FULLY SYMBOLIC GENERATION OF COMPLEX MULTIBODY MODELS*

Abstract

In this paper, a quasistatic finite element model of a spur gear pair is developed. A node-to-target contact formulation is given, where calculations of initial gaps are based upon the actual geometry of the gear flanks rather than upon a contact node and a facet or a line segment. By using a special contact search algorithm, profile modifications and mounting errors are easily incorporated in the analysis. The problem, which also includes friction, is solved by using a nonsmooth Newton method. The static transmission error can be calculated with accuracy with a relatively small number of nodes along the gear flanks. Several examples are given in order to demonstrate the model.     

Dust modelling using a combined CFD and discrete element formulation

The production and dispersal of airborne dust is an important issue in both environmental and industrial contexts. Dust pollution is a major environmental concern, and long exposure in occupational settings has been linked with numerous respiratory health issues. Industrial dust pollution can also present a significant explosion hazard, even in facilities with dust extraction systems. Computational models for dust generation and dispersal have, however, generally been formulated for specific geophysical applications and restricted to static, two‐dimensional, approaches. Here, we present a method for simulating dust production from a dynamic granular bed by using a three‐dimensional coupled discrete element method and Navier–Stokes computational model. Dust production is based on an energy formulation in which micro‐scale dust particles are assumed to overcome cohesion to macro‐scale grains. This model is used over the entire range of energies present within the system, from macro‐scale collisions to aerodynamic entrainment and bombardment of micro‐scale particles. The dust concentration is modelled as a scalar density field, which is advected and diffused through turbulence in the gas flow field. The model is tested against empirical predictions for two test cases, a slug of granular material dropped from a set height and air flow over a granular stockpile. Both give good agreement to the empirical relations, showing that the model can accurately predict the production and subsequent dispersal of dust from a dynamic granular bed. Copyright © 2012 John Wiley & Sons, Ltd.     

Application of DEM modified with enlarged particle model to simulation of bead motion in a bead mill

We applied the discrete element method （DEM） of simulation modified by an enlarged particle model to simulate bead motion in a large bead mill. The stainless-steel bead mill has inner diameter of 102 mm and mill length of 198 mm. The bead diameter and filling ratio were fixed respectively at 0.5 mm and 85%. The agitator rotational speed was changed from 1863 to 3261 rpm. The bead motion was monitored experimentally using a high-speed video camera through a transparent mill body. For the simulation, enlarged particle sizes were set as 3-6 mm in diameter. With the DEM modified by the enlarged particle model, the motion of enlarged particles in a mill was simulated.The velocity data of the simulated enlarged particles were compared with those obtained in the experiment. The simulated velocity of the enlarged particles depends on the virtual frictional coefficient in the DEM model. The optimized value of the virtual frictional coefficient can be determined by considering the accumulated mean value. Results show that the velocity of the enlarged particles simulated increases with an increase in the optimum virtual frictional coefficient, but the simulated velocity agrees well with that determined experimentally by optimizing the virtual frictional coefficient in the simulation. The computing time in the simulation decreases with increased particle size.     

Efficient stochastic FEM for flow in heterogeneous porous media. Part 1: random Gaussian conductivity coefficients

This paper is concerned with the development of efficient iterative methods for solving the linear system of equations arising from stochastic FEMs for single‐phase fluid flow in porous media. It is assumed that the conductivity coefficient varies randomly in space according to some given correlation function and is approximated using a truncated Karhunen–Loève expansion. Distinct discretizations of the deterministic and stochastic spaces are required for implementations of the stochastic FEM. In this paper, the deterministic space is discretized using classical finite elements and the stochastic space using a polynomial chaos expansion. The highly structured linear systems which result from this discretization mean that Krylov subspace iterative solvers are extremely effective. The performance of a range of preconditioned iterative methods is investigated and evaluated in terms of robustness with respect to mesh size and variability of the conductivity coefficient. An efficient symmetric block Gauss–Seidel preconditioner is proposed for problems in which the conductivity coefficient has a large standard deviation.The companion paper, herein, referred to as Part 2, considers the situation in which Gaussian random fields are transformed into lognormal ones by projecting the truncated Karhunen–Loève expansion onto a polynomial chaos basis. This results in a stochastic nonlinear problem because the random fields are represented using polynomial chaos containing terms that are generally nonlinear in the random variables. Copyright © 2013 John Wiley & Sons, Ltd.     

线弹性问题的一个四面体元分析

构造了一个新的locking-free非协调四面体元,研究了单元对三维纯位移弹性问题的一致收敛性,得到了最优的误差估计结果.     

A novel design of membrane mirror with small deformation and imaging performance analysis in infrared system

A method of diminishing the shape error of membrane mirror is proposed in this paper. The inner inflating pressure is considerably decreased by adopting the pre-shaped membrane. Small deformation of the membrane mirror with greatly reduced shape error is sequentially achieved. Primarily a finite element model of the above pre-shaped membrane is built on the basis of its mechanical properties. Then accurate shape data under different pressures can be acquired by iteratively calculating the node displacements of the model. Shape data are applicable to build up deformed reflecting surfaces for the simulative analysis in ZEMAX. Finally, ground-based imaging experiments of 4-bar targets and nature scene are conducted. Experiment results indicate that the MTF of the infrared system can reach to 0.3 at a high spatial resolution of 10l p/mm, and texture details of the nature scene are well-presented. The method can provide theoretical basis and technical support for the applications in lightweight optical components with ultra-large apertures.     

Unital affine semigroups

Affine semigroups are convex sets on which there exists an associative binary operation which is affine separately in either variable. They were introduced by Cohen and Collins in 1959. We look at examples of affine semigroups which are of interest to matrix and operator theory and we prove some new results on the extreme points and the absorbing elements of certain types of affine semigroups. Most notably we improve a result of Wendel that every invertible element in a compact affine semigroup is extreme by extending this result to linearly bounded affine semigroups.     

Analysis of the geometrical dependence of auxetic behavior in reentrant structures by finite elements

Materials with a negative Poisson's ratio(PR)are called auxetics;they are characterized by expansion/contraction when tensioned/compressed.Given this counterintuitive behavior,they present very particular characteristics and mechanical behavior.Geometrical models have been developed to justify and artificiall reproduce such materials' auxetic behavior.The focus of this study is the exploration of a reentrant model by analyzing the variation in the PR of reentrant structures as a function of geometrical and base material parameters.It is shown that,even in the presence of protruding ribs,there may not be auxetic behavior,and this depends on the geometry of each reentrant structure.Values determined for these parameters can be helpful as approximate reference data in the design and fabrication of auxetic lattices using reentrant geometries.     

Numerical analysis of enhanced mixing in a Gallay tote blender

The mixing performance of a multi-bladed baffle inserted into a traditional Gallay tote blender is explored by graphic processing unit-based discrete element method software. The mixing patterns and rates are investigated for a binary mixture, represented by two different colors, under several loading profiles. The baffle effectively enhances the convective mixing both in the axial and radial directions, because of the disturbance it causes to the initial flowing layer and solid-body zone, compared with a blender without a baffle. The axial mixing rate is affected by the gap between the baffle and the wall on the left and right sides, and an optimal blade length corresponds to the maximum mixing rate. However, the radial mixing rate increases with the blade length almost monotonically.