A Lagrange–Eulerian formulation of an axially moving beam based on the absolute nodal coordinate formulation

In the scope of this paper, a finite-element formulation for an axially moving beam is presented. The beam element is based on the absolute nodal coordinate formulation, where position and slope vectors are used as degrees of freedom instead of rotational parameters. The equations of motion for an axially moving beam are derived from generalized Lagrange equations in a Lagrange–Eulerian sense. This procedure yields equations which can be implemented as a straightforward augmentation to the standard equations of motion for a Bernoulli–Euler beam. Moreover, a contact model for frictional contact between an axially moving strip and rotating rolls is presented. To show the efficiency of the method, simulations of a belt drive are presented.     

A comparison of finite elements for nonlinear beams: the absolute nodal coordinate and geometrically exact formulations

Two of the most popular finite element formulations for solving nonlinear beams are the absolute nodal coordinate and the geometrically exact approaches. Both can be applied to problems with very large deformations and strains, but they differ substantially at the continuous and the discrete levels. In addition, implementation and run-time computational costs also vary significantly. In the current work, we summarize the main features of the two formulations, highlighting their differences and similarities, and perform numerical benchmarks to assess their accuracy and robustness. The article concludes with recommendations for the choice of one formulation over the other.     

Clamped end conditions and cross section deformation in the finite element absolute nodal coordinate formulation

In the finite element absolute nodal coordinate formulation (ANCF), the elimination of the relative translations and rotations at a point does not necessarily define a fully clamped joint, particularly in the case of fully parameterized ANCF finite elements that allow for the deformation of the cross section. In this investigation, the formulations and results of two different sets of clamped end conditions that define two different joints are compared. The first joint, called the partially clamped joint, eliminates only the translations and rotations at a point on the cross section. The second joint, called the fully clamped joint, eliminates all the translation, rotation and deformation degrees of freedom at a point on the cross section. The kinematic equations that define the partially and fully clamped joints are developed, and the dynamic equations used in the comparative numerical study presented in this paper are shown. As discussed in this investigation, the fully clamped joint does not allow for the deformation of the cross section at the joint node since the gradient vectors remain orthogonal unit vectors. The partially clamped joint, on the other hand, allows for the deformation of the cross section. Nanson’s formula is used as a measure of the deformation of the cross section in the case of the partially clamped joint. A very flexible pendulum that has a rigid body attached to its free end is used to compare the results of the partially and fully clamped joints. The numerical results obtained using this very flexible pendulum example show that, while the type of joint (partially or fully clamped) does not significantly affect the gross reference motion of the system, there are fundamental differences between the two joints since the partially clamped joint allows for the cross section deformations at the joint node.     

A formal procedure and invariants of a transition from conventional finite elements to the absolute nodal coordinate formulation

In this paper, finite elements based on the absolute nodal coordinate formulation (ANCF) are studied. The formulation has been developed by various authors for the dynamical simulation of large-displacement and large-rotation problems in flexible multibody dynamics. This study introduces a procedure to track the general geometrical properties of ANCF elements back to their prototypes in the conventional finite-element method (FEM), which deals with small-displacement problems. In this study, it is shown that each known ANCF element can be derived from a conventional FEM using a universal transform. Moreover, some important static and dynamic properties of the elements in small-displacement problems are automatically preserved. In the past, the authors of each newly proposed ANCF element have made unnecessary efforts to show the consistency of the above mentioned properties.     

Simulation of a viscoelastic flexible multibody system using absolute nodal coordinate and fractional derivative methods

This paper employs a new finite element formulation for dynamics analysis of a viscoelastic flexible multibody system. The viscoelastic constitutive equation used to describe the behavior of the system is a three-parameter fractional derivative model. Based on continuum mechanics, the three-parameter fractional derivative model is modified and the proposed new fractional derivative model can reduce to the widely used elastic constitutive model, which meets the continuum mechanics law strictly for pure elastic materials. The system equations of motion are derived based on the absolute nodal coordinate formulation (ANCF) and the principle of virtual work, which can relax the small deformation assumption in the traditional finite element implementation. In order to implement the viscoelastic model into the absolute nodal coordinate, the Grünwald definition of the fractional derivative is employed. Based on a comparison of the HHT-I3 method and the Newmark method, the HHT-I3 method is used to solve the equations of motion. Another particularity of the proposed method based on the ANCF method lies in the storage of displacement history only during the integration process, reducing the numerical computation considerably. Numerical examples are presented in order to analyze the effects of the truncation number of the Grünwald series (fading memory phenomena) and the value of several fractional model parameters and solution convergence aspects. An erratum to this article can be found at     

Three-dimensional beam propagation method based on the variable transformed Galerkin''''s method

A novel three-dimensional beam propagation method (BPM) based on the variable transformed Galerkin's method is introduced for simulating optical field propagation in three-dimensional dielectric structures. The infinite Cartesian x-y plane is mapped into a unit square by a tangent-type function transformation. Consequently, the infinite region problem is converted into the finite region problem. Thus, the boundary truncation is eliminated and the calculation accuracy is promoted. The three-dimensional BPM basic equation is reduced to a set of first-order ordinary differential equations through sinusoidal basis function, which fits arbitrary cladding optical waveguide, then direct solution of the resulting equations by means of the Runge-Kutta method. In addition, the calculation is efficient due to the small matrix derived from the present technique. Both z-invariant and z-variant examples are considered to test both the accuracy and utility of this approach.     

A finite element pressure gradient stabilization¶for the Stokes equations based on local projections

We present a variant of the classical weighted least-squares stabilization for the Stokes equations. Compared to the original formulation, the new method has improved accuracy properties, especially near boundaries. Furthermore, no modification of the right-hand side is needed, and implementation is simplified, especially for generalizations to more complicated equations. The approach is based on local projections of the residual terms which are used in order to achieve consistency of the method, avoiding local evaluation of the strong form of the differential operator. We prove stability and give a priori and a posteriori error estimates. We show convergence of an iterative method which uses a simplified stabilized discretization as preconditioner. Numerical experiments indicate that the approach presented is at least as accurate as the original method, but offers some algorithmic advantages. The ideas presented here also apply to the Navier–Stokes equations. This is the topic of forthcoming work. Received: March 2000 / Accepted: October 2000     

An analysis of the time integration algorithms for the finite element solutions of incompressible Navier–Stokes equations based on a stabilised formulation

This work is concerned with the analysis of time integration procedures for the stabilised finite element formulation of unsteady incompressible fluid flows governed by the Navier–Stokes equations. The stabilisation technique is combined with several different implicit time integration procedures including both finite difference and finite element schemes. Particular attention is given to the generalised-α method and the linear discontinuous in time finite element scheme. The time integration schemes are first applied to two model problems, represented by a first order differential equation in time and the one dimensional advection–diffusion equation, and subjected to a detailed mathematical analysis based on the Fourier series expansion. In order to establish the accuracy and efficiency of the time integration schemes for the Navier–Stokes equations, a detailed computational study is performed of two standard numerical examples: unsteady flow around a cylinder and flow across a backward facing step. It is concluded that the semi-discrete generalised-α method provides a viable alternative to the more sophisticated and expensive space–time methods for simulations of unsteady flows of incompressible fluids governed by the Navier–Stokes equations.     

Recursive formulations for multibody systems with frictional joints based on the interaction between bodies

In practice, the clearances of joints in a great number of mechanical systems are well under control. In these cases, some of the existing methods become unpractical because of the little differences in the order of magnitude between relative movements and computational errors. Assuming that the effects of impacts are negligible, we proved that both locations and forces of contacts in joints can be fully determined by parts of joint reaction forces. Based on this fact, a method particularly suited for multibody systems possessing frictional joints with tiny clearances is presented. In order to improve the efficiency of computation, recursive formulations are proposed based on the interactions between bodies. The proposed recursive formulations can improve the computation of joint reaction forces. With the methodology presented in this paper, not only the motion of bodies in a multibody system but also the details about the contacts in joints, such as forces of contacts and locations of contact points, can be obtained. Even with the assumption of impact free, the instants of possible impacts can be detected without relying upon any ambiguous parameters, as indicated by numerical examples in this paper.     

A study on wear evaluation of railway wheels based on multibody dynamics and wear computation

The wear evolution of railway wheels is a very important issue in railway engineering. In the past, the reprofiling intervals of railway vehicle steel wheels have been scheduled according to designers’ experience. Today, more reliable and accurate tools in predicting wheel wear evolution and wheelset lifetime can be used in order to achieve economical and safety benefits. In this work, a computational tool that is able to predict the evolution of the wheel profiles for a given railway system, as a function of the distance run, is presented. The strategy adopted consists of using a commercial multibody software to study the railway dynamic problem and a purpose-built code for managing its pre- and post-processing data in order to compute the wear. The tool is applied here to realistic operation scenarios in order to assess the effect of some service conditions on the wheel wear progression.     

Extracting exact answers from large-scale corpus based on hybrid strategy

This paper provides a novel and efficient method for extracting exact textual answers from the returned documents that are retrieved by traditional IR system in large-scale collection of texts. The main intended contribution of this paper is to propose System Similarity Model （SSM）, which can be considered as an extension of vector space model （VSM） to rank passages, It presents a method of formalized answer extraction based on pattern learning and applies binary logistic regression model （LRM）, which seldom be used in IE to extract special information from candidate data sets. The parameters estimated for the data gathers with serious problem of data sparse, therefore we take stratified sampling method, and improve traditional logistic regression model parameters estimated methods. The series of experimental results show that the overall performance of our system is good and our approach is effective. Our system, lnsun05QAl, which participated in QA track of TREC 2005 obtained excellent results.     

Fast exact feature based data correspondence search with an efficient bit-parallel MCP solver

The problem of finding the optimal correspondence between two sets of geometric entities or features is known to be NP-hard in the worst case. This problem appears in many real scenarios such as fingerprint comparisons, image matching and global localization of mobile robots. The inherent complexity of the problem can be avoided by suboptimal solutions, but these could fail with high noise or corrupted data. The correspondence problem has an interesting equivalent formulation in finding a maximum clique in an association graph. We have developed a novel algorithm to solve the correspondence problem between two sets of features based on an efficient solution to the Maximum Clique Problem using bit parallelism. It outperforms an equivalent non bit parallel algorithm in a number of experiments with simulated and real data from two different correspondence problems. This article validates for the first time, to the best of our knowledge, that bit parallel optimization techniques can greatly reduce computational cost, thus making feasible the use of an exact solution in real correspondence search problems despite their inherent NP computational complexity.     

A Prolate-Element Method for Nonlinear PDEs on the Sphere

A p-type spectral-element method using prolate spheroidal wave functions (PSWFs) as basis functions, termed as the prolate-element method, is developed for solving partial differential equations (PDEs) on the sphere. The gridding on the sphere is based on a projection of the prolate-Gauss-Lobatto points by using the cube-sphere transform, which is free of singularity and leads to quasi-uniform grids. Various numerical results demonstrate that the proposed prolate-element method enjoys some remarkable advantages over the polynomial-based element method: (i) it can significantly relax the time step size constraint of an explicit time-marching scheme, and (ii) it can increase the accuracy and enhance the resolution.     

A C° continuous linear beam/bilinear plate flexure element

Design of a simple C°-continuous beam/plate flexure element based on a shear-deformable theory is attempted. Emphasis is placed on development of a low order linear/bilinear element. However, past experience shows that such elements become very “stiff” especially when thickness is reduced (conforming to Kirchhoff mode). This phenomenon is called “locking.” Attempts have been made in the last several years by a few investigators to overcome this problem.The locking problem is resolved here through a new approach. The total strain energy is split into bending and shear energies and an antiparameter in the shear energy term is introduced to avoid locking. By numerical experimentation on beam and plate problems it is shown that the present approach gives good results in the thin limit. It is also shown that the additional/spurious zero energy modes do not arise here because reduced/selective integration is avoided.     

The χ-schemes: a new consistent high-resolution formulation based on the normalized variable methodology

This paper deals with the formulation and testing of a new class of consistent high-resolution schemes, denoted as the χ-schemes. These schemes, combine consistency, accuracy and boundedness across systems of equations and are suitable for use in the simulation of multi-phase and multi-component flows. The consistency feature refers to the capability of these schemes to implicitly satisfy the additional algebraic constraint representing a global conservation relation governing certain sets of equations (e.g., species mass fraction, volume fraction, etc.). Four χ-schemes are implemented within an unstructured grid finite-volume framework, tested by solving four multi-component pure-advection test problems, and shown to be consistent.     

Biologically-inspired robot spatial cognition based on rat neurophysiological studies

This paper presents a robot architecture with spatial cognition and navigation capabilities that captures some properties of the rat brain structures involved in learning and memory. This architecture relies on the integration of kinesthetic and visual information derived from artificial landmarks, as well as on Hebbian learning, to build a holistic topological-metric spatial representation during exploration, and employs reinforcement learning by means of an Actor-Critic architecture to enable learning and unlearning of goal locations. From a robotics perspective, this work can be placed in the gap between mapping and map exploitation currently existent in the SLAM literature. The exploitation of the cognitive map allows the robot to recognize places already visited and to find a target from any given departure location, thus enabling goal-directed navigation. From a biological perspective, this study aims at initiating a contribution to experimental neuroscience by providing the system as a tool to test with robots hypotheses concerned with the underlying mechanisms of rats’ spatial cognition. Results from different experiments with a mobile AIBO robot inspired on classical spatial tasks with rats are described, and a comparative analysis is provided in reference to the reversal task devised by O’Keefe in 1983.     

Geometric nonlinear effects on the planar dynamics of a pivoted flexible beam encountering a point-surface impact

Flexible-body modeling with geometric nonlinearities remains a hot topic of research by applications in multibody system dynamics undergoing large overall motions. However, the geometric nonlinear effects on the impact dynamics of flexible multibody systems have attracted significantly less attention. In this paper, a point-surface impact problem between a rigid ball and a pivoted flexible beam is investigated. The Hertzian contact law is used to describe the impact process, and the dynamic equations are formulated in the floating frame of reference using the assumed mode method. The two important geometric nonlinear effects of the flexible beam are taken into account, i.e., the longitudinal foreshortening effect due to the transverse deformation, and the stress stiffness effect due to the axial force. The simulation results show that good consistency can be obtained with the nonlinear finite element program ABAQUS/Explicit if proper geometric nonlinearities are included in the floating frame formulation. Specifically, only the foreshortening effect should be considered in a pure transverse impact for efficiency, while the stress stiffness effect should be further considered in an oblique case with much more computational effort. It also implies that the geometric nonlinear effects should be considered properly in the impact dynamic analysis of more general flexible multibody systems.     

AILU preconditioning for the finite element formulation of the incompressible Navier–Stokes equations

In this paper, the effect of a variable reordering method on the performance of “adapted incomplete LU (AILU)” preconditioners applied to the P2P1 mixed finite element discretization of the three-dimensional unsteady incompressible Navier–Stokes equations has been studied through numerical experiments, where eigenvalue distribution and convergence histories are examined. It has been revealed that the performance of an AILU preconditioner is improved by adopting a variable reordering method which minimizes the bandwidth of a globally assembled saddle-point type matrix. Furthermore, variants of the existing AILU(1) preconditioner have been suggested and tested for some three-dimensional flow problems. It is observed that the AILU(2) outperforms the existing AILU(1) with a little extra computing time and memory.