Minimal formulation of joint motion for biomechanisms

Biomechanical systems share many properties with mechanically engineered systems, and researchers have successfully employed mechanical engineering simulation software to investigate the mechanical behavior of diverse biological mechanisms, ranging from biomolecules to human joints. Unlike their man-made counterparts, however, biomechanisms rarely exhibit the simple, uncoupled, pure-axial motion that is engineered into mechanical joints such as sliders, pins, and ball-and-socket joints. Current mechanical modeling software based on internal-coordinate multibody dynamics can formulate engineered joints directly in minimal coordinates, but requires additional coordinates restricted by constraints to model more complex motions. This approach can be inefficient, inaccurate, and difficult for biomechanists to customize. Since complex motion is the rule rather than the exception in biomechanisms, the benefits of minimal coordinate modeling are not fully realized in biomedical research. Here we introduce a practical implementation for empirically-defined internal-coordinate joints, which we call "mobilizers." A mobilizer encapsulates the observations, measurement frame, and modeling requirements into a hinge specification of the permissible-motion manifold for a minimal set of internal coordinates. Mobilizers support nonlinear mappings that are mathematically equivalent to constraint manifolds but have the advantages of fewer coordinates, no constraints, and exact representation of the biomechanical motion-space-the benefits long enjoyed for internal-coordinate models of mechanical joints. Hinge matrices within the mobilizer are easily specified by user-supplied functions, and provide a direct means of mapping permissible motion derived from empirical data. We present computational results showing substantial performance and accuracy gains for mobilizers versus equivalent joints implemented with constraints. Examples of mobilizers for joints from human biomechanics and molecular dynamics are given. All methods and examples were implemented in Simbody?-an open source multibody-dynamics solver available at https://Simtk.org.     

Minimal plate design for singular regions

A method for solving the non-linear problem of minimal volume design of sandwich plates obeying the Mises criterion is presented for the class of plates for which the orientation of the principal directions depends solely upon the position of the stress point on the yield surface. The principal bending coordinates, the yield moment, and the deflection rate at plastic collapse for the optimum design are determined in their most general form. An example is presented for a plate supported over two edges but free on its remaining edge.     

Minimal formulation of joint motion for biomechanisms

Biomechanical systems share many properties with mechanically engineered systems, and researchers have successfully employed mechanical engineering simulation software to investigate the mechanical behavior of diverse biological mechanisms, ranging from biomolecules to human joints. Unlike their man-made counterparts, however, biomechanisms rarely exhibit the simple, uncoupled, pure-axial motion that is engineered into mechanical joints such as sliders, pins, and ball-and-socket joints. Current mechanical modeling software based on internal-coordinate multibody dynamics can formulate engineered joints directly in minimal coordinates, but requires additional coordinates restricted by constraints to model more complex motions. This approach can be inefficient, inaccurate, and difficult for biomechanists to customize. Since complex motion is the rule rather than the exception in biomechanisms, the benefits of minimal coordinate modeling are not fully realized in biomedical research. Here we introduce a practical implementation for empirically-defined internal-coordinate joints, which we call “mobilizers.” A mobilizer encapsulates the observations, measurement frame, and modeling requirements into a hinge specification of the permissible-motion manifold for a minimal set of internal coordinates. Mobilizers support nonlinear mappings that are mathematically equivalent to constraint manifolds but have the advantages of fewer coordinates, no constraints, and exact representation of the biomechanical motion-space—the benefits long enjoyed for internal-coordinate models of mechanical joints. Hinge matrices within the mobilizer are easily specified by user-supplied functions, and provide a direct means of mapping permissible motion derived from empirical data. We present computational results showing substantial performance and accuracy gains for mobilizers versus equivalent joints implemented with constraints. Examples of mobilizers for joints from human biomechanics and molecular dynamics are given. All methods and examples were implemented in Simbody?—an open source multibody-dynamics solver available at https://Simtk.org.     

高速列车用6008铝合金动态变形本构与损伤模型参数研究

高速列车在实际服役过程中会经受复杂的应力状态和环境条件,铝合金型材以其优良的力学和加工性能被广泛应用于新型高速列车的吸能结构,其防撞性能对高速列车的安全运行至关重要。本文针对一种新型轨道车辆用材料6008-T4铝合金型材进行了多种力学性能测试,包括动静态拉压实验、准静态高低温实验、不同应力路径的断裂实验等,提出了一种计算局部断裂应变的新方法,进而标定和获取了Johnson-Cook本构和损伤模型参数。最后利用平板侵彻实验来对所获取的参数进行检验,发现模拟和实验结果吻合良好,说明本文所获取的参数和参数标定方法都是有效的。     

Evaluation of subgrid-scale models in large-eddy simulation of flow past a two-dimensional block

Large-eddy simulations of flow past a two-dimensional (2D) block were performed to evaluate four subgrid-scale (SGS) models: (i) the traditional Smagorinsky model, (ii) the Lagrangian dynamic model, (iii) the Lagrangian scale-dependent dynamic model, and (iv) the modulated gradient model. An immersed boundary method was employed to simulate the 2D block boundaries on a uniform Cartesian grid. The sensitivity of the simulation results to grid refinement was investigated by using four different grid resolutions. The velocity streamlines and the vertical profiles of the mean velocities and variances were compared with experimental results. The modulated gradient model shows the best overall agreement with the experimental results among the four SGS models. In particular, the flow recirculation, the reattachment position and the vertical profiles are accurately reproduced with a relative coarse grid resolution of (N_x × N_y × N_z=) 160 × 40 × 160 (n_x × n_z = 13 × 16 covering the block). Besides the modulated gradient model, the Lagrangian scale-dependent dynamic model is also able to give reasonable prediction of the flow statistics with some discrepancies compared with the experimental results. Relatively poor performance by the Lagrangian dynamic model and the Smagorinsky model is observed, with simulated recirculating patterns that differ from the measured ones. Analysis of the turbulence kinetic energy (TKE) budget in this flow shows evidence of a strong production of TKE in the shear layer that forms as the flow is deflected around the block.     

Static and dynamic behavior of disk bearings for OSPG railway bridges under railway vehicle loading

The aim of the present study is to investigate the static and dynamic behavior of disk bearings under railway vehicle loadings. A disk bearing is operated as an elastic bearing in the vertical direction and is composed of a Polyether Urethane (Polyurethane) disk for elastic support and Polytetrafluoroethylene (PTFE) to accommodate lateral movements. Static tests are conducted in a laboratory to determine the static behavior of a Polyurethane disk. Finite Element (FE) analysis is also performed to assess the friction and the role of the pin inside a disk bearing. For dynamic behavior, four disk bearings having the identical Polyurethane disk, which are used in the static tests, are installed in a real railway bridge and tested under a running locomotive. From the test results, the static and dynamic stiffness of disk bearings are estimated and compared with each other. The estimated static stiffness of the disk bearing is almost half of that under dynamic loading. In addition, under relatively light loads the dynamic stiffness of a fixed disk bearing is approximately 80% greater than that of an expansion disk bearing since the PTFE deflects and the gap is closed in the expansion bearing. Deformation of the disk bearings in the real bridge is measured with varying locomotive speeds. The deformation of the disk bearings does not vary significantly with changes in the locomotive’s speed.     

Dynamic models of layered and block media with slip,friction, and separation

We use the concepts of slip theory to construct continual models of layered and block media. The medium structure elements, layers and blocks, are assumed to be elastic. The interaction conditions on the contact boundaries assume slip with friction and separation. We propose a numerical method for solving the obtained systems of equations. We also present examples of solution of dynamic and quasistatic problems about the development of slip regions for the types of media under study.     

Minimal loading conditions for higher-order numerical homogenisation schemes

The present study deals with the formulation of minimal loading conditions for microscale applications in numerical two-scale modelling (FE²) approaches. From the homogenisation concept, a set of volume average rules constrains the microscale PDE to be solved. They are considered to be the minimal set of loading conditions and can be specified by additional polynomial or periodic assumptions, for example, on the microscale displacement field. Whereas the resulting volume integrals can be transformed into surface integrals for so-called first-order homogenisation schemes, this is not possible for a second-order homogenisation of second gradient or micromorphic effective media substituting a heterogeneous microcontinuum represented by a volume element on the microscale. Several numerical examples compare the minimal loading condition concept with standard techniques discussed in literature.     

Free Energies and Minimal States for Scalar Linear Viscoelasticity

The concept of a minimal state was introduced in recent decades, based on earlier work by Noll. The property that a given quantity is a functional of the minimal state is of central interest in the present work. Using a standard representation of a free energy associated with a linear memory constitutive relation, a new condition, involving linear functionals, is derived which, if satisfied, ensures that the free energy is a functional of the minimal state. Using this result and recent work on constructing free energy functionals, it is shown that if the kernel of the rate of dissipation functional is given by sums of products, the associated free energy functional is a functional of the minimal state.     

Optimization of high-speed railway pantographs for improving pantograph-catenary contact

A crucial system for the operation of high-speed trains is the pantograph catenary interface as it is the sole responsible to deliver electrical power to the train. Being the catenary a stationary system with a long lifespan it is also less likely to be redesigned and upgraded than the pantographs that fit the train vehicles. This letter proposes an optimization procedure for the improvement of the contact quality between the pantograph and the catenary solely based on the redesign of the pantograph head suspension characteristics. A pantograph model is defined and validated against experimental dynamic characteristics of existing pantographs. An optimization strategy based on the use of a global optimization method, to find the vicinity of the optimal solution, followed by the use of a deterministic optimization algorithm, to fine tune the optimal solution, is applied here. The spring stiffness, damping characteristics and bow mass are the design variables used for the pantograph optimization. The objective of the optimal problem is the minimization of the standard deviation of the contact force history, which is the most important quantity to define the contact quality. The pantograph head suspension characteristics are allowed to vary within technological realistic limits. It is found that current high-speed railway pantographs have a limited potential for mechanical improvements, not exceeding 10%–15% on the decrease of the standard deviation of the contact force.     

Allowable crack sizes for railway wheels and rails

Determined are the critical crzes and crack growth characteristics for train car wheels and rails. Service and test limit size of cracks need to be distinguished in view of the difference between subcritical and the onset of rapid crack propagation. Probabilistic calculations have many advantages, but they cannot accurately predict neither the real critical minimum crack size (a_c)_min nor the real maximum crack growth increment Δa_max. As representative values of the minimum critical crack size a_c^* and maximum crack growth increment Δa^* are chosen for the calculations, therefore, that values which have a survival and crack growth probability, respectively, of 90%. Safety factors S(a) and are needed to account for the scatter of a_c and Δa for probabilities of more than 90%. Probabilistic fracture mechanics is applied to analyze the behavior of transverse cracks in the rim of tread-braked monobloc wheels, transverse head cracks in rails and aluminothermic rail welds. These informations are supplied by the German State Railways (DR) the Office of Research and Experiments (ORE) of the International Union of Railways (UIC).     

Polygonalization of railway wheels

Summary A model of a flexible wheelset running on flexible rails is presented which demonstrates the growth of out-of-round profiles of the wheels. This process of growing is called polygonalization. We divide the model into two parts. One part describes the oscillations of the wheelset and the rails. The excitations, which are a result of the out-of-round wheels, are due to geometrical terms, while excitations of unsprung masses are not considered. The second part describes the development of the wheel profiles and the wear rate due to wear and hardening, respectively. The two parts can be coupled by means of perturbation theory with multiple-time scales, [4], [10] as a wear-feedback loop proposed in [6]. As the calculation show, the greater is the phase shift between the-out-of-round profiles of the right and the left wheel the faster the wheels become out-of-round. Furthermore, it is shown, that the first and the second bending modes of the wheelset play an important role in the growth of polygonized wheels. It should be emphasized that other reasons for polygonalization may exist too, e.g. excitations due to unsprung masses, [14]. Received 10 February 1998; accepted for publication 20 August 1998     

Minimal Principal Solution at Infinity for Nonoscillatory Linear Hamiltonian Systems

In this paper we open a new direction in the study of principal solutions for nonoscillatory linear Hamiltonian systems. In the absence of the controllability assumption, we introduce the minimal principal solution at infinity, which is a generalization of the classical principal solution (sometimes called the recessive solution) for controllable systems introduced by W. T. Reid, P. Hartman, and/or W. A. Coppel. The term “minimal” refers to the rank of the solution. We show that the minimal principal solution is unique (up to a right nonsingular multiple) and state its basic properties. We also illustrate our new theory by several examples.     

准高速铁路路基动力响应数值模拟

为了研究高速铁路路基的动力响应,这里模拟秦沈客运专线的路基条件,采用有限元分析方法,计算分析了铁路路基的动力响应(位移)在列车荷载作用下的分布规律,分析了影响路基位移值的各种因素,提出了路基动力响应(位移)随车速变化的双峰现象并分析其成因,最后将数值模拟结果与秦沈客运专线现场动力测试试验数据进行了对比,得出模拟和试验结果规律性一致的结论。     

The influence of the brakes friction elements thickness on the contact temperature and wear

This paper is the continuation of the author's investigations [11] where the mathematical model for determination of the contact temperature, sliding speed and wear during braking was proposed. On contrary to the previous investigation, where the working elements were considered as the half-spaces, at the present paper their thickness is taken into account. For three different dependences of the friction coefficient upon the temperature the influence of thickness on the contact temperature and wear is studied. Received on 26 April 1999     

Optimal design of railway vehicles

Summary A well-designed railway vehicle has to meet two conflicting requirements. Firstly, it must be able to move freely through a curve. Secondly, the fundamental movement must be stable even at high running speeds.A. H. Wickens has indicated how these requirements can be formulated in a quantitative way. In the present paper we shall describe, explain and slightly extend his method and, moreover, we shall show that the calculations can be simplified by using linear algebra. The method is illustrated by applying the results on the case that the vehicle has a running gear with two wheelsets.

---

Optimaler Entwurf von Eisenbahnfahrzeugen

Übersicht Bin richtig entworfenes Eisenbahnfahrzeug soll zwei einander widersprechende Forderungen erfüllen. Erstens soll es imstande sein, frei durch einen Gleisbogen zu laufen. Zweitens soll die Grundbewegung auch bei großen Fahrgeschwindigkeiten stabil sein.A. H. Wickens hat angegeben, wie diese Forderungen quantitativ formuliert werden können. Im vorliegenden Aufsatz werden wir seine Methode beschreiben, erklären und ein wenig erweitern. Zudem werden wir zeigen, daß die Berechnungen sich vereinfachen lassen, indem man lineare Algebra benützt. Die Methode wird dadurch erläutert, daß die Ergebnisse auf den Fall eines Fahrzeug-Laufwerks mit zwei Radsätzen angewandt werden.

---

---

Dedicated to Academician Yu. A. Mitropolski, member of the Ukrainian Academy of Sciences, on the occasion of bis 70^th anniversary. January 3, 1987     

既有铁路钢桥剩余疲劳寿命的概率性评估

中国铁路线上大量既有钢桥承受着日益繁重的交通荷载,其疲劳剩余寿命与使用安全已受到桥梁管理部门的高度重视,为避免不必要的维护与更换,应建立合理的既有钢桥使用安全评估方法。在建立能反映铆接钢桥疲劳破坏机理的脆断和韧断概率失效模型基础上,给出了疲劳可靠性分析的极限状态方程,并合理确定了随机变量的参数取值。建立了铆接钢桥构件双角钢概率疲劳破坏模型,基于Monte Carlo算法实现了铆接钢桥构件双角钢疲劳断裂失效概率的计算,编制了相应的概率断裂分析程序DAPFF。进而将概率断裂力学评估方法应用于京九线赣江桥的时变疲劳可靠度分析,并给出了赣江桥概率疲劳剩余寿命评估结果与维护对策。