Showing papers on "Discontinuous Deformation Analysis published in 2002"

Computation of electromagnetic scattering with a non‐conforming discontinuous spectral element method

Abstract: In this paper we solve electromagnetic scattering problems by approximating Maxwell's equations in the time-domain with a high-order quadrilateral discontinuous spectral element method (DSEM). The method is a collocation form of the discontinuous Galerkin method for hyperbolic systems where the solution is approximated by a tensor product Legendre expansion and inner products are replaced with Gauss–Legendre quadratures. To increase flexibility of the method, we use a mortar element method to couple element faces. Mortars provide a means for coupling element faces along which the polynomial orders differ, which allows the flexibility to choose the approximation order within an element by considering only local resolution requirements. Mortars also permit local subdivision of a mesh by connecting element faces that do not share a full side. We present evidence showing that the convergence of the non-conforming approximations is spectral along with examples of their use. Copyright © 2001 John Wiley & Sons, Ltd.

Mixed mode fracture propagation by manifold method

Abstract: The numerical manifold method combined with the virtual crack extension method is proposed to study the mixed mode fracture propagation. The manifold method is a new numerical method, and it provides a unified framework for solving problems dealing with both continuums and jointed materials. This new method can be considered as a generalized finite element method and discontinuous deformation analysis. One of the most innovative features of the method is that it employs both physical mesh and mathematical mesh to formulate the physical problem. These two meshes are separated and independent. They are inter-related through the application of weighting functions. A local mesh refinement and auto-remeshing schemes previously proposed by the authors are adopted in this study. The proposed model is first verified by comparing the numerical stress intensity factors with the benchmark solutions, and the results show satisfactory accuracy. The maximum tangential stress criterion is adopted and the mixed mode fracture propagation problems are then fully investigated. The numerical solutions by the present method agree well with the experimental results.

Displacement Accuracy of Discontinuous Deformation Analysis Method Applied to Sliding Block

Abstract: Discontinuous deformation analysis (DDA) is a discrete element method that was developed for computing large deformation in fractured rock masses. In this paper, we present an alternative derivation of the basic theory of DDA for planar (two-dimensional) problems, and we address the accuracy of the DDA method for sliding blocks using sensitivity analyses. Results of analyses with different parameters show that the residual and relative errors in the displacement of a frictional sliding block are controlled by the perturbation in the initial time steps of the simulation. In addition, we expose a systematic error induced by the DDA penalty formulation. Overall, the initial perturbation of the solution decreases with decreasing friction angle and increasing contact penalty and, counterintuitively, decreases with increasing time step size. All analyses show that the long runout behavior of the system trends toward the analytic solution, independent of the initial perturbation. The resulting precision of the long runout simulation is more than sufficient for all problems of engineering interest.

Analysis of a Discontinuous Least Squares Spectral Element Method

Abstract: This paper addresses the development of a Discontinuous Spectral Least-Squares method Based on pre-multiplication with a mesh-dependent function a discontinuous functional can be set up Coercivity of this functional will be established An example of the approximation to a continuous solution and a solution in which a jump is prescribed will be presented The discontinuous least-squares method preserves symmetry and positive definiteness of the discrete system

Coupling of FEM and DDA Methods

Abstract: Problems governed by both continuum and discontinuum like tunnels and caverns are best analyzed by the coupling distinct element method and finite element or boundary element method. This article introduces a technique in coupling FEM and DDA; this technique has been applied to some examples to demonstrate the effectiveness of the proposed coupling method.

On discontinuous Galerkin methods for nonlinear convection-diffusion problems and compressible flow

Abstract: The paper is concerned with the discontinuous Galerkin finite element method for the numerical solution of nonlinear conservation laws and nonlinear convection-diffusion problems with emphasis on applications to the simulation of compressible flows. We discuss two versions of this method: (a) Finite volume discontinuous Galerkin method, which is a generalization of the combined finite volume—finite element method. Its advantage is the use of only one mesh (in contrast to the combined finite volume—finite element schemes). However, it is of the first order only. (b) Pure discontinuous Galerkin finite element method of higher order combined with a technique avoiding spurious oscillations in the vicinity of shock waves.

The three dimensional discontinuous deformation analysis (3d dda) and its application to rock toppling

Abstract: Since the orientations of discontinuities in the field are not truly perpendicular to the two dimensional (2D) blocks of simulation, the applications of 2D discontinuous deformation analysis (2D DDA) computations have limited accuracy. In order to simulate the three dimensional (3D) block behaviors more accurately, Shi (2001) developed the 3D DDA theory to the blocks with general shape. In this paper, the basic formulations of contributed components of 3D DDA are presented briefly, and a new 3D DDA program developed by the authors is applied to rock-slope toppling failure at the Amatoribashi-Nishi site to demonstrate the capability of this new method. The results show the ability of 3D DDA to study the mechanisms of slope failure.

Study on the Rigid Body Rotation Problem in Discontinuous Deformation Analysis (DDA)

Abstract: The separation of rigid body rotation term, r0, from the other displacement variables is a breakthrough idea in original discontinuous deformation analysis (DDA) formula. Although the original linear displacement function is a fast and efficient method in computation, it loses accuracy when blocks undergo large rigid body rotations. It can be a significant problem especially when solving the problem with high speed rigid body rotation, such as rock fall problem, or the larger time interval is introduced to the problem with rigid body rotation to obtain the results within less computation steps. Up to date, it is only known that the large rigid body rotation can cause free expansion and change the weight of block in the analysis. However, the authors consider that the problem can also affect the contact judgments in open-close iterations and cause wrong contact forces in the computation. In this paper, this problem will be discussed, and a new method named \"post contact adjustment\" is developed and applied to the contact computation terms of DDA. After the improvements, the simulation results show better contact computations and block area preservations even when the large rigid body rotation is carried out.

Simulation of Landslide Movement Process by Discontinuous Deformation Analysis

Abstract: Landslide is a dynamic process. The movement of landslide body is a complex dynamic process composed of sliding, rotational, and tensile movements. Either the traditional limit equilibrium calculation or finite element analysis cannot be used to describe the characteristics and process of landslide movements. The discontinuous deformation analysis (DDA), a new discrete numerical simulation method, incorporates both the massive dynamic theory and the numerical analysis, so as to make a static and dynamic calculation of the massive body. In this paper, the discontinuous deformation analysis is applied to the numerical simulation of the dynamic movement process of Xintan landslide in the Three Gorges reservoir. This simulation classifies the landslide profile as 504 units in terms of geology, topography, soil and rock body types and geological structural surface types. The simulation results show that the Xintan landslide started with the partial failure of the Jiangjiapo belt in the middle of the landslide, and then the upper part of the landslide was further trailed upward and the lower part of the landslide was further pushed downward. Both the displacement variation curves and the sliding speed variation curves of the representative massive units show that the deformation of the massive body system of the sliding slope is discontinuous in the sliding process, and that the movements of different masses are quite different in shape, reflecting well the whole dynamic process of the landslide and revealing the dynamic mechanism of the landslide.A) ,anewdiscretenumerica

The basis of discontinuous motion

Abstract: We show that the instant motion of particle should be essentially discontinuous and random This gives the logical basis of discontinuous motion Since what quantum mechanics describes is the discontinuous motion of particles, this may also answer the question 'why the quantum?'

Application of DDA Approach to Simulation of Ice Breaking Process and Evaluation of Ice Force Acting on A Structure

Abstract: The sea ice is idealized as an elastic-brittle material. When an ice sheet moves toward a structure, the dynamic in-teraction between ice and the structure is analyzed by the DDA (Discontinuous Deformation Analysis) approach, wherethe ice sheet and the structure are considered as assemblages of blocky masses. This has the advantages that the wholeprocess of collision between the ice and structure can be shown visually with a series of pictures. Meanwhile, the dynamicresponse of the structure at each time step after the bumping of the ice against the structure is calculated. And with theaid of inverse analysis developed by the authors, the time history of the resultant ice force exerting on the structure isevaluated. A numerical example shows that the proposed approach is suitable to the simulation of the ice-breaking processand reasonable result of ice force acting on the structure can be obtained.

Discontinuous deformation analysis for the wave-induced settlement of a seawall

Abstract: When ocean wave arrive a coastal structure such as a seawall, the wave pressure acting on the surface of seabed and seawall will change the pore pressure distribution in the seabed. These external loadings will cause the instability of the seabed and seawalls. In this paper, the settlement of a seawall block placed on soft seabed is investigated. Discontinuous Deformation Analysis (DDA) will be applied, in which deformable particles are generated to simulate the deformation characteristics of soils under seawall. Numerical results indicate the significant effects of wave height on the wave-induced settlement of caisson in a porous seabed.