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There has been interest recently in analysing soil, ceramic powders and other materials on the microscopic level so that macroscopic phenomena, such as failure, can be…
There has been interest recently in analysing soil, ceramic powders and other materials on the microscopic level so that macroscopic phenomena, such as failure, can be related to microscopic properties. The discrete element method provides a numerical tool for conducting such analyses. Here the basic theory behind the method is reviewed and various formulations derived from a finite element basis. The automatic detection of contact surfaces between bodies is a major problem in analysing the interaction of numerous bodies, common to both finite elements and discrete elements. Various approaches to geometric contact detection and the need for efficient algorithms and data structures utilizing recent developments in the field of computer graphics and solid modelling are discussed. Examples are given of the collapse of a soil embankment, penetration of a projectile into a soil and the large deformation of a space structure.
This paper discusses advances in interactive discrete element simulation for use in computer‐aided concurrent design. We highlight the computational problems of creating a…
This paper discusses advances in interactive discrete element simulation for use in computer‐aided concurrent design. We highlight the computational problems of creating a ‘virtual world’ populated by objects which behave much as real world objects and propose a system based on a new class of volumetric models, called superquadrics. These functions have significant advantages for calculating multibody interactions, and by coupling volumetric representation to a modal decomposition method for the physical dynamics we have been able to gain up to two orders of magnitude in efficiency. The modal method allows us to trade off high order modes for improved stability, time step magnitude, temporal aliasing and speed of response, and so provide almost real time feedback to the designer. We believe that virtual manufacturing systems will be especially useful in conceptual design, in design for manufacture and in the new thrust in concurrent design.
Volume mapping of large spherical particles to a Cartesian grid with smaller grid elements is typically required in application of simple immersed boundary conditions in…
Volume mapping of large spherical particles to a Cartesian grid with smaller grid elements is typically required in application of simple immersed boundary conditions in coupled engineering simulations. However, there exists no unique analytical solution to computation of the volume of intersection between spheres and cubes. The purpose of this paper is to determine a suitable solution to this problem depending on the required level of accuracy.
In this work, existing numerical techniques for computing intersection volume are reviewed and compared in terms of accuracy and performance. In addition to this, a more efficient linear relationship is proposed and included in this comparison.
The authors find in this work that a simple linear relationship is both acceptably accurate and more computationally efficient than the contemporary techniques.
This simple linear approach may be applied to accurately compute solutions to fluid-particle systems with very large numbers of particles.
We describe how wavelets may be used to solve partial differential equations. These problems are currently solved by techniques such as finite differences, finite elements…
We describe how wavelets may be used to solve partial differential equations. These problems are currently solved by techniques such as finite differences, finite elements and multigrid. The wavelet method, however, offers several advantages over traditional methods. Wavelets have the ability to represent functions at different levels of resolution, thereby providing a logical means of developing a hierarchy of solutions. Furthermore, compactly supported wavelets (such as those due to Daubechies) are localized in space, which means that the solution can be refined in regions of high gradient, e.g. stress concentrations, without having to regenerate the mesh for the entire problem. To demonstrate the wavelet technique, we consider Poisson's equation in two dimensions. By comparison with a simple finite difference solution to this problem with periodic boundary conditions we show how a wavelet technique may be efficiently developed. Dirichlet boundary conditions are then imposed, using the capacitance matrix method described by Proskurowski and Widlund and others. The convergence of the wavelet solutions are examined and they are found to compare extremely favourably to the finite difference solutions. Preliminary investigations also indicate that the wavelet technique is a strong contender to the finite element method.
The efficiency of a discrete element implementation relies on several factors, including the particle representation, neighbor‐sorting algorithm, contact resolution, and…
The efficiency of a discrete element implementation relies on several factors, including the particle representation, neighbor‐sorting algorithm, contact resolution, and force generation. The focus of this paper is on the four‐arc approximation for an ellipsoid – a geometrical representation useful in simulations of large numbers of smoothly shaped particles. A new contact resolution algorithm based on the four‐arc approximation is presented, which takes advantage of the properties of the geometry to provide favorable empirical convergence properties compared with the method proposed earlier. Special attention is given to the software implementation of the algorithm, and a discussion of the computational efficiency of the algorithm is provided.
A new spatial reasoning algorithm that can be used in multi‐body contact detection is presented. The algorithm achieves the partitioning of N bodies of arbitrary shape and…
A new spatial reasoning algorithm that can be used in multi‐body contact detection is presented. The algorithm achieves the partitioning of N bodies of arbitrary shape and size into N lists in order O(N) operations, where each list consists of bodies spatially near to the target object. The algorithm has been tested for objects of arbitrary shape and size, in two and three dimensions. However, we believe that it can be extended to dimensions of four and higher. The algorithm (CGRID) is a binning algorithm that extends traditional binning algorithms so that the arbitrary sizes and shapes can be handled efficiently. The algorithm has applications in discrete element, finite element, molecular dynamics, meshless methods, and lattice‐Boltzmann codes and also in domains such as path planning, target acquisition and general clustering problems.
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A coupled numerical method for the direct simulation of particle‐fluid systems is formulated and implemented. The Navier‐Stokes equations governing fluid flow are solved…
A coupled numerical method for the direct simulation of particle‐fluid systems is formulated and implemented. The Navier‐Stokes equations governing fluid flow are solved using the lattice Boltzmann method, while the equations of motion governing particles are solved with the discrete element method. Particle‐fluid coupling is realized through an immersed moving boundary condition. Particle forcing mechanisms represented in the model to at least the first‐order include static and dynamic fluid‐induced forces, and intergranular forces including particle collisions, static contacts, and cementation. The coupling scheme is validated through a comparison of simulation results with the analytical solution of cylindrical Couette flow. Simulation results for the fluid‐induced erosive failure of a cemented particulate constriction are presented to demonstrate the capability of the method.
Presents a new contact detection algorithm based on double‐ended spatial sorting (DESS) that is insensitive to variations in object size. It was developed to address the…
Presents a new contact detection algorithm based on double‐ended spatial sorting (DESS) that is insensitive to variations in object size. It was developed to address the problems that arise when objects with non‐spherical geometry and non‐uniform sizes are simulated using discrete element techniques. The algorithm is applicable to general spatial reasoning problems. While techniques based on spatial hashing (sometimes called bining methods) perform well for objects of similar size, they degrade significantly when the objects vary in size. The DESS algorithm overcomes this problem by using a spatial sorting technique applied to both ends of the object’s projection along each orthogonal axis. Discrete element test simulations comparing DESS and spatial hashing (NBS) are detailed. The results demonstrate that when object sizes vary significantly (size ratios greater than 8:1), DESS outperforms NBS up to around 100,000 objects. It is noted, however, that the superior scaling properties of NBS will always outperform DESS for some large numbers of objects.
The discrete element methods (DEM) are numerical techniques that have been specifically developed to enable simulations of systems of multiple distinct, typically…
The discrete element methods (DEM) are numerical techniques that have been specifically developed to enable simulations of systems of multiple distinct, typically infinitely rigid, bodies that interact with each other through contact forces. However, there are multibody systems for which it is useful to consider the deformability of the simulated bodies and enable the evaluation of their stress and strain distributions. This paper focuses on the simulation of deformable multibody systems using a combination of DEM and finite element methods (FEM). In particular, an updated Lagrangian (UL) finite element (FE) formulation and an explicit time integration scheme are used together with some simplifying assumptions to linearize this highly nonlinear contact problem and obtain solutions with realistic computational cost and sufficiently good accuracy. In addition, this paper describes a software implementation of this formulation, which utilizes the Java programming language and the Java3D graphics application programming interface (API), as well as database technology.