Discrete element calculations of the impact of a sand column against rigid structures

Discrete particle simulations of column of an aggregate of identical particles impacting a rigid, fixed target and a rigid, movable target are presented with the aim to understand the interaction of an aggregate of particles upon a structure. In most cases the column of particles is constrained against lateral expansion. The pressure exerted by the particles upon the fixed target (and the momentum transferred) is independent of the co-efficient of restitution and friction co-efficient between the particles but are strongly dependent upon the relative density of the particles in the column. There is a mild dependence on the contact stiffness between the particles which controls the elastic deformation of the densified aggregate of particles. In contrast, the momentum transfer to a movable target is strongly sensitive to the mass ratio of column to target. The impact event can be viewed as an inelastic collision between the sand column and the target with an effective co-efficient of restitution between 0 and 0.35 depending upon the relative density of the column. We present a foam analogy where impact of the aggregate of particles can be modelled by the impact of an equivalent foam projectile. The calculations on the equivalent projectile are significantly less intensive computationally and yet give predictions to within 5% of the full discrete particle calculations. They also suggest that "model" materials can be used to simulate the loading by an aggregate of particles within a laboratory setting. © 2012 Elsevier Ltd. All rights reserved.

SIMPLE REMESHING SCHEME FOR THE FINITE ELEMENT BASED SIMULATION OF DOPANT DIFFUSION IN SILICON.

Process simulation programs are valuable in generating accurate impurity profiles. Apart from accuracy the programs should also be efficient so as not to consume vast computer memory. This is especially true for devices and circuits of VLSI complexity. In this paper a remeshing scheme to make the finite element based solution of the non-linear diffusion equation more efficient is proposed. A remeshing scheme based on comparing the concentration values of adjacent node was then implemented and found to remove the problems of oscillation.

Stress-strain response of hydrate-bearing sands: Numerical study using discrete element method simulations

Gas hydrate is a crystalline solid found within marine and subpermafrost sediments. While the presence of hydrates can have a profound effect on sediment properties, the stress-strain behavior of hydrate-bearing sediments is poorly understood due to inherent limitations in laboratory testing. In this study, we use numerical simulations to improve our understanding of the mechanical behavior of hydrate-bearing sands. The hydrate mass is simulated as either small randomly distributed bonded grains or as "ripened hydrate" forming patchy saturation, whereby sediment clusters with 100% pore-filled hydrate saturation are distributed within a hydrate-free sediment. Simulation results reveal that reduced sand porosity and higher hydrate saturation cause an increase in stiffness, strength, and dilative tendency, and the critical state line shifts toward higher void ratio and higher shear strength. In particular, the critical state friction angle increases in sands with patchy saturation, while the apparent cohesion is affected the most when the hydrate mass is distributed in pores. Sediments with patchy hydrate distribution exhibit a slightly lower strength than sediments with randomly distributed hydrate. Finally, hydrate dissociation under drained conditions leads to volume contraction and/or stress relaxation, and pronounced shear strains can develop if the hydrate-bearing sand is subjected to deviatoric loading during dissociation.

Centrifuge and discrete element modelling of tunnelling effects on pipelines

The paper presents centrifuge test data of the problem of tunnelling effects on buried pipelines and compares them to predictions made using DEM simulations. The paper focuses on the examination of pipeline bending moments, their distribution along the pipe, and their development with tunnel volume loss. Centrifuge results are obtained by PIV analysis and compared to results obtained using the DEM model. The DEM model was built to replicate the centrifuge model as closely as possible and included numerical features formulated specially for this task, such as structural elements to replicate the tunnel and pipeline. Results are extremely encouraging, with deviations between DEM and centrifuge test bending moment results being very small. © 2010 Taylor & Francis Group, London.

Energy stable and momentum conserving hybrid finite element method for the incompressible Navier-Stokes equations

A hybrid method for the incompressible Navier-Stokes equations is presented. The method inherits the attractive stabilizing mechanism of upwinded discontinuous Galerkin methods when momentum advection becomes significant, equal-order interpolations can be used for the velocity and pressure fields, and mass can be conserved locally. Using continuous Lagrange multiplier spaces to enforce flux continuity across cell facets, the number of global degrees of freedom is the same as for a continuous Galerkin method on the same mesh. Different from our earlier investigations on the approach for the Navier-Stokes equations, the pressure field in this work is discontinuous across cell boundaries. It is shown that this leads to very good local mass conservation and, for an appropriate choice of finite element spaces, momentum conservation. Also, a new form of the momentum transport terms for the method is constructed such that global energy stability is guaranteed, even in the absence of a pointwise solenoidal velocity field. Mass conservation, momentum conservation, and global energy stability are proved for the time-continuous case and for a fully discrete scheme. The presented analysis results are supported by a range of numerical simulations. © 2012 Society for Industrial and Applied Mathematics.

Implementation of a PI phase angle controller for finite element analysis of the BDFM

Time-stepping finite element analysis of the BDFM for a specific load condition is shown to be a challenging problem because the excitation required cannot be predetermined and the BDFM is not open loops stable for all operating conditions. A simulation approach using feedback control to set the torque and stabilise the BDFM is presented together with implementation details. The performance of the simulation approach is demonstrated with an example and computed results are compared with measurements.

A subdivision-based implementation of the hierarchical b-spline finite element method

A novel technique is presented to facilitate the implementation of hierarchical b-splines and their interfacing with conventional finite element implementations. The discrete interpretation of the two-scale relation, as common in subdivision schemes, is used to establish algebraic relations between the basis functions and their coefficients on different levels of the hierarchical b-spline basis. The subdivision projection technique introduced allows us first to compute all element matrices and vectors using a fixed number of same-level basis functions. Their subsequent multiplication with subdivision matrices projects them, during the assembly stage, to the correct levels of the hierarchical b-spline basis. The proposed technique is applied to convergence studies of linear and geometrically nonlinear problems in one, two and three space dimensions. © 2012 Elsevier B.V.

Series-parallel six-element synthesis of biquadratic impedances

The object of this paper is to give a complete treatment of the realizability of positive-real biquadratic impedance functions by six-element series-parallel networks comprising resistors, capacitors, and inductors. This question was studied but not fully resolved in the classical electrical circuit literature. Renewed interest in this question arises in the synthesis of passive mechanical impedances. Recent work by the authors has introduced the concept of a regular positive-real functions. It was shown that five-element networks are capable of realizing all regular and some (but not all) nonregular biquadratic positive-real functions. Accordingly, the focus of this paper is on the realizability of nonregular biquadratics. It will be shown that the only six-element series-parallel networks which are capable of realizing nonregular biquadratic impedances are those with three reactive elements or four reactive elements. We identify a set of networks that can realize all the nonregular biquadratic functions for each of the two cases. The realizability conditions for the networks are expressed in terms of a canonical form for biquadratics. The nonregular realizable region for each of the networks is explicitly characterized. © 2004-2012 IEEE.

Finite element modelling of the sismic behaviour of water front structures

Water front structures have suffered significant damage in many of the recent earthquakes. These include gravity type quay walls, vertically composite walls, cantilever retaining walls, anchored bulkheads and similar structures. One of the primary causes for the poor performance of these classes of structures is the liquefaction of the foundation soil and in some instances liquefaction of the backfill soil. The liquefaction of the soil in-front of the quay wall tends to cause large lateral displacements and rotation of the wall. Often such gravity walls are placed on rubble mound deposited onto the sea bed.This paper presents finite element analyses of such a problem in which strength degradation of the foundation soil and the backfill material will be modelled using PZ mark III constitutive model. The performance of the wall in terms of its lateral displacement, vertical settlement and/or the rotation suffered by the wall will be presented. In addition, the contours of the horizontal and vertical effective stresses and the excess pore pressure ratio will be presented at different time instants together with hyrdraulic gradients. Immediately after the earthquake, the hydraulic gradients indicate migration of pore water into the region below the wall, suggesting further softening of the foundation soil below the wall.

3D modeling of high-T c superconductors by finite element software

A three-dimensional (3D) numerical model is proposed to solve the electromagnetic problems involving transport current and background field of a high-T c superconducting (HTS) system. The model is characterized by the E-J power law and H-formulation, and is successfully implemented using finite element software. We first discuss the model in detail, including the mesh methods, boundary conditions and computing time. To validate the 3D model, we calculate the ac loss and trapped field solution for a bulk material and compare the results with the previously verified 2D solutions and an analytical solution. We then apply our model to test some typical problems such as superconducting bulk array and twisted conductors, which cannot be tackled by the 2D models. The new 3D model could be a powerful tool for researchers and engineers to investigate problems with a greater level of complicity.

A finite element model of magnetization of superconducting bulks using a solid-state flux pump

Superconductors have a bright future; they are able to carry very high current densities, switch rapidly in electronic circuits, detect extremely small perturbations in magnetic fields, and sustain very high magnetic fields. Of most interest to large-scale electrical engineering applications are the ability to carry large currents and to provide large magnetic fields. There are many projects that use the first property, and these have concentrated on power generation, transmission, and utilization; however, there are relatively few, which are currently exploiting the ability to sustain high magnetic fields. The main reason for this is that high field wound magnets can and have been made from both BSCCO and YBCO, but currently, their cost is much higher than the alternative provided by low-Tc materials such as Nb3Sn and NbTi. An alternative form of the material is the bulk form, which can be magnetized to high fields. This paper explains the mechanism, which allows superconductors to be magnetized without the need for high field magnets to perform magnetization. A finite-element model is presented, which is based on the E-J current law. Results from this model show how magnetization of the superconductor builds up cycle upon cycle when a traveling magnetic wave is induced above the superconductor. © 2011 IEEE.