A novel method for predicting the power outputs of wave energy converters

This paper focuses on realistically predicting the power outputs of wave energy converters operating in shallow water nonlinear waves. A heaving two-body point absorber is utilized as a specific calculation example, and the generated power of the point absorber has been predicted by using a novel method(a nonlinear simulation method) that incorporates a second order random wave model into a nonlinear dynamic filter. It is demonstrated that the second order random wave model in this article can be utilized to generate irregular waves with realistic crest–trough asymmetries, and consequently, more accurate generated power can be predicted by subsequently solving the nonlinear dynamic filter equation with the nonlinearly simulated second order waves as inputs. The research findings demonstrate that the novel nonlinear simulation method in this article can be utilized as a robust tool for ocean engineers in their design, analysis and optimization of wave energy converters.     

Geometric nonlinear dynamic analysis of curved beams using curved beam element

Instead of using the previous straight beam element to approximate the curved beam,in this paper,a curvilinear coordinate is employed to describe the deformations,and a new curved beam element is proposed to model the curved beam.Based on exact nonlinear strain-displacement relation,virtual work principle is used to derive dynamic equations for a rotating curved beam,with the effects of axial extensibility,shear deformation and rotary inertia taken into account.The constant matrices are solved numerically utilizing the Gauss quadrature integration method.Newmark and Newton-Raphson iteration methods are adopted to solve the differential equations of the rigid-flexible coupling system.The present results are compared with those obtained by commercial programs to validate the present finite method.In order to further illustrate the convergence and efficiency characteristics of the present modeling and computation formulation,comparison of the results of the present formulation with those of the ADAMS software are made.Furthermore,the present results obtained from linear formulation are compared with those from nonlinear formulation,and the special dynamic characteristics of the curved beam are concluded by comparison with those of the straight beam.     

Nonlinear numerical simulation method for galloping of iced conductor

Based on the principle of virtual work, an updated Lagrangian finite element formulation for the geometrical large deformation analysis of galloping of the iced conductor in an overhead transmission line is developed. In numerical simulation, a three-node isoparametric cable element with three translational and one torsional degrees-of-freedom at each node is used to discretize the transmission line. The nonlinear dynamic system equation is solved with the Newmark time integration method and the Newton-Raphson nonlinear iteration. Numerical examples demonstrate the efficiency of the presented method and the developed finite element program. A new possible galloping mode, which may reflect the saturation phenomenon of a nonlinear dynamic system, is discovered under the condition that the lowest order of vertical natural frequency of the transmission line is approximately two times of the horizontal one.     

Development of a simulation model for dynamic derailment analysis of high-speed trains

The running safety of high-speed trains has become a major concern of the current railway research with the rapid development of high-speed railways around the world.The basic safety requirement is to prevent the derailment.The root causes of the dynamic derailment of highspeed trains operating in severe environments are not easy to identify using the field tests or laboratory experiments.Numerical simulation using an advanced train–track interaction model is a highly efficient and low-cost approach to investigate the dynamic derailment behavior and mechanism of high-speed trains.This paper presents a three-dimensional dynamic model of a high-speed train coupled with a ballast track for dynamic derailment analysis.The model considers a train composed of multiple vehicles and the nonlinear inter-vehicle connections.The ballast track model consists of rails,fastenings,sleepers,ballasts,and roadbed,which are modeled by Euler beams,nonlinear spring-damper elements,equivalent ballast bodies,and continuous viscoelastic elements,in which the modal superposition method was used to reduce the order of the partial differential equations of Euler beams.The commonly used derailment safety assessment criteria around the world are embedded in the simulation model.The train–track model was then used to investigate the dynamic derailment responses of a high-speed train passing over a buckled track,in which the derailmentmechanism and train running posture during the dynamic derailment process were analyzed in detail.The effects of train and track modelling on dynamic derailment analysis were also discussed.The numerical results indicate that the train and track modelling options have a significant effect on the dynamic derailment analysis.The inter-vehicle impacts and the track flexibility and nonlinearity should be considered in the dynamic derailment simulations.     

STUDY ON DYNAMIC STRESS INTENSITY FACTORS OF DISK WITH A RADIAL EDGE CRACK SUBJECTED TO EXTERNAL IMPULSIVE PRESSURE

A dynamic weight function method is presented for dynamic stress intensity factors of circular disk with a radial edge crack under external impulsive pressure. The dynamic stresses in a circular disk are solved under abrupt step external pressure using the eigenfunction method. The solution consists of a quasi-static solution satisfying inhomogeneous boundary conditions and a dynamic solution satisfying homogeneous boundary conditions. By making use of Fourier-Bessel series expansion, the history and distribution of dynamic stresses in the circular disk are derived. Furthermore, the equation for stress intensity factors under uniform pressure is used as the reference case, the weight function equation for the circular disk containing an edge crack is worked out, and the dynamic stress intensity factor equation for the circular disk containing a radial edge crack can be given. The results indicate that the stress intensity factors under sudden step external pressure vary periodically with time, and the ratio of the maximum value of dynamic stress intensity factors to the corresponding static value is about 2.0.     

Pseudo-beam method for compressive buckling characteristics analysis of space inflatable load-carrying structures

This paper extends Le van＇s work to the case of nonlinear problem and the complicated configuration. The wrinkling stress distribution and the pressure effects are also included in our analysis. Pseudo-beam method is presented based on the inflatable beam theory to model the inflatable structures as a set of inflatable beam elements with a prestressed state. In this method, the discretized nonlinear equations are given based upon the virtual work principle with a 3-node Timoshenko＇s beam model. Finite element simulation is performed by using a 3-node BEAM189 element incorporating ANSYS nonlinear program. The pressure effect is equivalent included in our method by modifying beam element cross-section parameters related to pressure. A benchmark example, the bending case of an inflatable cantilever beam, is performed to verify the accuracy of our proposed method. The comparisons reveal that the numerical results obtained with our method are close to open published analytical and membrane finite element results. The method is then used to evaluate the whole buckling and the loadcarrying characteristics of an inflatable support frame subjected to a compression force. The wrinkling stress and region characteristics are also shown in the end. This method gives better convergence characteristics, and requires much less computation time. It is very effective to deal with the whole load-carrying ability analytical problems for large scale inflatable structures with complex configuration.     

A new absolute nodal coordinate formulation beam element with multilayer circular cross section

A systematic numerical integration method is applied to the absolute nodal coordinate formulation(ANCF)fully parameterized beam element with smooth varying and continuous cross section.Moreover,the formulation for the integration points and weight coefficients are given in the method which is used to model the multilayer beam with a circular cross section.To negate the effect of the bending stiffness for the element used to model the high-voltage electrical wire,the general continuum mechanical approach is adjusted.Additionally,the insulation cover for some particular types of the wire is described by the nearly incompressible Mooney-Rivlin material model.Finally,a static problem is presented to prove the accuracy and convergence properties of the element,and a dynamic problem of a flexible pendulum is simulated whereby the balance of the energy can be ensured.An experiment is carried out in which a wire is released as a pendulum and falls on a steel rod.The configurations of the wire are captured by a high-speed camera and compared with the simulation results.The feasibility of the wire model can therefore be demonstrated.     

Symplectic analysis for wave propagation in one-dimensional nonlinear periodic structures

The wave propagation problem in the nonlinear periodic mass-spring structure chain is analyzed using the symplectic mathematical method. The energy method is used to construct the dynamic equation, and the nonlinear dynamic equation is linearized using the small parameter perturbation method. Eigen-solutions of the symplectic matrix are used to analyze the wave propagation problem in nonlinear periodic lattices. Nonlinearity in the mass-spring chain, arising from the nonlinear spring stiffness effect, has profound effects on the overall transmission of the chain. The wave propagation characteristics are altered due to nonlinearity, and related to the incident wave intensity, which is a genuine nonlinear effect not present in the corresponding linear model. Numerical results show how the increase of nonlinearity or incident wave amplitude leads to closing of transmitting gaps. Comparison with the normal recursive approach shows effectiveness and superiority of the symplectic method for the wave propagation problem in nonlinear periodic structures.     

Dynamic analysis of an offshore pipe laying operation using the reel method

A system designed for a rigid and flexible pipe laying purposes is presented in the paper.Mathematical and numerical models are developed by using the rigid finite element method(RFEM).The RFEM is an efficient solution in the time domain.Static and dynamic problems related to pipe installation are solved by taking the advantage of simple interpretation and implementation of the method.Large deformations of the pipe during spooling and when it is reeled out at sea are considered.A material model implemented is used to take into consideration nonlinear material properties.In particular,the full elasto-plastic material characteristics with hardening and Bauschinger effect are included.Dynamic analyses are performed and the results attached in this work demonstrates how the sea conditions influence the machinery and pipeline,assuming a passive reel drive system. The influence of several other operational parameters on dynamic loads is verified.An active system,implemented as a part of the mathematical model,improves the system performance.Some results are presented as well.     

Geometric nonlinear formulation for thermal-rigid-flexible coupling system

This paper develops geometric nonlinear hybrid formulation for flexible multibody system with large deformation considering thermal efect. Diferent from the conventional formulation, the heat flux is the function of the rotational angle and the elastic deformation, therefore, the coupling among the temperature, the large overall motion and the elastic deformation should be taken into account. Firstly,based on nonlinear strain–displacement relationship, variational dynamic equations and heat conduction equations for a flexible beam are derived by using virtual work approach,and then, Lagrange dynamics equations and heat conduction equations of the first kind of the flexible multibody system are obtained by leading into the vectors of Lagrange multiplier associated with kinematic and temperature constraint equations. This formulation is used to simulate the thermal included hub-beam system. Comparison of the response between the coupled system and the uncoupled system has revealed the thermal chattering phenomenon. Then, the key parameters for stability, including the moment of inertia of the central body, the incident angle, the damping ratio and the response time ratio, are analyzed. This formulation is also used to simulate a three-link system applied with heat flux. Comparison of the results obtained by the proposed formulation with those obtained by the approximate nonlinear model and the linear model shows the significance of considering all the nonlinear terms in the strain in case of large deformation. At last, applicability of the approximate nonlinear model and the linear model are clarified in detail.     

高拱坝气幕隔震的动力模型试验

为了研究高拱坝的气幕隔震效果,基于动力相似准则,设计了坝体-坝基-气幕-库水三相耦合系统的动力试验模型。其中,坝体材料采用河沙、重晶石粉、铁粉、松香、酒精调制而成,坝基材料采用膨胀珍珠岩和石膏调制的轻质材料,气幕厚度为1cm,均匀地覆盖在坝体上游面,气室壁材料选用ABS工程塑料。基于该模型,完成了两种实测地震波不同峰值加速度共计12个工况的大型振动台试验。试验结果表明:气幕使动水压力显著降低,坝体加速度也相应减小;靠近坝底的测点动水压力削减达70%以上,坝顶加速度减小约20%。因此,气幕可提高坝体的抗震性能。     

地震作用下高拱坝损伤开裂分析

采用应变率相关的砼非线性损伤模型模拟拱坝横缝,研究了砼非线性本构情况下整体拱坝与考虑分缝拱坝的应力响应和损伤开裂的特点与差别。对实际拱坝的地震响应分析表明,基于非线性砼模型的整体拱坝动力响应模型可以基本反映拱坝的实际应力分布情况。     

非线性子结构方法中实现对结构抗震措施阻尼器的数值模拟

应用子结构理论，对设置伸缩横缝的小湾高拱坝结构，分别就正常高水位常遇低水位两种水位工况，考虑坝体伸缩横缝在地震交变荷载作用下反复开合引起的缝面问滑移．接触等效应的影响，坝体一库水的相互作用而产生的动水压力的影响，对坝体的抗震性能进行了地震反应分析。对伸缩缝问设置阻尼器这一新的设计思想进行了可行性的研究，论证推导了阻尼器的计算模型，探讨了阻尼器对坝体结构抗震性能的影响。     

高拱坝动力特性与动力响应模型试验研究

高拱坝的动力破坏特性越来越受到关注,动力特性和动力响应是其研究的一个重要方面。通过模型试验的方法研究高拱坝动力特性和动力响应的特征,动力特性试验比较了完好结构与有施工横缝结构的基阶动力特性,表明当结构存在施工横缝时,结构基阶频率降低,阻尼增大。结构动力响应采用振动台模拟地震波激励,试验结果表明,完整结构与有施工缝结构动力响应具体数据不同,但规律相同。加速度最大响应沿拱顶水平向在坝中拱顶的值最大,向两边的坝肩处,加速度最大响应逐渐减小。沿拱坝垂向加速度最大响应从坝顶到基础,响应均逐渐减小。试验结果可为高拱坝结构动力安全研究提供技术依据。     

考虑局部切向约束接触问题的直接刚度法

针对工程中大量存在的切向滑移受到约束的接触问题,提出了基于Lagrange乘子的点-面及点-点接触直接刚度法,该方法生成的接触协调条件可以直接组装到结构刚度阵中,从而可直接用于考虑存在结构几何非线性及材料非线性的接触问题分析中。采用这一算法进行了考虑拱坝横缝张合效应的地震响应分析,结果表明考虑切向滑移约束对接触中的张开度有明显影响。     

Reservoir water level effects on nonlinear dynamic response of arch dams

In this study, reservoir water level effects on nonlinear dynamic response of arch dams are investigated. For this purpose, the nonlinear behaviour of the dam concrete is idealized as elasto-plastic using the Drucker–Prager model based on the associated flow rule assumption. Water in the reservoir is represented by the Lagrangian (displacement-based) fluid finite elements. The program NONSAP is modified for elasto-plastic analysis of fluid–structure systems and employed in the response calculations. Nonlinear dynamic analysis of an arch dam subjected to earthquake ground motion is performed for five different water levels. The El-Centro N–S component of the Imperial Valley earthquake, on May 18, 1940, has been used as the ground motion. The crest displacements, the maximum tensile stresses on the upstream and downstream faces of the dam and the time history of the yield function of an element in the dam body are presented. The results obtained from nonlinear analyses for different water levels are compared with each other. It is apparent that the reservoir water level effects must be considered in the elasto-plastic analyses of arch dams to earthquake ground motion.     

考虑混凝土应变率变化的高拱坝非线性动力响应研究

提出一种新的应变率相关的混凝土非线性弹塑性损伤模型。采用此模型对混凝土拱坝的非线性地震响应作了分析。在综合考虑坝-地基-库水动力相互作用和坝缝非线性接触的基础上，着重研究了混凝土应交率相关效应及加载历史对混凝土极限强度等重要参数及拱坝响应的影响，并与采用不考虑应交率影响的混凝土损伤模型计算结果进行了对比分析。结果表明，拱坝考虑横缝作用后的坝面应变率分布不同于整体拱坝。应交率分布形态不仅可以很好地表征拱坝的振动形态，而且对于高拱坝的动力响应的影响也不可忽略。     

A comparison of two formulations of the fin efficiency for straight fins

A formulation of the fin efficiency based on Newton’s law of cooling is compared with a formulation based on a ratio of heat transferred from the fin surface to the surrounding fluid to the heat conducted through the base.The first formulation requires that the solution of the nonlinear fin equations for constant heat transfer coefficient and constant thermal conductivity is known,whilst the second formulation of the fin efficiency requires only that a first integral of the model equation is known.This paper shows the first formulation of the fin efficiency contains approximation errors as only power series and approximate solutions to the nonlinear fin equations have been determined.The second formulation of the fin efficiency is exact when the first integrals can be determined.     

Regional plantar foot pressure distributions on high-heeled shoes-shank curve effects

Forefoot pain is common in high-heeled shoe wearers due to the high pressure caused by the center of body mass moving forward and the increased arch height with heel elevation.Sufficient arch support could reduce the high pressure over forefoot.However,too much arch support could lead to abnormal foot alignment and pain over midfoot.Little information is reported on the relationship among plantar arch height,shank curve design and plantar pressure.This study aimed at quantifying the plantar arch height changes at different heel heights and investigating the effect of shank curve on plantar pressure distribution.The plantar arch height increased to(7.6±1.3) mm at heel height of 75 mm.The Chinese standard suggests the depth of last should be 8.5 mm for heel height of 75 mm.When a shank curve with higher depth of last(11 mm) was used,the peak pressure over forefoot further decreased in midstance phase,which might ease the forefoot problems,while the peak pressure over midfoot increased but not exceeded the discomfort pressure thresholds.To achieve a more ideal pressure distribution in high-heeled shoes,a higher than expected depth of last would be suggested that would not cause discomfort over midfoot.