共查询到19条相似文献，搜索用时 250 毫秒
1.
断裂问题的扩展有限元法研究 总被引：3，自引：0，他引：3
扩展有限元（extended finite element method,XFEM）是近年来发展起来的、在常规有限元框架内求解不连续问题的有效数值计算方法,其基于单位分解的思想,在常规有限元位移模式中加入能够反映裂纹面不连续性的跳跃函数及裂尖渐进位移场函数,避免了采用常规有限元计算断裂问题时需要对裂纹尖端重新加密网格造成的不便。在推导扩展有限元算法的基础上,分析了应力强度因子的J积分计算方法及积分区域的选取。采用XFEM对I型裂纹进行了计算,有限元网格独立于裂纹面,无需在裂纹尖端加密网格;分析了积分区域、网格密度对应力强度因子计算精度的影响,指出了计算应力强度因子的合适参数,验证了此方法的可靠性和准确性。 相似文献
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传统数值流形法（NMM）在处理非连续变形问题时,仅限于几何构型不发生破坏的情况。针对这一不足,通过在裂纹尖端附近的物理片上增加用于模拟应力奇异性的增强位移函数,进一步发展了可用于几何构型破坏的扩展的高阶NMM。然后,将其应用到重力坝由连续到非连续的破坏过程分析中。首先,针对一含单裂纹的重力坝模型进行了敏感性分析,结果表明,在不同的扩展长度或网格密度下,其扩展路径基本相同且与文献结果保持一致。进而在此模型基础上又开展了多裂纹扩展分析,结果仅一条主导裂纹发生扩展,与文献结果基本一致。最后,针对印度的Koyna重力坝,通过设置不同的漫顶高度研究了其裂纹扩展路径的变化。结果表明,随着漫顶高度的增大,裂纹扩展路径逐渐趋向于水平方向扩展,而且坝体抵抗破坏的能力逐渐减弱。总体表明,NMM在求解实际工程问题时具有很好的数值稳定性和鲁棒性。 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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模拟三维裂纹问题的扩展有限元法 总被引：4，自引：1，他引：3
扩展有限元法是一种在常规有限元框架内求解强和弱不连续问题的新型数值方法,其计算网格与不连续面相互独立,因此模拟移动不连续面时无需对网格进行重新剖分。给出了模拟三维裂纹问题的扩展有限元法。在常规有限元位移模式中,基于单位分解的思想加进一个阶跃函数和二维渐近裂尖位移场,反映裂纹处位移的不连续性。用两个水平集函数表示裂纹。采用线性互补法求解裂纹面非线性接触条件,不需要迭代,提高了计算效率。采用两点位移外推法计算裂纹前缘应力强度因子。给出了3个三维弹性静力问题算例,其结果显示了所提方法能获得高精度的应力强度因子,并能有效地处理裂纹面间的接触问题,同时表明扩展有限元结合线性互补法求解不连续问题具有较好的前景。 相似文献
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在岩土工程分析中求解精度控制常常是必需的,在数值流形法中可以通过控制数学覆盖网格的稀疏和覆盖位移的阶数来达到精度的要求。提出了基于等几何分析的数值流形方法,定义了相应的数学覆盖的构造形式,推导了基于二次B样条的9节点数值流形方法分析格式;针对基于Lagrange插值函数的4节点数值流形方法提出了基于T样条思想的数学覆盖网格的局部加密方法。算例计算结果表明,相对于4节点的数值流形方法,基于非均匀有理B样条的9节点数值流形方法具有更高的精度;基于T样条思想的加密网格在保持计算精度的前提下降低了自由度的数量,表明T样条加密是一种自然的局部加密算法。 相似文献
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《岩土力学》2017,(4)
数值流形法的数学网格不需要适应求解域内各种不连续界面和边界,因此,总可以用规则的结构化网格建立数学覆盖。但对于大多数问题,在整个求解域上布置统一密度的网格显得浪费。因此,需要研究在结构化网格上实施局部加密,建立了加密物理片的方法用以解决这一问题。具体的实施过程中,确定了需要加密的区域后,先在这些区域布置规则的精细网格,然后找到这些区域中包含的原始网格中的物理片,用精细网格上建立的插值代替被加密物理片上的局部近似,从而提高了局部近似的阶次。数值算例结果表明,该方法收敛性良好。另外,如果所有物理片上的局部近似都采用0阶多项式(常数),那么将会得到正定的刚度矩阵。 相似文献
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数值流形方法中一般采用有限元网格或规则网格作为其数学覆盖系统,而规则的网格突出的优点是不需要适应求解域的边界和各种不连续面。采用规则的矩形网格作为数值流形方法中的数学网格,并借助适合分析的T样条实现了数值流形方法中的局部加密。适合分析的T样条定义在一个限制的T网格上,其基函数具有线性无关、单位分解、局部加密等许多重要性质,使得其非常适合用于工程设计及分析。当对一个适合分析的T网格加密后,所产生的新的网格往往不再是适合分析的T网格。基于此,提出了一种简单的数学网格加密算法,该算法能保证局部加密后的数学网格仍然是适合分析的。算例结果表明:在应力集中区和裂纹尖端等应力梯度较大区域,该算法均具有较强的适用性。 相似文献
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在处理含有裂隙这类不连续问题时,常规有限元方法需要对裂隙尖端部位进行局部网格加密,当裂隙扩展时还需要进行网络重构。基于单位分解思想的扩展有限元成功解决了常规有限元难以处理的裂隙类不连续问题。在研究复合裂隙时,通常需要考虑裂隙的接触问题。基于互补理论,建立了裂隙面上相对位移和接触力的互补方程,并采用牛顿法求解,无需开闭迭代,且能够快速收敛。最后,对含裂隙平板进行受压数值试验,计算结果表明,基于互补理论的扩展有限元接触算法能够有效地阻止裂隙两端网格的相互嵌入,且获得裂隙面上的应力分布与实际一致。 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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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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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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数值流形方法中覆盖函数选用的建议 总被引：5，自引：0，他引：5
在数值流形方法中,常用的覆盖函数基并非是最佳选择。循着刚度矩阵的形成过程,分析了选用常用覆盖函数时,在非对角元上出现绝对值很大的元素之成因,且发现这会增加刚度矩阵的条件数,尤其是在用刚性弹簧约束位移的情况下,而这在数值流形方法中普遍而基本。建议采用局部化较好的覆盖函数,取代常用的关联于全局坐标的覆盖函数,可显著消除这一情况。建议方式简单明了,程序改动极小,对改善刚度矩阵性态却有很大作用。算例验证了这一建议的合理性,通过比较局部化的覆盖函数及全局性的覆盖函数所形成的刚度矩阵,表明前者形成了较小条件数的刚度矩阵。 相似文献
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It is well accepted that severe numerical difficulties arise when using the conventional finite element displacement method to analyse incompressible, or nearly incompressible, solids. These effects are caused by the kinematic constraints imposed on the nodal velocities by the constant volume condition. In elastic-plastic analysis, these effects are due to a conflict between the plastic flow rule and the finite element discretization. Although several methods have been proposed to cope with this problem, none has been based on the appropriate choice of displacement interpolation to minimise the constraints. In this paper, a new displacement interpolation, which is able to reduce the imposed constraints, is adopted. Comparisons of the results with those from a conventional linear displacement interpolation are made for predictions of cylindrical and spherical cavity expansion limit pressures in elastic-plastic solids. This study suggests that the proposed displacement interpolation is preferable to the conventional one in the elastic-plastic finite element analysis of one dimensional-axisymmetric problems which involve nearly incompressible material behaviour. 相似文献
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数值流形方法（NMM）的最大优势在于可以统一地处理岩土力学中的连续和非连续变形问题。它在求解断裂力学问题时无需强制裂纹与数学网格保持一致,非常适合应用于岩土工程中由连续到非连续的破坏过程模拟。在裂纹扩展过程中,裂纹与数学网格的相对位置将会是任意的,如裂纹尖端可能落在网格内部、网格节点上或网格边上等。因此,对同一条裂纹,通过旋转和移动数学网格构造了它们之间的这种相对位置关系以及一些可能对计算结果产生影响的极端情况,并以应力强度因子作为衡量标准,研究了NMM在处理线弹性断裂力学问题时的网格依赖性。研究表明,NMM即使在处理强奇异性问题时依然有着很好的网格无关性,进一步证实了它在模拟裂纹扩展问题时的鲁棒性。 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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Summary Numerical Manifold Method (NMM) is an extension of Discontinuous Deformation Analysis which contains and combines FEM and
joint/block oriented DDA in a unified form. At present, application of NMM is mainly limited to two-dimensional analysis which
is not realistic for many underground excavation works. In the present paper, three-dimensional NMM based on tetrahedron and
hexahedron elements is proposed. The corresponding three-dimensional cover contact detection algorithms which have some fundamental
properties different from the corresponding two-dimensional analysis are also developed. Based on the present formulations,
engineering problems with arbitrarily oriented discontinuities can be modeled and realistic modeling of construction works
becomes possible.
Author’s address: Y. M. Cheng, Department of Civil and Structural Engineering, Hong Kong Polytechnic University, Room TV707,
Hung Hom Kowloon, Hong Kong, P.R. China 相似文献