二维浅水波方程的间断-连续Galerkin方法

将基于二维简化浅水波模型的间断Galerkin有限元与连续Galerkin有限元耦合方法推广至形式更为复杂的浅水波方程,并给出了误差分析以及模型问题的数值算例。     

Implementation of the finite element method in the three‐dimensional discontinuous deformation analysis (3D‐DDA)

A modified three‐dimensional discontinuous deformation analysis (3D‐DDA) method is derived using four‐noded tetrahedral elements to improve the accuracy of current 3D‐DDA algorithm in practical applications. The analysis program for the modified 3D‐DDA method is developed in a C++ environment and its accuracy is illustrated through comparisons with several analytical solutions that are available for selected problems. The predicted solutions for these problems using the modified 3D‐DDA approach all show satisfactory agreement with the corresponding analytical results. Results presented in this paper demonstrate that the modified 3D‐DDA method with discontinuous modeling capabilities offers a useful computational tool to determine stresses and deformations in practical problems involving fissured elastic media with reasonable accuracy. Copyright © 2008 John Wiley & Sons, Ltd.     

Local problem-based <Emphasis Type="Italic">a posteriori</Emphasis> error estimators for discontinuous Galerkin approximations of reactive transport

We consider adaptive discontinuous Galerkin (DG) methods for solving reactive transport problems in porous media. To guide anisotropic and dynamic mesh adaptation, a posteriori error estimators based on solving local problems are established. These error estimators are efficient to compute and effective to capture local phenomena, and they apply to all the four primal DG schemes, namely, symmetric interior penalty Galerkin, nonsymmetric interior penalty Galerkin, incomplete interior penalty Galerkin, and the Oden–Babuška-Baumann version of DG. Numerical results are provided to illustrate the effectiveness of the proposed error estimators.     

非连续变形分析方法中人为参数的影响

非连续变形分析方法(DDA) 自创立以来,已在分析不连续体的大变形、大位移的问题中显示了其优越性。但DDA方法需要人为设置一些控制参数,通过一个简单的滑块模型,分别采用不同的时步大小、不同的接触弹簧刚度、并比较相对误差,分析了人为设定的参数对DDA计算结果的影响,指出仅在合理的取值范围内,大时步和大的接触弹簧刚度才能产生较好的计算结果;同时对造成这种影响的原因做了一定的探讨,并建议了参数取值的上下限原则。     

膨胀土边坡稳定性非连续变形分析新方法

许多膨胀土边坡在长期的地质和干湿循环的自然气候作用下裂隙逐渐发展,以致被裂隙分割成块体系统。将膨胀土边坡看成是一个具有非饱和土本构关系、块体间存在摩擦力和膨胀力和具有牵引式滑动及时空效应特点的块体系统,建立了一种新的边坡稳定性非连续变形分析方法,并应用于某高速公路段膨胀土边坡稳定性的分析中,获到了很好的效果。     

强度折减DDA方法及其在稳定分析中的应用

在自行研制的非连续变形分析（discontinuous deformation analysis,DDA）程序中实现了自动强度折减法以模拟边坡的稳定性和安全系数。通过锦屏高边坡和某重力坝深层滑动的计算分析以及与刚体极限平衡法和有限元方法的比较研究可以看出,强度折减DDA法可以较高精度求出岩石高边坡的安全系数,但求得的重力坝深层抗滑稳定安全系数要低于刚体极限平衡法的结果。基于强度折减技术的DDA与FEM的耦合方法,可以较准确地求出重力坝深层抗滑稳定安全系数。     

Generalized contact model for polyhedra in three‐dimensional discontinuous deformation analysis

We present a generalized contact computation model for arbitrarily shaped polyhedra to simplify the contact analysis in discontinuous deformation analysis. A list of generalized contact constraints can be established for contacting polyhedra during contact detection. Each contact constraint contains information for 2 contact points, unique contact plane, and related contact modes (open, locked, or sliding). Computational aspects of the generalized contact model include identification of contact positions and contact modes, uniform penalty formulation of generalized contact constraint, and uniform updating of contact modes and contact planes in the open‐close iteration. Compared with previous strategies, the generalized contact computation model has a simpler data structure and fewer memory requirements. Meanwhile, it simplifies the penalty formulation and facilitates the open‐close iteration check while producing enough accuracy. Illustrative examples show the ability of the method to handle the full range of polyhedral shapes.     

双排弹性桩隔振屏障对平面SH波的多重散射

提出了一种新的求解任意排列、任意半径的弹性桩对平面SH波的多重散射的理论方法,以解决以往假设单重散射的计算方法中不考虑桩列作为整体屏障从而忽略桩间相互干涉关系的不足,并且可用于分析多排弹性桩对平面SH波的散射性状。在数值计算分析中讨论了散射重数,排间距,桩土剪切模量比,桩数等对双排弹性桩屏障隔离效果的影响,从而对实际工程中利用排桩进行振动污染的治理和屏障隔振设计提出了重要的理论依据。     

Discontinuous deformation analysis with second‐order finite element meshed block

The discontinuous deformation analysis (DDA) with second‐order displacement functions was derived based on six‐node triangular mesh in order to satisfy the requirement for the accurate calculations in practical applications. The matrices of equilibrium equations for the second‐order DDA were given in detail for program coding. By close comparison with widely used finite element method and closed form solutions, the advantages of the modified DDA were illustrated. The program coding was carried out in C++ environment and the new code applied to three examples with known analytical solutions. A very good agreement was achieved between the analytical and numerical results produced by the modified DDA code. Copyright © 2006 John Wiley & Sons, Ltd.