherical cavity and poroelastic inclusion with permeable and impermeable boundary are investigated for incident plane PI and SV waves. The scattering characteristics are examined for a range of material properties, such as porosity and shear modulus contrast, over a range of frequency. Compared with other boundary‐based numerical strategy, such as the boundary element method and the indirect boundary integral equation method, the current SWP‐MFS is a meshless method that does not need elements to approximate the geometry and is free from the treatment of singularities. The SWP‐MFS is a highly accurate and efficient solution methodology for wave scattering problems of arbitrary geometry, particularly when a part of the domain extends to infinity. 相似文献