共查询到18条相似文献，搜索用时 125 毫秒
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运用布尔碎片运算实现了简单的三维块体切割功能，形成覆盖整个求解域的六面体网格，再将六面体单元拆分生成48个四面体单元，从而生成四面体数学覆盖。运用布尔交运算将四面体单元与求解域求交集得到流形块体，再根据三维拓扑有向性原理和三维单纯形积分理论，形成了有向边、有向环、有向面和有向壳4种有向几何数据结构，用来构造生成封闭的有向三维流形单元。定义了有向流形单元的连通内面对和连通的有向流形单元的概念，利用有向流形单元的连通内面对搜索生成物理覆盖体系。概括总结了基于修正对称和反对称分解的三维数值流形元法的求解计算要点，在不考虑三维接触、三维裂纹尖端奇异场和三维裂纹扩展的假设下，模拟了三维节理面的有限塑性变形张拉过程，得到了比较合理的数值模拟结果，验证了前处理和计算求解算法的正确性。 相似文献
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覆盖系统生成效率低是当前制约三维数值流形法在大型实际工程中应用的瓶颈问题。通过改进三维覆盖系统的生成算法,提出了改进的布尔交运算生成三维覆盖系统的算法,并采用C++语言编写了相应的程序。根据数学网格与物理域的拓扑几何关系,确定采用传统布尔交运算还是由数学网格直接生成流形块体,并对生成的流形块体进行三维块体有效性检查,满足要求后即可生成新的三维流形单元,进而生成所有前处理三维覆盖系统。选取两个简单算例和一个边坡工程问题来说明所提方法的可行性和计算程序的正确性,并通过对比分析说明方法的计算效率。计算结果表明,改进的布尔交运算比传统布尔交运算更高效;随着网格密度的增加,生成一个单元的平均耗时逐渐减少;随着物理域边界复杂程度增加,所提方法计算效率逐渐降低。为今后采用数值流形法进行结构分析奠定基础,具有较强的实际应用价值。 相似文献
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《岩土力学》2020,(1)
运用布尔碎片运算实现了简单的三维块体切割功能，形成覆盖整个求解域的六面体网格，再将六面体单元拆分生成48个四面体单元，从而生成四面体数学覆盖。运用布尔交运算将四面体单元与求解域求交集得到流形块体，再根据三维拓扑有向性原理和三维单纯形积分理论，形成了有向边、有向环、有向面和有向壳四种有向几何数据结构，用来构造生成封闭的有向三维流形单元。定义了有向流形单元的连通内面对和连通的有向流形单元的概念，利用有向流形单元的连通内面对搜索生成物理覆盖体系。概括总结了基于修正对称和反对称分解的三维数值流形元法的求解计算要点，在不考虑三维接触、三维裂纹尖端奇异场和三维裂纹扩展的假设下，模拟了三维节理面的有限塑性变形张拉过程，得到了比较合理的数值模拟结果，验证了前处理和计算求解算法的正确性。 相似文献
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对三维问题的分析是数值流形方法发展的必然,在数值流形方法覆盖位移函数的基础上构造了一种六面体有限覆盖的三维流形单元,推导了相应的应变矩阵、刚度矩阵及平衡方程等表达式。同时,由于目前数值流形方法的模拟分析主要是采用线弹性模型,而对于非线性模型分析研究很少;根据数值流形方法的特点和岩土体的本构模型,给出了适用于数值流形方法进行非线性分析的算法。该方法利用中点增量法进行求解,以改变E-μ模型和K-G模型中弹性模量的方式来反映非线性,其实质是用分段线性来取代非线性。通过地基沉降计算算例表明,数值流形方法在三维岩土体中进行非线性分析中是有效的。 相似文献
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《岩土力学》2016,(9)
三维流形单元的生成是进行三维数值流形分析的首要问题之一。详细研究了三维流形单元的生成过程,并采用C++语言编写了相应的程序。借鉴二维流形单元的形成技术,基于拓扑学的"有向性"原理,将点、有向边、有向环、有向面和有向壳等作为三维块体的基本数据结构。将材料体和数学网格进行布尔交运算,并对形成的流形块体进行有效性检测,满足要求后即形成新的三维流形单元。每个数学网格的顶点作为新流形单元的数学覆盖,再对数学覆盖进行细分,形成流形单元的物理覆盖。分别选取凹形体、空心体和包含有限结构面的材料体与数学网格进行布尔交运算,并选取一个典型工程来检查该方法和程序的可行性。计算结果表明,该方法可以对复杂块体(凹形体、空心体和包含有限结构面的体)进行处理,为今后进行复杂结构计算和分析奠定基础,具有较强的适应性和可靠性。 相似文献
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针对数值流形方法特有的覆盖剖分方式,提出了一种模拟岩土工程中开挖过程的算法。该算法采取某种措施,在覆盖剖分过程中将开挖面视为特殊的不连续面,这种不连续面将其所在的数学网格剖分成不同的流形单元,但却不对所在的数学覆盖作剖分。这样,开挖面两侧虽分属不同的流形单元,但开挖面两侧同一数学网格内的流形单元却具有相同的物理覆盖。采用该算法,无需对开挖面处的单元进行特殊处理,可在整个分析域采用统一的网格形式;同时,打破了原有数值流形方法的限制,将开挖面的位置完全当作连续介质来处理,避免了因将其视为不连续面而产生的误差。验证了算法的可靠性后,将其应用于某假想隧道的开挖模拟,计算结果表明该算法具有一定的应用前景。 相似文献
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裂隙岩体热-水-应力(THM)耦合是目前研究的热点和难点。首先总结了裂隙岩体多场耦合的机制、模型、方法及研究内容,并通过分析裂隙对THM耦合的重要控制作用,提出了在THM耦合中考虑裂隙网络扩展演化及模拟的关键问题,同时指出了研究的3个关键点:(1)建立考虑裂隙网络演化的耦合模型;(2)裂隙扩展的数值模拟方法;(3)THM耦合及岩体变形、失稳全过程的数值模拟算法。随后通过对模拟多场耦合和裂隙扩展数值方法的归类比较,重点论述了目前适用于模拟多场耦合下裂隙扩展模拟的各种数值方法(包括有限单元法、无单元法、单位分解法、离散单元法、岩石破裂过程分析方法和数值流形方法)的优缺点,并通过对比研究,推荐采用数值流形方法(NMM)来实现对关键问题的模拟研究。最后,对研究思路和难点进行了初步探讨。 相似文献
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水是影响岩土工程安全性的活跃因素,开挖是岩土工程中常见的工程作用,作为一种较新的数值方法,数值流形方法在这两方面的研究仍然较少,影响了数值流形方法在实际工程中的应用。针对结构面可能承受三种不同类型的水压力作用,分别给出了相应的计算公式以计算水压力对岩体结构的影响。数值方法中常删除开挖区域块体和单元的做法模拟开挖,这种处理方法易于描述且物理意义明确,相应的算例表明将它引入数值流形方法之后,数值流形方法能够合理地模拟开挖后的围岩变形,扩展了数值流形方法的应用范围并为更深入研究流形方法奠定了基础。 相似文献
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数值流形法（NMM）在接触处理过程包括：接触方式判断,包括点-点和点-线接触;开-闭迭代,确定块体系统的约束状态;以及接触传递,将有效的接触对传递到下一个时步。过程稍显繁琐和耗时,且与真实的物理接触状态有异。由Munjiza所提出的NBS（no binary search）接触检测算法,将单元映射到规则格子中,以链表结构将其有效地连接在一起,只在单元所在格子以及周围格子内部进行接触判断,接触检测效率大为提高,计算量仅随单元数线性增长,内存需求也很低。在计算接触力时以所定义的势为媒介,用重叠面积来衡量接触力的大小,属于分布式接触力,更接近于实际,避免了原NMM接触处理过程的繁琐。因此,将其作为一种平行的接触处理方法引入到NMM中,并以算例验证,证实了算法的可行性。 相似文献
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A major challenge in seepage analysis is to locate the phreatic surface in an unconfined aquifer. The phreatic surface is unknown and assumed as a discontinuity separating the seepage domain into dry and wet parts, thus should be determined iteratively with special schemes. In this study, we systematically developed a new numerical manifold method (NMM) model for unconfined seepage analysis. The NMM is a general numerical method for modeling continuous and discontinuous deformation in a unified mathematical form. The novelty of our NMM model is rooted in the NMM two‐cover‐mesh system: the mathematical covers are fixed and the physical covers are adjusted with iterations to account for the discontinuity feature of the phreatic surface. We developed an energy‐work seepage model, which accommodates flexible approaches for boundary conditions and provides a form consistent with that in mechanical analysis with clarified physical meaning of the potential energy. In the framework of this energy‐work seepage model, we proposed a physical concept model (a pipe model) for constructing the penalty function used in the penalty method to uniformly deal with Dirichlet, Neumann, and material boundaries. The new NMM model was applied to study four example problems of unconfined seepage with varying geometric shape, boundary conditions, and material domains. The comparison of our simulation results to those of existing numerical models for these examples indicates that our NMM model can achieve a high accuracy and faster convergence speed with relatively coarse meshes. This NMM seepage model will be a key component of our future coupled hydro‐mechanical NMM model. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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It is well known that the Babuska–Brezzi stability criterion or the Zienkiewicz–Taylor patch test precludes the use of the finite elements with the same low order of interpolation for displacement and pore pressure in the nearly incompressible and undrained cases, unless some stabilization techniques are introduced for dynamic analysis of saturated porous medium where coupling occurs between the displacement of solid skeleton and pore pressure. The numerical manifold method (NMM), where the interpolation of displacement and pressure can be determined independently in an element for the solution of u–p formulation, is derived based on triangular mesh for the requirement of high accurate calculations from practical applications in the dynamic analysis of saturated porous materials. The matrices of equilibrium equations for the second‐order displacement and the first‐order pressure manifold method are given in detail for program coding. By close comparison with widely used finite element method, the NMM presents good stability for the coupling problems, particularly in the nearly incompressible and undrained cases. Numerical examples are given to illustrate the validity and stability of the manifold element developed. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
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Boundary settings for the seismic dynamic response analysis of rock masses using the numerical manifold method 
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下载免费PDF全文 Aiming to accurately simulate seismic dynamic response of rock masses using the numerical manifold method (NMM), boundary settings must be treated carefully. In this paper, 4 issues in boundary settings are investigated to improve the performance of NMM: (1) Nonreflecting boundaries including the viscous boundary and viscoelastic boundary are considered; (2) A free‐field boundary is incorporated into NMM to accurately simulate external source wave motion; (3) A seismic input boundary is considered, and the force input method is introduced; and (4) A static‐dynamic unified boundary is incorporated for the convenience of transforming displacement boundary into other types of boundaries, such as nonreflecting boundaries and seismic input boundary. Several benchmark problems are solved to validate the improved NMM. Simulation results agree well with analytical ones, indicating that the improved NMM is able to simulate seismic dynamic response of rock masses reliably and correctly. 相似文献
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Particle manifold method (PMM) is a new extension of the numerical manifold method (NMM). PMM uses a mathematical cover system to describe the motion and deformation of a particle‐based physical domain. By introducing the concept of particle into NMM, PMM takes the advantages of easy topological and contact operations with particles. In this article, the methodology, formulations and implementation of the method are presented, together with modelling examples for validation. It is found that good solutions for both continuous and discontinuous problems are obtained by the new developed PMM. Due to the underlying coupled continuum‐discontinuum property of PMM, it has great potential for modelling of geomechanical problems. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
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Development of a discontinuous approach for modeling fluid flow in heterogeneous media using the numerical manifold method 下载免费PDF全文
下载免费PDF全文 In the numerical modeling of fluid flow in heterogeneous geological media, large material contrasts associated with complexly intersected material interfaces are challenging, not only related to mesh discretization but also for the accurate realization of the corresponding boundary constraints. To address these challenges, we developed a discontinuous approach for modeling fluid flow in heterogeneous media using the numerical manifold method (NMM) and the Lagrange multiplier method (LMM) for modeling boundary constraints. The advantages of NMM include meshing efficiency with fixed mathematical grids (covers), the convenience of increasing the approximation precision, and the high integration precision provided by simplex integration. In this discontinuous approach, the elements intersected by material interfaces are divided into different elements and linked together using the LMM. We derive and compare different forms of LMMs and arrive at a new LMM that is efficient in terms of not requiring additional Lagrange multiplier topology, yet stringently derived by physical principles, and accurate in numerical performance. To demonstrate the accuracy and efficiency of the NMM with the developed LMM for boundary constraints, we simulate a number of verification and demonstration examples, involving a Dirichlet boundary condition and dense and intersected material interfaces. Last, we applied the developed model for modeling fluid flow in heterogeneous media with several material zones containing a fault and an opening. We show that the developed discontinuous approach is very suitable for modeling fluid flow in strongly heterogeneous media with good accuracy for large material contrasts, complex Dirichlet boundary conditions, or complexly intersected material interfaces. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献