Time domain modeling of self-excited aerodynamic forces for cable-supported bridges: A comparative study

Prediction of the wind-induced dynamic response of suspension bridges, emphasizing self-excited forces, is discussed in this paper. The self-excited forces have been modeled by two commonly applied unsteady models and an unsteady model introduced and explained in this article. A novel frequency-independent approximation of the self-excited forces, which for the suspension bridge considered provides results as accurate as those from the unsteady models, is also presented. An integration method that may reduce the number of time steps necessary to avoid amplitude and phase distortion of the self-excited forces has been introduced and applied successfully in a comprehensive case study.     

Beam and plate stability by boundary elements

The direct boundary element method is used for the linear elastic stability analysis of Bernoulli-Euler beams and Kirchhoff thin plates. The formulation is based on the reciprocal work theorem of Betti and utilizes either fundamental solutions which incorporate the effect of axial and in-plane forces on bending, or fundamental solutions which correspond to pure flexure. In the former case. only a boundary discretization of the structure is required, while in the latter case discretization of the boundary as well as of the interior is necessary. However, the fundamental solutions in the latter case are less complicated than the ones in the former case. Numerical examples are subsequently presented to illustrate the methodology. The basic conclusion is that the simpler fundamental solutions are adequate and, by virtue of being more general, greatly expand the versatility of the boundary element method.     

Finite element formulation for dynamics of planar flexible multi-beam system

In some previous geometric nonlinear finite element formulations, due to the use of axial displacement, the contribution of all the elements lying between the reference node of zero axial displacement and the element to the foreshortening effect should be taken into account. In this paper, a finite element formulation is proposed based on geometric nonlinear elastic theory and finite element technique. The coupling deformation terms of an arbitrary point only relate to the nodal coordinates of the element at which the point is located. Based on Hamilton principle, dynamic equations of elastic beams undergoing large overall motions are derived. To investigate the effect of coupling deformation terms on system dynamic characters and reduce the dynamic equations, a complete dynamic model and three reduced models of hub-beam are prospected. When the Cartesian deformation coordinates are adopted, the results indicate that the terms related to the coupling deformation in the inertia forces of dynamic equations have small effect on system dynamic behavior and may be neglected, whereas the terms related to coupling deformation in the elastic forces are important for system dynamic behavior and should be considered in dynamic equation. Numerical examples of the rotating beam and flexible beam system are carried out to demonstrate the accuracy and validity of this dynamic model. Furthermore, it is shown that a small number of finite elements are needed to obtain a stable solution using the present coupling finite element formulation.     

Buffet suppression in long-span suspension bridges

We study the aerodynamic control of long-span suspension bridges and seek to raise the critical flutter wind speeds, while simultaneously suppressing buffeting. The control system design study is based on a simple flexible bridge section model that interacts with a constant-velocity air stream. A streamlined bridge deck is assumed and non-steady thin aerofoil theory is used to describe the interactions between the bridge deck and the air stream. Classical turbulence models, first developed in the aircraft industry, are used to model the buffet forces acting on the deck. While a wide variety of control systems is possible, we focus on a compensation scheme that can be implemented using passive mechanical components such as springs, dampers and a rack and pinion mechanism. A single-loop control system is investigated that controls a trailing-edge flap by sensing movements of the bridge deck; several such mechanisms are contemplated. The first finding is that the critical wind speed for flutter can be greatly increased, with good robustness characteristics, through passive feedback control. It is also possible simultaneously to suppress flutter using the same passive mechanical controller by solving a passive mixed H₂/H_∞ control problem. The effect of flexible controller mounting arrangements are considered briefly.     

Physically based real-time interactive assembly simulation of cable harness

In this paper, we designed and developed an interactive assembly simulation system of cable harness. First, we establish a real-time physical model of cable harness based on an extension of the mass–spring model. We use various kinds of springs to describe the different properties of the cable harness: linear springs for stretching, bending springs for bending, and torsion springs for geometrical torsion and material twisting. The constraints of connectors and clips on cable harness are both considered. We also associate the elastic coefficients of various springs with the material parameters of the cable. Moreover, we use spherical bounding volume hierarchy and triangular facets for collision detection of cable harness during the assembly simulation. By applying contact forces to both ends of the cable links that collide with the surrounding environment, we obtain the real-time contact response of cable harness. Finally, we apply the proposed model to a cable assembly task. The results show that the proposed model successfully expressed the deformation of the cable harness and the interactive manipulation is computationally efficient.     

A comparison of equivalence and finite element methods

The displacement field of a homogeneous, isotropic elastic disk that is free from body forces is analyzed by a method of equivalence and a method of finite elements. It is shown that both methods have the degree of precision 3, and that they furnish displacement fields that would occur in the disk if this was subjected to certain body forces. The corrective body forces required by the two methods are compared and conditions are discussed under which they equal each other. It is found that no general statement can be made regarding the superiority of one or the other method.     

An automatic incrementation technique for contact problems with friction

A numerical method for analysis of elastostatic contact problems with friction has been developed. This class of problems are load history dependent because of the irreversible nature of frictional forces. An automatic incrementation technique of the applied load has been developed and implemented in the algorithm. The method is a direct method based on an iterative procedure applied to a set of linear equations established with the finite element method. The size of the applied load increments, automatically chosen by the algorithm, is in general influenced both by the nature of the problem and of the discretization of the bodies involved. The frictional forces occurring in the slip zone of the contact area are treated as known tangential forces calculated from the normal forces in the previous iteration. This piecewise linear treatment of the frictional contact problem requires an innermost iteration loop over the applied tangential force.The tangential force must coincide with the coefficient of friction times the normal force obtained in the last iteration, otherwise a new tangential force has to be calculated and the system of equations must be solved for a new right hand side vector. The automatic incrementation technique is based on the fact that each iteration is a linear problem. A tentative load increment is used in the solution of a certain iteration. A linear scaling of this solution is performed afterwards. A load scale factor is calculated in each contact node pair where a change of contact condition will occur. The change in contact status corresponding to the node pair with the smallest load scale factor is the only change which is accomplished in a certain iteration. The uniqueness of this kind of contact problem with friction has not been mathematically proven for a general case.The method has been applied to a case of loading and unloading of an elastic halfspace by a rigid cylindrical stamp and compared to solutions by Spence and Turner.     

A node-centric indirect boundary element method: three-dimensional displacement discontinuities

An indirect boundary element formulation based on unknown physical values, defined only at the nodes (vertices) of a boundary discretization of a linear elastic continuum, is introduced. As an adaptation of this general framework, a linear displacement discontinuity density distribution using a flat triangular boundary discretization is considered. A unified element integration methodology based on the continuation principle is introduced to handle regular as well as near-singular and singular integrals. The boundary functions that form the basis of the integration methodology are derived and tabulated in the appendix for linear displacement discontinuity densities. The integration of the boundary functions is performed numerically using an adaptive algorithm which ensures a specified numerical accuracy. The applications include verification examples which have closed-form analytical solutions as well as practical problems arising in rock engineering. The node-centric displacement discontinuity method is shown to be numerically efficient and robust for such problems.     

Analytical approach to sensitivity analysis of flutter speed in bridges considering variable deck mass

Design techniques based upon sensitivity analysis are not usual in the current design of suspension bridges. However, sensitivity analysis has been proved to be a useful tool in the car and aircraft industries. Evaluation of sensitivity analysis is a mandatory step in the way towards an efficient automated optimum design process which would represent a huge jump in the conception of long span bridges. Some of the authors of this paper were pioneers in establishing a methodology for obtaining the sensitivity analysis of flutter speed in suspension bridges a few years ago. That approach was completely analytical and required the evaluation of many matrices related to the phenomenon. In those works the total mass of the deck was considered as constant and such a circumstance supposed a limitation of the method. In the present paper the complete analytical formulation of the sensitivity analysis problem in bridges considering variable deck mass is presented, as well as its application to the design problem of the Great Belt Bridge. Analytical evaluation of sensitivities is a time demanding task, and in order to avoid excessive computation times, distributed computing strategies have been implemented which can be considered as an additional benefit of this approach. For the application example, it has been found that deck cross-section area and torsional inertia are the structural properties with the greatest influence on the flutter performance.     

Identification of a human walking force model based on dynamic monitoring data from pedestrian bridges

A general investigation procedure for the vibration serviceability of pedestrian bridges is accomplished by comparing the dynamic response of structures to vibration effects on serviceability limiting states. The purposes of this study were to investigate the dynamic response characteristics of pedestrian bridges and to develop a human walking force model to assist in the development and design of pedestrian bridges. Human walking force parameters were identified by a genetic algorithm (GA) from experimental forced vibration data. The results of the dynamic response obtained by the GA were in agreement with the experimental results. Therefore, the GA system was useful in the identification of pedestrian walking forces, and from the experimental and calculated results, it is considered that the walking force model identified by the GA is substantially accurate.     

A computer-oriented method for reducing linearized multibody system equations by incorporating constraints

Consider a spatial multibody system with rigid and elastic bodies. The bodies are linked by rigid interconnections (e.g. revolute joints) causing constraints, as well as by flexible interconnections (e.g. springs) causing applied forces. Small motions of the system with respect to a given nominal configuration can be described by linearized dynamic equations and kinematic constraint equations. We present a computer-oriented procedure which allows to develop a minimum number of these equations. There are three problems. First: algorithmic selection of position coordinates; second: condensation of the dynamic equations; third: evaluation of the constraint forces. To demonstrate the procedure, a closed loop multibody system is used as an example.     

A finite element scheme with a high order absorbing boundary condition for elastodynamics

A high-order absorbing boundary condition (ABC) is devised on an artificial boundary for time-dependent elastic waves in unbounded domains. The configuration considered is that of a two-dimensional elastic waveguide. In the exterior domain, the unbounded elastic medium is assumed to be isotropic and homogeneous. The proposed ABC is an extension of the Hagstrom–Warburton ABC which was originally designed for acoustic waves, and is applied directly to the displacement field. The order of the ABC determines its accuracy and can be chosen to be arbitrarily high. The initial boundary value problem including this ABC is written in second-order form, which is convenient for geophysical finite element (FE) analysis. A special variational formulation is constructed which incorporates the ABC. A standard FE discretization is used in space, and a Newmark-type scheme is used for time-stepping. A long-time instability is observed, but simple means are shown to dramatically postpone its onset so as to make it harmless during the simulation time of interest. Numerical experiments demonstrate the performance of the scheme.     

A splitting integration scheme for the SPH simulation of concentrated particle suspensions

Simulating nearly contacting solid particles in suspension is a challenging task due to the diverging behavior of short-range lubrication forces, which pose a serious time-step limitation for explicit integration schemes. This general difficulty limits severely the total duration of simulations of concentrated suspensions. Inspired by the ideas developed in [S. Litvinov, M. Ellero, X.Y. Hu, N.A. Adams, J. Comput. Phys. 229 (2010) 5457–5464] for the simulation of highly dissipative fluids, we propose in this work a splitting integration scheme for the direct simulation of solid particles suspended in a Newtonian liquid. The scheme separates the contributions of different forces acting on the solid particles. In particular, intermediate- and long-range multi-body hydrodynamic forces, which are computed from the discretization of the Navier–Stokes equations using the smoothed particle hydrodynamics (SPH) method, are taken into account using an explicit integration; for short-range lubrication forces, velocities of pairwise interacting solid particles are updated implicitly by sweeping over all the neighboring pairs iteratively, until convergence in the solution is obtained. By using the splitting integration, simulations can be run stably and efficiently up to very large solid particle concentrations. Moreover, the proposed scheme is not limited to the SPH method presented here, but can be easily applied to other simulation techniques employed for particulate suspensions.     

一类齐次离散双线性系统可控性分析

在系统分析中,可控性是系统的一个重要特性.在工程实际操作中,往往需要对一个连续系统进行离散化处理,人们希望系统在离散化后能保留原系统的重要系统特征,比如可控性.对于线性系统,我们有成熟的判断方法.然而,对于非线性系统则无统一的判别方法.Elliott在2005年给出了一个二阶双线性系统经过离散化后,可控性发生变化的例子.它表明一个系统在离散化前后,它的可控性可能会发生改变.本文旨在给出一类二阶离散化双线性系统可控性充分条件,并和已有结果作比较,表明本文结果更具有一般性.另外,本文对于3阶及以上的这类系统可控性做出了不可控的判断.     

A connection rule for alpha-carbon coarse-grained elastic network models using chemical bond information

A sparser but more efficient connection rule (called a bond-cutoff method) for a simplified alpha-carbon coarse-grained elastic network model is presented. One of conventional connection rules for elastic network models is the distance-cutoff method, where virtual springs connect an alpha-carbon with all neighbor alpha-carbons within predefined distance-cutoff value. However, though the maximum interaction distance between alpha-carbons is reported as 7 angstroms, this cutoff value can make the elastic network unstable in many cases of protein structures. Thus, a larger cutoff value (>11 angstroms) is often used to establish a stable elastic network model in previous researches. To overcome this problem, a connection rule for backbone model is proposed, which satisfies the minimum condition to stabilize an elastic network. Based on the backbone connections, each type of chemical interactions is considered and added to the elastic network model: disulfide bonds, hydrogen bonds, and salt-bridges. In addition, the van der Waals forces between alpha-carbons are modeled by using the distance-cutoff method. With the proposed connection rule, one can make an elastic network model with less than 7 angstroms distance cutoff, which can reveal protein flexibility more sharply. Moreover, the normal modes from the new elastic network model can reflect conformational changes of a given protein better than ones by the distance-cutoff method. This method can save the computational cost when calculating normal modes of a given protein structure, because it can reduce the total number of connections. As a validation, six example proteins are tested. Computational times and the overlap values between the conformational change and infinitesimal motion calculated by normal mode analysis are presented. Those animations are also available at UMass Morph Server (http://biomechanics.ecs.umass.edu/umms.html).     

板弹簧用作称重弹性体时的迟滞与补偿

采用车辆板弹簧作为称重传感器的弹性体检测车辆载荷时,板弹簧的迟滞严重影响了载荷检测的精度。以一种卡车的后车桥板弹簧为例,介绍采用单片机对车辆板弹簧迟滞现象进行补偿的方法。这种方法简单可行,试验结果表明:补偿后,迟滞对称重结果的影响可减小为原来的20%,提高了这种称重装置的检测精度和实用性。     

A parametric subdomain discretization for the analysis of the multiaxial response of reinforced concrete sections

The paper presents an improved sectional discretization method for evaluating the response of reinforced concrete sections. The section is subdivided into parametric subdomains that allow the modelization of any complex geometry while taking advantage of the Gauss quadrature techniques. In particular, curved boundaries are dealt with two nested parametric transformations, reducing the modeling approximation. It is shown how the so-called fiber approach is simply a particular case of the present more general method. Many benchmarks are presented in order to assess the accuracy of the results. The influence of the discretization into subdomains and of the quadrature rules, chosen for integration, is discussed. The numerical tests highlight also the effects of spurious stress distributions in the tensile concrete zone, due the interpolation functions adopted for the Gauss integration. It is shown how balancing the number of subdomains and the number of sampling points such spurious effects vanish. The method shows to be accurate, very flexible in the discretization process and robust in analyzing any sectional state. Moreover, it converges faster than the fiber method, reducing the computational demand. All these properties are of great importance when the computations are iteratively repeated, as for the case of the sectional analysis within a computational procedure for a R.C. frame analysis.     

Comparison of models for finite plasticity: A numerical study

We introduce a general framework for the numerical approximation of finite multiplicative plasticity. The method is based on a fully implicit discretization in time which results in an iteratively evaluated stress response; the arising nonlinear problem is then solved by a Newton method where the linear subproblems are solved with a parallel multigrid method. The procedure is applied to models with different elastic free energy functionals and a plastic flow rule of von Mises type. In addition these models are compared to a recently derived frame indifferent approximation of finite multiplicative plasticity valid for small elastic strains which leads to linear balance equations. Rate independent and rate dependent realizations of the former models are considered. We demonstrate by various 3D simulations that the choice of the elastic free energy is not essential (for material parameters representative for metals) and that the new model gives the same response quantitatively and qualitatively as the standard models.     

On Clamping Planning in Workpiece-Fixture Systems

Deformations of contacts between the workpiece and locators/clamps resulting from large contact forces cause overall workpiece displacement, and affect the localization accuracy of the workpiece. An important characteristic of a workpiece-fixture system is that locators are passive elements and can only react to clamping forces and external loads, whereas clamps are active elements and apply a predetermined normal load to the surface of workpiece to prevent it from losing contact with the locators. Clamping forces play an important role in determining the final workpiece quality. This paper presents a general method for determining the optimal clamping forces including their magnitudes and positions. First, we derive a set of “compatibility” equations that describe the relationship between the displacement of the workpiece and the deformations at contacts. Further, we develop a locally elastic contact model to characterize the nonlinear coupling between the contact force and elastic deformation at the individual contact. We define the minimum norm of the elastic deformations at contacts as the objective function, then formulate the problem of determining the optimal clamping forces as a constrained nonlinear programming problem which guarantees that the fixturing of the workpiece is force closure. Using the exterior penalty function method, we transform the constrained nonlinear programming into an unconstrained nonlinear programming which is, in fact, the nonlinear least square. Consequently, the optimal magnitudes and positions of clamping forces are obtained by using the Levenberg–Marquardt method which is globally convergent. The proposed planning method of optimal clamping forces, which may also have an application to other passive, indeterminate problems such as power grasps in robotics, is illustrated with numerical example.