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1.
S. Amir Reza Beyabanaki Roozbeh Geraili Mikola Kianoosh Hatami 《Computers and Geotechnics》2008,35(3):346-356
This paper presents a new contact calculating algorithm for contacts between two polyhedra with planar boundaries in the three-dimensional discontinuous deformation analysis (3-D DDA). In this algorithm, all six type contacts in 3-D (vertex-to-face, vertex-to-edge, vertex-to-vertex, face-to-face, edge-to-edge, and edge-to-face) are simply transformed into the form of point-to-face contacts. The presented algorithm is a simple and efficient method and it can be easily coded into a computer program. In this paper, formulations of normal contact, shear contact and frictional force submatrices based on the new method are derived and the algorithm has been programmed in VC++. Examples are provided to demonstrate the new contact rule between two blocks. 相似文献
2.
In this paper, a new disk-based DDA formulation is presented. In the original disk-based DDA, disks are considered to be rigid and the penalty method is used to enforce disk contact constraints. In order to improve the accuracy of the disk-based DDA, new formulations of stiffness and force matrices for non-rigid disks using a new efficient contact model are presented in this paper. Blocks are considered deformable without need to do more computations for contact detection. In the proposed contact model, disk–disk and disk–boundary contacts are transformed into the form of point-to-line contacts and normal spring, shear spring and frictional force sub-matrices are derived by vector analysis. The penalty method is quite simple to implement, but has some major disadvantages. In the presented contact model, not only the simplicity of the penalty method is retained but also the limitations are overcome by using the augmented Lagrangian method. Moreover, unlike the contact model used in the original disk-based DDA, reference line can be obtained directly by using only coordinates of disk centers and their radii, and no more computations are needed. The validity and capability of the new disk-based DDA formulation are demonstrated by several illustrative examples. 相似文献
3.
The discontinuous deformation analysis (DDA) is a discontinuum‐based method, which employs a penalty method to represent the contact between blocks. The penalty method is easy to be implemented in the program, but the contact constraint is only approximately satisfied. Penetrations between contacting blocks are unavoidable even if the penalty value is very large. To improve the contact precision in the DDA, an augmented Lagrangian method is introduced, which can make use of advantages of both the Lagrangian multiplier method and the penalty method. This paper provides a detailed implementation of the augmented Lagrangian method in the DDA program and compares it with the standard DDA on the computational efficiency and contact precision. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
4.
S. Amir Reza Beyabanaki Ahmad Jafari S. Omid Reza Biabanaki M. Ronald Yeung 《Computers and Geotechnics》2009
This paper presents a new numerical model that can add a finite element mesh into each block of the three-dimensional discontinuous deformation analysis (3-D DDA), originally developed by Gen-hua Shi. The main objectives of this research are to enhance DDA block’s deformability. Formulations of stiffness and force matrices in 3-D DDA with conventional Trilinear (8-node) and Serendipity (20-node) hexahedral isoparametric finite elements meshed block system due to elastic stress, initial stress, point load, body force, displacement constraints, inertia force, normal and shear contact forces are derived in detail for program coding. The program code for the Trilinear and Serendipity hexahedron elements have been developed, and it has been applied to some examples to show the advantages achieved when finite element is associated with 3-D DDA to handle problems under large displacements and deformations. Results calculated for the same models by use of the original 3-D DDA are far from the theoretical solutions while the results of new numerical model are quite good in agreement with theoretical solutions; however, for the Trilinear elements, more number of elements are needed. 相似文献
5.
David M. Doolin 《国际地质力学数值与分析法杂志》2005,29(12):1199-1207
Displacement boundary constraints in discontinuous deformation analysis (DDA) are applied using stiff penalty springs. A co‐ordinate‐free formulation for displacement boundary constraints is presented here for DDA, which unifies previous derivations for points of fixity, and for points constrained to induce or prohibit block motion in specified directions as a function of location or time. Examples for each type of constraint are used to illustrate the behaviour of the algorithm and provide a link with previous formulations for each case. The new, unified formulation has five benefits: (1) simple to express algorithmically; (2) easy to program and verify; (3) penalty values in different directions may be chosen to allow fixed points, lines, curves or planes; (4) formulation works for 2D and 3D; (5) displacement constraint may be a function of time or location or both. Feedback in the algorithm may induce internal resonance in homogeneously deformable discrete elements used in DDA, and resonance in block‐to‐block contact interactions. Consequently, high mass problems with insufficient damping may suffer from excessive ‘vibrational hammering’, inducing physically implausible behaviour such as elastic rebound. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
6.
In modelling particulate media, such as soils, using 3-D DDA, there are four types of contacts: sphere to sphere, sphere to boundary face, sphere to boundary edge, and sphere to boundary corner contacts. The first two were studied by the authors in a previous work (Beyabanaki and Bagtzoglou 2012). In this paper, we present a new contact model for sphere-boundary edge and sphere-boundary corner contacts in sphere-based 3-D DDA. The model includes a new algorithm to search for contacts, detect the contact types and calculate contact points. Moreover, formulas for contact sub-matrices are derived. The proposed contact model has been implemented into a sphere-based 3-D DDA program and three test cases are studied in order to verify the workability of the new contact model. The numerical results obtained demonstrate the capability of the model to deal with sphere-boundary interaction in particulate media. 相似文献
7.
A Model of Point-to-Face Contact for Three-Dimensional Discontinuous Deformation Analysis 总被引：15，自引：0，他引：15
Summary The key to three-dimensional discontinuous deformation analysis (3D DDA) is a rigorous contact theory that governs the interaction of many three-dimensional blocks. This theory must provide algorithms to judge contact types and locations and the appropriate state of each contact, which can be open, sliding or locked. This paper presents a point-to-face contact model, which forms a part of the contact theory, to be used in 3D DDA. Normal spring, shear spring and frictional force submatrices are derived by vector analysis and the penalty method. Also given are the open-close iteration criteria and operations performed for different changes in contact state. Sliding at a contact can occur in any direction parallel to the contact face, as opposed to one of two directions in two-dimensional DDA. This point-to-face contact model has been implemented into a 3D DDA computer program, and numerical results from several test cases demonstrate the validity of the model and the capability of the program. 相似文献
8.
Frictionless contact formulation for dynamic analysis of nonlinear saturated porous media based on the mortar method 
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下载免费PDF全文 A finite element algorithm for frictionless contact problems in a two‐phase saturated porous medium, considering finite deformation and inertia effects, has been formulated and implemented in a finite element programme. The mechanical behaviour of the saturated porous medium is predicted using mixture theory, which models the dynamic advection of fluids through a fully saturated porous solid matrix. The resulting mixed formulation predicts all field variables including the solid displacement, pore fluid pressure and Darcy velocity of the pore fluid. The contact constraints arising from the requirement for continuity of the contact traction, as well as the fluid flow across the contact interface, are enforced using a penalty approach that is regularised with an augmented Lagrangian method. The contact formulation is based on a mortar segment‐to‐segment scheme that allows the interpolation functions of the contact elements to be of order N. The main thrust of this paper is therefore how to deal with contact interfaces in problems that involve both dynamics and consolidation and possibly large deformations of porous media. The numerical algorithm is first verified using several illustrative examples. This algorithm is then employed to solve a pipe‐seabed interaction problem, involving large deformations and dynamic effects, and the results of the analysis are also compared with those obtained using a node‐to‐segment contact algorithm. The results of this study indicate that the proposed method is able to solve the highly nonlinear problem of dynamic soil–structure interaction when coupled with pore water pressures and Darcy velocity. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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10.
非连续变形分析(DDA)方法是一种新的用来分析块体系统运动和变形的非连续介质数值计算方法。研究的核心工作是致力于对现有DDA接触问题处理方法的改进。DDA主要采用罚函数法和Lagrange乘子法处理接触问题,合理设定罚参数很困难,此外,因开闭迭代而引起的刚度矩阵的不连续变化也会导致收敛方面的困难。为避免引入罚参数及传统意义上的开闭迭代,用混合线性互补模型(LCDDA)对DDA方法进行了重新描述。在此基础上,综合基于非光滑分析的Newton法的局部平方收敛和最速下降法的全局线性收敛的优势,提出求解LCDDA模型的有效算法。根据上述思想及理论研究成果编制了完整的计算程序,算例计算结果证明了方法的精度及可行性。 相似文献
11.
双曲线接触面本构模型能比较真实地模拟堆石材料与混凝土面板间的接触关系,扩展Lagrange乘子法能比较精确地计算接触面间接触状态。在吸取Clough双曲线接触面本构关系应用于无厚度的Goodman单元和有厚度的Desai薄层单元的成功经验的基础上,将Clough双曲线接触面模型引入扩展Lagrange乘子法进行摩擦接触问题的求解。介绍了基于扩展Lagrange乘子法的序列二次规划法（SQP）提法,详细推导了在扩展Lagrange算法的非线性接触计算中引入Clough双曲线接触面本构关系的数值列式和实施步骤。数值算例和工程实例的计算结果证明该方法是成功的,能够比较真实地模拟堆石-混凝土墙（混凝土面板）之间的接触状态。 相似文献
12.
Accurate estimation of rockfall trajectory and motion behaviors is essential for rockfall risk assessment and the design and performance evaluation of preventive structures. Numerical simulation using discontinuous deformation analysis (DDA) is effective and helpful in rockfall analysis. Up to now, there have been many reports on application of two-dimensional (2-D) DDA programs. In this paper, the major advantages of rockfall analysis using 2-D and extensions to three-dimensional (3-D) analysis are presented. A practical 3-D DDA code is demonstrated to be capable of simulating free falling, rolling, sliding, and bouncing with high accuracy. Because rockfall trajectories and motion behaviors can be described as combinations of these four types, this demonstration indicates that the implemented code is capable of providing reliable rockfall analysis. Finally, specific tests are conducted to compare 2-D and 3-D DDA rockfall analysis in predicting trajectory and dynamic behavior. The results indicate that 3-D DDA simulations are more appropriate for rough tree-laden inclined slopes in providing detailed spatial distribution, whereas 2-D DDA simulations have better efficiency for slopes dominated by valleys and ravines. These results can help in selecting the appropriate DDA simulation for rockfall analysis. 相似文献
13.
Orienting the circular and rigid particle medium, the variational inequality-based discontinuous deformation analysis (DDA) is established. In the proposed DDA, the global stiffness matrix, the penalty parameters, and the open-close iteration are successfully avoided. The contact constraint is transferred into the problem of variational or quasi-variational inequalities. And explicit variational expression on the contact force is firstly established. To speed up the rate of solving contact force, on the basis of the two-stage prediction-correction method, we design a compatibility iteration algorithm (PPC-CI). The C++ code is developed in multicore environment through the open multi-processing (OpenMP) in order to take advantage of the parallelizable features of the new DDA. Numerical tests suggest that the presented DDA is effective and promising. 相似文献
14.
A 3-D large eddy simulation model that was first transformed to smoothed particle hydrodynamics (LES-SPH)-based model was
employed to study breaking tsunami waves in this paper. LES-SPH is a gridless (or mesh-free), purely Lagrangian particle approach
which is capable of tracking the free surface of violent deformation with fragmentation in an easy and accurate way. The Smagorinsky
closure model is used to simulate the turbulence due to its simplicity and effectiveness. The Sub-Particle Scale scheme, plus
the link-list algorithm, is applied to reduce the demand of computational power. The computational results show that the 3-D
LES-SPH model can capture well the breaking wave characteristics. Spatial evolution features of breaking wave are presented
and visualized. The detailed mechanisms of turbulence transport and vorticity dynamics are demonstrated as well. This application
also presents an example to validate the SPH model. 相似文献
15.
This paper outlines the development as well as implementation of a numerical procedure for coupled finite element analysis of dynamic problems in geomechanics, particularly those involving large deformations and soil-structure interaction. The procedure is based on Biot’s theory for the dynamic behaviour of saturated porous media. The nonlinear behaviour of the solid phase of the soil is represented by either the Mohr Coulomb or Modified Cam Clay material model. The interface between soil and structure is modelled by the so-called node-to-segment contact method. The contact algorithm uses a penalty approach to enforce constraints and to prevent rigid body interpenetration. Moreover, the contact algorithm utilises a smooth discretisation of the contact surfaces to decrease numerical oscillations. An Arbitrary Lagrangian–Eulerian (ALE) scheme preserves the quality and topology of the finite element mesh throughout the numerical simulation. The generalised-α method is used to integrate the governing equations of motion in the time domain. Some aspects of the numerical procedure are validated by solving two benchmark problems. Subsequently, dynamic soil behaviour including the development of excess pore-water pressure due to the fast installation of a single pile and the penetration of a free falling torpedo anchor are studied. The numerical results indicate the robustness and applicability of the proposed method. Typical distributions of the predicted excess pore-water pressures generated due to the dynamic penetration of an object into a saturated soil are presented, revealing higher magnitudes of pore pressure at the face of the penetrometer and lower values along the shaft. A smooth discretisation of the contact interface between soil and structure is found to be a crucial factor to avoid severe oscillations in the predicted dynamic response of the soil. 相似文献
16.
传统的非连续变形分析法（DDA）法采用简单的线性位移模式计算效率高,描述大块体的高阶多项式位移模式在一定程度保留了该特点,并提高了计算精度。近年来流行的耦合有限元、自然单元的DDA法实质上是引入相应的插值形函数构成块体位移函数,计算相对低效,但具有计算更精细、更容易施加边界条件等优点。为结合传统DDA法与DDA耦合法各自的优点,建立了一种同时利用传统DDA法线性位移模式与耦合型DDA法非线性位移模式的混合法。该方法非线性模式主要针对大块体,采用了自然单元插值,缘于其具有一定无网格特征,且效率比有限元高。建立了混合模式下的整体矩阵并推导出接触等因素刚度子矩阵和荷载子向量的具体表达式。该方法建模更加方便合理,计算精度、效率介于线性模式的传统DDA法和非线性位移模式的耦合法之间。通过基本算例验证了混合法的有效性,并给出了节理围岩-隧道衬砌整体分析模型的计算结果,体现了新方法的优越性。 相似文献
17.
通过定义距离势函数,提出一种适用于空间任意凸多面体单元的三维距离势函数离散单元法。该方法采用归一化的计算方式,将势函数表征为接触体间的距离函数,并基于此建立接触力计算方程,明确了势函数的物理意义,使接触力计算更加合理,无需对各种可能的接触形式进行差异化处理。新方法克服了原有势函数物理意义不明、接触力计算受单元形式影响等重要缺陷,并突破了四面体单元的限制,可采用空间任意凸多面体单元。通过若干算例说明新方法的正确性和有效性。数值模拟结果表明新方法能够很好处理空间任意多面体单元复杂接触变换过程,准确处理复杂非连续介质的运动过程。 相似文献
18.
A robust contact theory can be regarded as key to three dimensional discontinuous deformation analyses (3D-DDA). Not only must this theory provide an efficient algorithm to judge the type and location of contacts but also it must be able to present comprehensive formulations for every kind of contact (open, sliding and locked contact). There are six types of contact in three dimensional discontinuous deformation analyses (vertex-to-vertex, vertex-to-edge, vertex-to-face, edge-to-edge, edge-to-face and face-to-face) that can be converted to vertex-to-face and edge-to-edge contacts. This paper presents a new model of edge-to-edge contact to three dimensional discontinuous deformation analyses (3D-DDA). This new model considers both kinds of edge-to-edge contact (cross-over and parallel edge-to-edge contact) and presents a criterion for inter-penetration. Sub matrices of normal and shear spring and friction force are derived by geometrical analysis and penalty method. This new model is implemented in a 3D-DDA computer programme, and the example results demonstrate the validity of the model. 相似文献
19.
Discontinuous deformation analysis (DDA), a discrete numerical analysis method, is used to simulate the behaviour of falling rock by applying a linear displacement function in the computations. However, when a block rotates, this linear function causes a change in block size called the free expansion phenomenon. In addition, this free expansion results in contact identification problems when the rotating blocks are close to each other. To solve this problem of misjudgment and to obtain a more precise simulation of the falling rock, a new method called Post‐Contact Adjustment Method has been developed and applied to the program. The basic procedure of this new method can be divided into three stages: using the linear displacement function to generate the global matrix, introducing the non‐linear displacement function to the contact identification, and applying it to update the co‐ordinates of block vertices. This new method can be easily applied to the original DDA program, demonstrating better contact identification and size conservation results for falling rock problems than the original program. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
20.
非连续变形分析方法（DDA）是一种平行于有限元法的新型数值计算方法,该方法基于最小势能原理,把每个离散块体的变形、运动和块体之间的接触统一到平衡方程中进行隐式求解。然而,传统DDA方法在计算过程中需组装整体刚度矩阵并联立求解方程组,在用于大型岩土工程问题的三维数值模拟时占用内存较大、耗时较长、计算效率极低。因此,提出一种基于显式时间积分的三维球颗粒DDA方法。该方法在求解过程中不需要组装整体刚度矩阵,在求解加速度时,由于质量矩阵为对角矩阵,可存储为一维向量占用内存较少,且可分块逐自由度求解,效率较高,在接触判断上采用最大位移准则简化了接触算法,采用较小的时步,保证了计算的精确性;通过几个典型算例验证了该方法的准确性及计算效率。 相似文献