A machine for static and dynamic triaxial testing

A machine has been developed for studying the static and dynamic triaxial constitutive behavior of large specimens of geologic and construction materials. Test specimens can also contain a cylindrical tunnel cavity to permit study of tunnel-reinforcement structures and rock-structure interaction. The specimens are 0.3 m in diameter and 0.3 to 0.45 m high; the model tunnels can be up to 50 mm in diameter. Static and dynamic triaxial loads can be applied with maximum pressures of 200 MPa in static tests and 100 MPa in dynamic tests. Dynamic loading can also be superimposed on a static preload as large as 20 MPa. To facilitate study of tunnel reinforcement, the tunnel is maintained at ambient pressure, with access at both ends for instrumentation and photography. Example results show the influence on tunnel deformation of loading rate as well as the presence of joints and their orientation. For a given allowable tunnel closure, substantially greater pressures can be sustained under dynamic loading than under static loading, and substantially greater pressures can be sustained by an intact specimen than by a jointed specimen.     

大型渡槽动力设计方法研究

根据大型渡槽结构的特点,在缺乏适用的抗震分析模型前提下,提出支撑-渡槽-水伪三维流固耦合动力分析方法。模型基于结构动力分析理论和流固耦合分析理论,整体结构分析采用Newmark方法进行动力时程分析,分析中考虑渡槽结构整体受力性能,包括下部支撑结构、地基等多种因素的影响作用;渡槽-水耦合体子结构分析采用任意拉格朗日-欧拉(Arbitrary Lagrangian Eulerian,ALE)有限元方法进行动力分析,考虑渡槽-水的耦合相互作用,模拟渡槽中水体的大幅晃动作用,相应得出渡槽中动力压力值及其分布。以某排架支撑矩形渡槽为例,采用本文提出的伪三维模型进行地震时程分析,计算结果与三维模型计算结果吻合良好。本文提出的伪三维动力分析方法计算效率高,满足渡槽结构抗震设计要求,便于工程应用,是大型渡槽结构动力分析研究和抗震设计的实用静、动力分析方法。     

Dynamics of Articulated Structures. Part I. Theory

ABSTRACT

A finite element based method is developed for geometrically nonlinear dynamic analysis of spatial articulated structures; i.e., structures in which kinematic connections permit large relative displacement between components that undergo small elastic deformation. Vibration and static correction modes are used to account for linear elastic deformation of components. Kinematic constraints between components are used to define boundary conditions for vibration analysis and loads for static correction mode analysis. Constraint equations between flexible bodies are derived in a systematic way and a Lagrange multiplier formulation is used to generate the coupled large displacement-small deformation equations of motion. A lumped mass finite element structural analysis formulation is used to generate deformation modes. An intermediate-processor is used to calculate time-independent terms in the equations of motion and to generate input data for a large-scale dynamic analysis code that includes coupled effects of geometric nonlinearity and elastic deformation. Examples are presented and the effects of deformation mode selection on dynamic prediction are analyzed in Part II of the paper.     

基于有限元法的车载炮摇架和上架的静动态设计

讨论了应用有限元法进行车载炮摇架和上架静动态设计的方法,建立了摇架和上架的有限元模型,叙述了摇架和上架作为一个整体时的受力分析及单元类型的选择.通过静态刚度和强度分析,得到摇架和上架静载作用下的最大位移和应力,通过动态响应分析了解到其动态特性.由此找出了原方案结构设计中存在的问题及结构的薄弱环节,通过对结构的改进使其逐步达到设计要求.所提到的方法可推广到火炮其它部件的结构动态设计中.     

冲击波荷载作用下拉线塔的非线性动力分析

拉线塔是一种含有柔索的非线性结构。在冲击波荷载作用下,拉线塔在三维空间内会产生大范围的非线性位移,用工程上常用的模型简化方法来分析大变形拉线塔的误差比较大。本文采用非线性有限元法编制的可在微机上运行的拉线塔非线性静、动力分析程序,计算了单根柔索的阶跃冲击响应与冲击波荷载作用下拉线塔的非线性几何大变形动力响应,计算结果与有关文献的计算结果以及试验结果非常吻合。     

Aeroelastic analysis of large horizontal wind turbine baldes

A nonlinear aeroelastic analysis method for large horizontal wind turbines is described. A vortex wake method and a nonlinear finite element method (FEM) are coupled in the approach. The vortex wake method is used to predict wind turbine aerodynamic loads of a wind turbine, and a three-dimensional (3D) shell model is built for the rotor. Average aerodynamic forces along the azimuth are applied to the structural model, and the nonlinear static aeroelastic behaviors are computed. The wind rotor modes are obtained at the static aeroelastic status by linearizing the coupled equations. The static aeroelastic performance and dynamic aeroelastic responses are calculated for the NH1500 wind turbine. The results show that structural geometrical nonlinearities significantly reduce displacements and vibration amplitudes of the wind turbine blades. Therefore, structural geometrical nonlinearities cannot be neglected both in the static aeroelastic analysis and dynamic aeroelastic analysis.     

A Simple Methodology to Measure the Dynamic Flexural Strength of Brittle Materials

A simple methodology is proposed for measuring the dynamic flexural strength of brittle materials. The proposed technique is based on 1-point impact experimental setup with (unsupported) small beam specimens. All that is needed is a measurement of the prescribed velocity as a boundary condition and the fracture time for a failure criterion, both to be input in a numerical (FE) model to determine the flexural strength. The specimen was modeled numerically and observed to be essentially loaded in bending until its final inertial failure. The specimen’s geometry was optimized, noting that during the very first moments of the loading, the specimen length does not affect its overall response, so that it can be considered as infinite. The use of small beam specimens allow large scale testing of the flexural strength and comparison between static and dynamic loading configurations. Preliminary experiments are presented to illustrate the proposed approach.     

Measuring static yield stress of electrorheological fluids using the slotted plate device

An electrorheological (ER) response is defined as the dramatic change in rheological properties of a suspension of small particles due to the application of a large electric field transverse to the direction of flow. ER fluids are typically composed of nonconducting or semiconducting particles dispersed in a nonconducting continuous phase. A sufficiently large electric field will cause ER fluids to solidify, giving rising to a yield stress. Many applications in torque and stress transfer devices were proposed employing the reversible yielding behavior of ER fluids. Successful applications depend on a large yield stress of ER fluids and therefore accurate measurements of the yield stress of ER fluids are required. Reported experimental yield stresses of ER fluids have been dynamic yield stresses obtained by extrapolating the shear stress–shear rate data to zero-shear rate. It would be very helpful to the understanding of ER behaviors and the applications of ER fluids to be able to measure the static yield stress of ER fluids accurately. The slotted plate technique has been shown to be a successful method to determine the static yield stress of suspensions. The values obtained via the slotted plate method are static yield stress as the platform is designed for extremely low-speed motion. In this study, we modified the slotted plate device for the application of large electric fields and measured the static yield stress of TiO₂ ER fluids under various electric fields. The measured static yield stress values are also compared with the static yield stress values from a commercial rheometer.     

A viscoelastic constitutive model of rubber under small oscillatory load superimposed on large static deformation

Summary  A viscoelastic constitutive equation of rubber that is under small oscillatory load superimposed on large static deformation is proposed. The model is derived through linearization of Simo's nonlinear viscoelastic constitutive model and reference configuration transformation. Most importantly, in this model, static deformation correction factor is introduced to consider the influence of pre-strain on the relaxation function. Natural statically pre-deformed state is served as reference configuration. The proposed constitutive equation is extended to a generalized viscoelastic constitutive equation that includes widely used Morman's model as a special case using objective stress increment. The proposed constitutive model is tested for dynamic behavior of rubber specimens with different carbon black content. It is concluded from the test that the assumption that the effects of static deformation can be separated from time effects, which is the basis of Morman's model, is only applicable to unfilled rubber. The viscoelastic constitutive equation for filled rubber must include, therefore, the influence of the static deformation on the time effects. The suggested constitutive equation with static deformation correction factor shows good agreement with test values. Received 4 January 2001; accepted for publication 13 June 2001     

结构-地基系统静-动力联合分析模型

以有限区域模拟无限区域的动力计算必须考虑边界上波的传播效应,应不使波在边界上发生反射再返回到计算域中,并且应考虑初始静力场对其动力反应的影响。因此,基于无限元的静、动力特性提出静-动力统一无限元,通过算例验证无限元静-动力统一人工边界在静-动力联合分析模型中的精度和稳定性。结果表明:无限元静-动力统一人工边界在静力、动力及静-动力联合分析模型中具有很高的精度和良好的稳定性,突破了传统动力人工边界不能兼顾静力效应的局限。     

按叠加于静态悬垂位形上小变形理论分析索的微幅振动

采用叠加于初应力位形上小变形问题的理论框架,分析叠加于索的静态悬垂位形上的微幅振动;给出了附加于静态位形上微幅振动的微分方程。在小拉伸柔度和附加于静态悬垂位形上的变形为微小变形的条件下,利用解析方法得出了悬垂面外与面内的微幅振动无耦合、悬垂面内竖向振动和水平振动可以解耦算出的结论。算例将微分方程的数值解法与ABAQUS有限元算法的计算结果进行了比较,误差小于4％,且前种算法得到的计算结果随时间衰减较快,计算精度和效率较高。     

含孔von Karman板中非线性波散射与边值问题

基于ｖｏｎ Ｋａｒｍａｎ板大挠度弯曲理论,利用小参数摄动法,分析研究了含孔ｖｏｎＫａｒｍａｎ板的非线性波散射与动应力集中问题,其中一类可看成是薄板弯曲波动问题的控制方程。当有单频波入射时,由于弯曲应力与膜应力状态的非线性耦合,孔洞会产生高次谐波散射现象。建立了求解本问题的边界积分方程法,利用积分方程法交替求求这两类问题,最终可获得问题的近似分析解。     

The effect of underplatform dampers on the forced response of bladed disks by a coupled static/dynamic harmonic balance method

Friction contacts are often used in turbomachinery design as passive damping systems. In particular, underplatform dampers are mechanical devices used to decrease the vibration amplitudes of bladed disks.Numerical codes are used to optimize during designing the underplatform damper effectiveness in order to limit the resonant stress level of the blades. In such codes, the contact model plays the most relevant role in calculation of the dissipated energy at friction interfaces. One of the most important contact parameters to consider in order to calculate the forced response of blades assembly is the static normal load acting at the contact, since its value strongly affects the area of the hysteresis loop of the tangential force, and therefore the amount of dissipation.A common procedure to estimate the static normal loads acting on underplatform dampers consists in decoupling the static and the dynamic balance of the damper. A preliminary static analysis of the contact is performed in order to get the static contact/gap status to use in the calculation, assuming that it does not change when vibration occurs.In this paper, a novel approach is proposed. The static and the dynamic displacements of the system (bladed disk+underplatform dampers) are coupled together during the forced response calculation. Static loads acting at the contacts follow from static displacements and no preliminary static analysis of the system is necessary.The proposed method is applied to a numerical test case representing a simplified bladed disk with underplatform dampers. Results are compared with those obtained with the classical approach.     

Longitudinal dynamics of a tracked vehicle: Simulation and experiment

In recent years virtual dynamic system simulation has become very important in the design and development stage, as new strategies can be examined without expensive measurements and with reduced time. This paper describes the development of a simulation model for transient analysis of the longitudinal dynamics of a heavy tracked vehicle. The driving inputs for this simulation model are obtained from a powertrain model. The main elements of the powertrain include the engine, Torque Converter (TC), transmission and drivetrain. Here the engine is modeled based on the engine maps from steady-state experiments. The TC is modeled based on its characteristic map from experiments. A fairly simple transmission model is used which is based on static gear ratios assuming small shift times. The final drivetrain model however includes the rotational dynamics of the sprocket. The simulation model developed is validated by comparing the predicted values with the measured data from experiments. The results have demonstrated that the developed model is able to predict fairly accurately the acceleration and braking performance of the heavy tracked vehicle on both soft and hard terrain.     

Geometrically exact planar beams with initial pre-stress and large curvature: Static configurations,natural frequencies,and mode shapes

Within this paper, an analytical formulation is provided and used to determine the natural frequencies and mode shapes of a planar beam with initial pre-stress and large variable curvature. The static configuration, mode shapes, and natural frequencies of the pre-stressed beam are obtained by using geometrically exact, Euler–Bernoulli beam theory. The beam is assumed to be not shear deformable and inextensible because of its slenderness and uniform, closed cross-section, as well as the boundary conditions under consideration. The static configuration and the modal information are validated with experimental data and compared to results obtained from nonlinear finite-element analysis software. In addition to the modal analysis about general static configurations, special consideration is given to an initially straight beam that is deformed into semi-circular and circular static configurations. For these special circular cases, the partial differential equation of motion is reduced to a sixth-order differential equation with constant coefficients, and solutions of this system are examined. This work can serve as a basis for studying slender structures with large curvatures.     

特种泡沫塑料的动态力学性能研究

通过大尺寸分离式Hopkinson压杆对特种泡沫塑料进行了高应变率冲击实验，完整地给出了该材料在高应变率下的动态应力应变曲线，并将结果和理论上的Eyring模型进行了比较，指出了这种材料在一定的应变率范围内，具有明显的应变率效应，同时从应力应变曲线的特点来看，这种材料又有良好的吸能特性，最后通过对实验数据的拟合，提出了便于工程应用的动态本构方程。     

Dynamic stability of uncertain laminated beams subjected to subtangential loads

Because of the inherent complexity of fiber-reinforced laminated composites, it can be challenging to manufacture composite structures according to their exact design specifications, resulting in unwanted material and geometric uncertainties. Thus the understanding of the effect of uncertainties in laminated structures on their static and dynamic responses is highly important for a reliable design of such structures. In this research, we focus on the probabilistic stability analysis of laminated structures subject to subtangential loading, a combination of conservative and nonconservative tangential loads, using the dynamic criterion. In order to study the dynamic behavior by including uncertainties into the problem, three models were developed: exact Monte Carlo simulation, sensitivity-based Monte Carlo simulation, and probabilistic FEA. These methods were integrated into the existing finite element analysis. Also, perturbation and sensitivity analysis have been used to study nonconservative problems to study the stability analysis using the dynamic criterion.     

The Mori–Tanaka method for composite materials with nonlinear interface debonding

We have used the Mori–Tanaka method to study the effect of nonlinear interface debonding on the constitutive behavior of composite material with high particle volume fraction. The interface debonding is characterized by a nonlinear cohesive law determined from the fracture test of the high explosive PBX 9501. Using the example of the composite material with spherical particles subject to hydrostatic tension, we show that the particle size has an important effect on the behavior of the composite material, namely hardening for small particles and softening for large particles. The critical particle size that separates the hardening and softening behavior of the composite material is determined. For the composite material with large particles, the particle/matrix interface may undergo catastrophic debonding, i.e., sudden, dynamic debonding even under static load. The energy release during catastrophic debonding can be very large, thus may trigger the reaction or detonation of high explosives. For the high explosive PBX 9501, the energy release due to catastrophic debonding of coarse (large) particles is equivalent to the free drop of the high explosive from a height of 110 m. This value become much higher, 455 m, once the debonding of fine (small) particle is accounted for.     

A viscoelastic constitutive model of rubber under small oscillatory load superimposed on large static deformation considering the Payne effect

The viscoelastic behavior of carbon-black-filled rubber under small oscillatory loads superimposed on large static deformation is dealt with. In this class of problems, as the strain amplitudes of the load increase, the dynamic stiffness decreases, and this phenomenon is known as the Payne effect. Besides the effects of the static deformation and the frequencies of the superimposed dynamic load, the Payne effect is considered in this study. Influence factors are introduced in this model in order to consider the influence of static predeformation, the dynamic-strain-dependent properties, and frequency-dependent properties. For simplicity, separation of the three dominant variables, frequency, prestatic deformation, and dynamic amplitude of strain, is assumed. The Kraus model is used for describing the Payne effect. Dynamic tension tests are executed to obtain the model parameters and also for the verification of the proposed model. The suggested constitutive equation shows reasonable agreement with test data.