Wilson非协调数值流形方法

三维数值流形方法中,当数学覆盖取六面体体单元时流形单元总体位移函数中所包含的多项式并不是完全的,非完全的高次项非但对改善精度不起作用,而且还可能起相反的作用。为此,基于Wilson非协调元理论,推导了附加非协调位移基本项的流形元通用公式,通过内参静力凝聚处理,导出了消除单元内参后的单元应变矩阵、单元刚度矩阵,建立了非协调数值流形方法。数值试验表明,在规则数学网格覆盖下它们能够保证收敛,有较高的精度,从而证明所建方法的可行性。     

加筋材料动态松弛有限元模型的建立及应用

为分析加筋材料的抗弯刚度对加筋性能的影响,加筋材料采用梁单元形式。基于动态松弛法,通过定义梁单元的刚度矩阵,求解内力矢量,随后定义虚拟质量密度而建立总质量矩阵,将加筋材料的梁单元有限元模型嵌入到已有的动态松弛法求解程序中。通过对简支梁的简单加载模拟验证了该梁单元模型的准确性能。随后,将该有限元模型与已有的动态松弛法计算程序结合（含砂土本构及弱面单元模型）,对加筋砂土地基室内模型试验进行了数值模拟。将梁单元的模拟结果与杆单元（梁单元的特例）模拟结果进行了比较,并分别探讨了抗拉刚度和抗弯刚度对加筋砂土地基承载性能的影响。结果表明：抗拉刚度对承载能力的影响较小;抗弯刚度对承载力的影响程度与加筋材料的布置形式有关,特别是当加筋砂土中出现剪切带以后,其影响逐渐增大。因此,在分析加筋砂土结构的增强机制时,建议采用梁单元（具有一定的抗弯刚度）对加筋材料进行模拟。     

复合单元法动力分析初步研究

复合单元法是一种适用于不连续介质结构分析的数值计算方法,优点是建立网格时不用考虑结构中不连续面,计算时能离散模拟不连续面。在复合单元法静力计算模型的基础上,提出了复合单元的动力分析方法。给出了复合单元动力分析的质量矩阵和阻尼矩阵的具体表达式,通过质量矩阵、刚度矩阵和阻尼矩阵将分布于复合单元内部的惯性力和阻尼力分别转移到复合单元的广义节点上。建立了惯性力、阻尼力、动力荷载及弹性力作用下的复合单元动力系统的控制方程组。以一个基岩内含有两条断层的混凝土重力坝模型地震为例,采用复合单元法动力分析程序进行计算,其结果与有限单元法解吻合得较好,说明所提出方法的正确性和有效性。     

EFG法在土体固结中的应用

EFGM作为一种新的数值计算方法，具有只需节点信息而无段单元的特性，故在解固结方程方面有很大的优势。在计算分析中，此法容易构造固结方程的EFGM刚度矩阵和处理不同边界条件。对单面排水等条件的计算结果表明，EFGM在解决固结变形问题上，精度较高，处理边界准确。     

浅层顶管施工引起的土体移动

顶管施工引起包括地面沉降和土地向在内的土地的运动，土的这些运动呆能导致近构筑物和管线的损害。理论分析和现场实测都显示，在类似于上海等地的软土地层中顶管施工，顶管周围土的运动问题是三维的。基于半解析数值方法的基本原理，将轴向离散而在径向和环向选取位移函数，构造了解析解函数。给出了包括位移函数，刚度矩阵和荷载矩阵在内的理论分析过程，从而建立了半解析单元法。利用半解析单元法将顶管施工中三维土运动问题转化成一维数值计算。利用所建立的半解析单元法，就软土地层中顶管工程实例计算了施工所引起的土体位移。结果表明，半解析元法用于计算顶管施工中顶管周围土的移动，可以得到较为满意的结果。由于计算所需要的单元减少，处理该问题所需要的时间也明显减少。根据分析与计算结果还得到了一些有价值的结论。     

引入接触单元模拟桩土共同作用

在桩与桩侧土界面引入接触单元模型，并采用参变量变分原理及基于此原理的参变量二次规划法，对接触单元刚度矩阵进行了推导。模型计算结果与实测比较表明，接触单元能较好地模拟桩与土之间的剪力传递和相对位移。     

隔离非线性平面应变单元模型及其在Drucker-Prager模型中的应用

提出了一种基于隔离非线性理论的平面应变单元分析模型。对于线性的四边形等参单元,采用2×2个高斯积分点作为单元的非线性应变插值点。考虑到平面应变单元面外无应变分量存在,故仅在面内的3个方向建立非线性应变场以及相应的控制方程。采用Woodbury公式与组合近似法联合求解控制方程,使得整个非线性分析过程仅为多次的初始弹性刚度矩阵回代计算以及稀疏矩阵与向量的乘积,极大地提高了控制方程的求解效率。基于时间复杂度的计算效率分析表明：本文算法的计算效率相对传统变刚度法显著提高,且相对于精确的Woodbury公式则大大提高了非线性自由度的临界比例。将Drucker- Prager准则的转移应力解析解法用于典型平面应变模型的非线性分析,数值算例验证了平面应变单元模型的正确性以及算法的高效性,为平面应变类型的非线性分析提供了一种新思路。     

隔离非线性平面应变单元模型及其在Drucker-Prager模型中的应用

提出了一种基于隔离非线性理论的平面应变单元分析模型。对于线性的四边形等参单元,采用2×2个高斯积分点作为单元的非线性应变插值点。考虑到平面应变单元面外无应变分量存在,故仅在面内的3个方向建立非线性应变场以及相应的控制方程。采用Woodbury公式与组合近似法联合求解控制方程,使得整个非线性分析过程仅为多次的初始弹性刚度矩阵回代计算以及稀疏矩阵与向量的乘积,极大地提高了控制方程的求解效率。基于时间复杂度的计算效率分析表明:所提算法的计算效率相对传统变刚度法显著提高,且相对于精确的Woodbury公式,则大大提高了非线性自由度的临界比例。将Drucker-Prager准则的转移应力解析解法用于典型平面应变模型的非线性分析,数值算例验证了平面应变单元模型的正确性以及算法的高效性,为平面应变类型的非线性分析提供了一种新思路。     

数值流形方法中覆盖函数选用的建议

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。     

数值流形方法中覆盖位移函数的改进

通过对数值流形方法刚度矩阵形成的研究,提出一种改进的覆盖位移函数,以改善刚度矩阵计算。分析表明,改进的覆盖位移函数可使刚度矩阵的局部大数数量级明显的降低,提高计算效率,给矩阵求解提供适当的意见,并给出算例验证方法的正确性。     

砂土边坡深埋桩变形破坏的三维数值分析

利用三维弹塑性有限元,对砂土斜坡上刚性深埋桩水平载荷时的变形破坏进行了解析.在有限元解析中,考虑了砂土材料的低抗拉特点.结果表明,有限元计算所得到的桩基水平荷载与水平位移关系与现场实测值基本一致.此外,还利用三维有限元的解析结果,对深埋桩基随深度方向的土压与位移分布以及受压、受拉破坏的渐进性状态进行了合理的分析.     

Numerical manifold method for dynamic nonlinear analysis of saturated porous media

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.     

Analysis of dynamic behaviour of piles

The finite element approach has been used to derive element matrices suitable for the analysis of the dynamic behaviour of piles. Using this method, piles with arbitrary cross-section and soil with nonhomogeneous properties can be dealt with.     

Transient infinite elements for seepage problems in infinite media

In this paper, a time-dependent infinite element which can be used to simulate transient seepage problems in infinite media is presented. The hydraulic head distribution function of the element has been derived in detail and the property matrices of the element have been well formulated. Since both space and time variables are used in the course of constructing the hydraulic head distribution function of the element, the present infinite element can be referred to as a transient one. Using the present infinite element to model the far field of a system, the mechanism of transient seepage problems in infinite media can be rigorously simulated because the property matrices of the element are evaluated at any time of interest in the analysis. Since explicit expressions can be written for the property matrices of the infinite element, they may be evaluated quite easily and this can be carried out by writing a simple subroutine in a computer program. In order to examine the accuracy and efficiency of the present infinite element, both a one-dimensional (ID) transient seepage problem in a semi-infinite medium and a 2D transient seepage problem in a full plane have been solved using the finite and infinite element technique. It has been demonstrated that the present infinite element is very useful for the numerical simulation of transient seepage problems in infinite media.     

应力奇异问题自适应有限元分析初探

讨论了应力奇异问题的ｈ型自适应分析非收敛性和伪收敛性，并从理论上进行了分析。从工程应用出发，在保证一定计算粘度的前题下，提出了一种避免自适应分析失败的方法。算例验证了其适用性。     

移动荷载作用下层状饱和土的动力响应

根据Biot波动理论,采用传递、反射矩阵（TRM）方法研究了移动荷载作用下层状饱和土动力响应问题。由快速Fourier逆变换法（IFFT）得到层状土地基位移、应力及孔压在时间-空间域内的数值解。计算结果与已有文献结果相吻合,验证了算法的正确性。通过算例分析表明：移动荷载作用下含有软弱夹层的层状土体比均质土具有更显著的动力响应,同时会引起土体孔隙水压升高、土体波动性增强;硬夹层时情况则相反。     

土工格栅加筋砂土的变形与破坏机理解析

利用可考虑局部破坏的非线性弹塑性有限元，对无加筋和加筋砂土的平面应变压缩试验结果进行了从小变形到破坏的全过程数值解析。加筋砂土试验体用土工格栅分6层和11层进行加筋加固。将等价二维有限元解析所得到的解析结果与试验得到的实测值进行了较为伞面的比较，结果表明：合理的二维非线性弹塑性有限元解析，不仅可以较为精确的模拟加筋砂土的平均心力-应变特性，而且还可以全面地调查试验体的局部应力-应变分布以及剪切破坏发生状况，从而，对加筋砂土的变彤破坏以及加筋材的加州机理有一个更加全面合理的认识。     

Consolidation analysis of non-homogeneous soil by the weak form quadrature element method

A weak form quadrature element formulation for consolidation analysis of non-homogeneous saturated soil is established based on Biot’s theory. Numerical examples are given, and the results are compared with the analytical solutions available or those from the commercial finite element software ABAQUS, demonstrating accuracy and rapid convergence of quadrature element solutions. The disparity between various treatments of non-homogenous soil is discussed, and the effectiveness and advantages of the quadrature element formulation in consolidation analysis of non-homogeneous soil are demonstrated.     

Non-linear analysis of geomechanical problems using coupled finite and infinite elements

In modeling of many geomechanics problems such as underground openings, soil-foundation structure interaction problems, and in wave propagation problems through semi-infinite soil medium the soil is represented as a region of either infinite or semi-infinite extent. Numerical modeling of such problems using conventional finite elements involves a truncation of the far field in which the infinite boundary is terminated at a finite distance. In these problems, appropriate boundary conditions are introduced to approximate the solution of the infinite or semi-infinite boundaries as closely as possible. However, the task of positioning the finite boundary in conventional finite element discretization and the definition of the boundary and its conditions is very delicate and depends on the modeller's skill and intuition. Moreover, such a choice is influenced by the size of the domain to be discretized. Consequently, the dimensions of the global matrices and the time required for solution of the problem will increase considerably and also selection of the arbitrary location of truncated boundary may lead to erroneous result. In order to over come these problems, mapped infinite elements have been developed by earlier researchers (Simoni and Schrefier, 1987). In the present work the applicability of infinite element technique is examined for different geomechanics problems. A computer program INFEMEP is developed based on the conventional finite element and mapped infinite element technique. It is then validated using selected problems such as strip footing and circular footing. CPU time taken to obtain solutions using finite element approach and infinite element approach was estimated and presented to show the capability of coupled modeling in improving the computational efficiency. Mesh configurations of different sizes were used to explore the enhancement of both computational economy and solution accuracy achieved by incorporation of infinite elements to solve elastic and elasto-plastic problems in semi-infinite/finite domain as applied to geotechnical engineering. © Rapid Science Ltd. 1998     

一种高温下混凝土化学塑性-损伤耦合本构模型

提出了一个用于模拟高温下混凝土化学塑性-损伤耦合本构行为的数值模型。发展了一个化学塑性-损伤耦合分析的一致性应力返回映射算法。为了保证对于全局守恒方程Newton迭代过程的2阶收敛率,推导并形成了一致性切线模量矩阵。数值算例显示了文中发展的化学塑性-损伤耦合本构模型在模拟高温下混凝土中复杂破坏过程的能力和有效性。