柔性头颅模型撞击弹性板的动态响应分析

将柔性接触撞击过程处理为一个振动系统响应,采用机械网络图和求机械阻抗的方法解决了这一动态响应问题。柔性接触撞击模型考虑了头部的实际结构,把头部简化成撞击部位的头皮和头骨的质量、头部其它部分的头骨和脑液的质量、头部的刚度、头皮和脑液的阻尼系数组成的振动模型,弹性板也同样简化成由质量、刚度和阻尼构成的振动模型。采用求激振点速度阻抗的方法,得到了系统的动态撞击力、头部所受到的撞击加速度值,以及板的弹性变形、系统的固有频率等动态响应。实验数据与计算数据符合较好,证明方法是计算撞击作用下系统动态响应的实用方法,从而为头部撞击保护设计提供参考。     

不可压饱和多孔弹性杆动力响应的多辛方法

研究了不可压饱和多孔弹性杆的一维动力响应问题.基于多孔介质理论,在流相和固相微观不可压、固相骨架小变形的假定下,建立了不可压流体饱和多孔弹性杆一维轴向动力响应的数学模型.利用Hamilton空间体系的多辛理论,构造了不可压饱和多孔弹性杆轴向振动方程的多辛形式及其多种局部守恒律.采用中点Box离散方法得到轴向振动方程的多辛离散格式和局部能量守恒律以及局部动量守恒律的离散格式;数值模拟了不可压饱和多孔弹性杆的轴向振动过程,记录了每一时间步的局部能量数值误差和局部动量数值误差.结果表明,已构造的多辛离散格式具有很高的精确性和较长时间的数值稳定性,这为解决饱和多孔介质的动力响应问题提供了新的途径.     

接触与大变形问题的光滑有限元分析

橡胶材料因具有良好的抗震、吸能作用,在实际工程中应用广泛.然而橡胶超弹性材料的碰撞属于强非线性问题,分析橡胶材料的接触碰撞和大变形问题对于提高装置的缓冲性能具有重要意义.光滑有限元法(smoothed finite element method, S-FEM)是一种弱形式的数值计算方法,相比于传统的有限元方法,光滑有限元法对网格的质量要求不高,允许单元在计算过程中发生较大的变形,且光滑域的构造比较灵活,在不增加自由度的前提下,可以达到较高的精度.在光滑有限元法的基础上,采用双势方法进行接触计算,以充分利用光滑有限元法计算大变形问题的优点和双势方法求解接触力的优势.通过与有限元软件MSC.Marc的数值结果对比,验证了该算法的准确性和能量守恒性,并且分析了摩擦因数对碰撞体的影响.     

由纵向振动引起的质点与圆锥形杆碰撞问题的解析解

给出细长圆锥形的截面杆受到质点纵向碰撞时的精确解析解．提出了一种新方法用于分析质点-圆锥形杆碰撞,使用了叠加法给出杆的响应．其结果可验证数值解和其他解析解．所提出方法的优点之一是响应解的解析形式简洁．结论是质量比和一些描述杆几何形状的变量,如倾斜度、杆长和半径在撞击分析中具有重要作用．     

接触表面的边界条件奇异性及其随机扰动

碰撞表面的随机边界条件反映了粘弹性材料在不同碰撞条件下的复杂性质.数值的不确定性和确定模型的渐近估计都可以利用计算机系统来计算.运用有限元方法来模拟碰撞表面的变形,得出远离接触表面部分的结构保持稳定.     

基于浸入边界-有限元法的流固耦合碰撞数值模拟方法

针对流固耦合碰撞问题,建立了流体中固体与固体碰撞界面解析直接模拟方法,采用清晰界面浸入边界法模拟流体中的动边界问题,避免了传统贴体网格方法在求解流体中存在固体间碰撞问题时网格出现负体积的问题,采用基于罚函数的有限元方法对固体的运动和碰撞进行求解,以分域耦合方式实现流体域和固体域的耦合求解.通过与静止流体中球形颗粒与壁面正碰撞和斜碰撞的实验数据对比,验证了建立的数值模拟方法对流体中固体与固体碰撞数值模拟的正确性,获得了流体域流场在碰撞前后随时间的变化,同时通过该文建立的数值模拟方法也获得了固体域中固体的碰撞力和应力.未来,将把该数值模拟方法应用到流体流动环境中,如固体颗粒对管道的冲蚀、流体诱导海洋立管之间的碰撞、坠物对海底管道的撞击等.     

常曲率大深宽比河湾拟序扰动结构与床面响应关系探讨

蜿蜒河流床面形态既是其复杂动力结构响应的结果,同时也是决定河流进一步演化方向的重要因素.以蜿蜒河流中一种典型的大深宽比河湾为背景,探索其动力结构与床面响应的关系,将黏性不可压缩流体方程、泥沙输移方程和床面变形方程耦合,通过摄动方法求解床面响应,分析床面形态变化特性.研究成果显示在水流二维扰动作用下,河道中浅滩深槽呈现规则响应.当弯曲度等于0时,床面响应形态围绕河道中轴线基本呈反对称分布;当弯曲度不等于0时,床面响应形态呈不对称分布,中轴线向凹岸偏移.该文给出了由Reynolds(雷诺)数、扰动波数、床面形态增减率等构成的床面响应发展趋势稳定关系的判别方法.     

弹性接触问题的一种新的力学模型

从机械系统的角度出发,描述了系统中构件间局部接触与构件弹性变形间的耦合关系;用多组坐标系描述机械系统中物体的位形;用分离接触边界法描述物体接触边界间的约束;通过接触虚功原理建立了更加广泛意义上的接触系统静力学模型．作为算例,将该力学模型应用于内啮合少齿差行星齿轮多齿啮合问题的研究,揭示了行星齿轮传动中有多对轮齿相互接触,获得了其接触应力分布状态．通过实验验证了力学模型、计算方法和计算结果的正确性．     

广义布朗单的容度估计

研究了既没有平稳增量性,也没有scaling性质的N指标d维广义布朗单的容度问题．证明了广义布朗单“好象”一个局部平稳增量过程,应用Cairoli极大不等式和多参数鞅的方法得到了广义布朗单的碰撞概率与容度之间的关系,给出了其碰撞概率的确切容度估计．所得结果包含了布朗单和可加布朗运动的相应结果．     

球形塑性薄壳在平头圆柱体冲击下贯穿过程的研究

对球形塑性壳在平头圆柱体冲击下的动力贯穿行为进行了分析．通过引入等度量变换,给出了壳体的变形模态．在此基础上对球壳在平头圆柱体撞击下的贯穿机制进行了分析研究,给出了贯穿模型,由此结合Hamilton原理,导出了运动方程组．采用Runge-Kutta方法求解了该方程组,最后分别给出了贯穿时间-弹体初速度;残余窝陷半径-弹体初速度;贯穿后弹体剩余速度-弹体初速度的关系曲线．     

A characteristic line based method to build finite-dimensional medoels of heat exchangers

surface heat exchngers are typical simulated with simplified models obtained through segmentation of the heat exchanging fluid path in a number of consecutive lumps In order to aviod major drawbacks of this approach, which may be very misleading for control design purpose, we propose a method, based on the intergration of the PDE system by the method of characteristic lines, for the construction of numerical heat exchangers models. It can be proved that the time response of such new models is indeed rid of parasitic oscillation and suitable for the understanding of complex dynamic phenomena occurring and suitable for the understanding of complex dynamic phenomena occurring in long residence time heat exchangers, both with one- and two- phase flow. In this paper, particular attention is paid to the problem of generating finite dimensional dynamic system by application of the characteristic lines method and computing the frequency responce of such models. Actually, since the characteristic lines method is not naturally is not straightforward to define Finally, the accuracy of CL models is compared with classical models of comparable complexity, with special reference to real application cases, taken from the power generation field.     

弹性直杆中一类动力屈曲问题的渐近解

对于弹性杆受刚性块轴向撞击的动力屈曲问题而言,由于轴向载荷形式较为复杂,问题将归结为关于非线性偏微分方程组解的讨论,至今仍未能得到一个理论上的解析解,为此,讨论了有限长理想弹性直杆的此类动力屈曲问题,采用小参数的摄动展开和变分法,成功地得到了这一问题的一个理论上的近似解,并给出了相应的算例,从中得到了一些有益的结论.     

柱形弹体撞击塑性变形的G.I.泰勒理论的分析解及其改进

柱形弹体对刚性靶体的纵向撞击塑性变形理论是G.I.泰勒[1]首先提出的.这个理论的重要性在于通过这个理论可以从实验数据计算动力屈服强度,而且从实验结果[2]中看到,动力屈服强度和撞击速度无关,动力屈服强度高于静力屈服强度,对某些材料而言,可以超出好几倍.这样就为弹塑性撞击研究提供了一个重要的根据.但是,泰勒理论由于微分方程的复杂性,求解过程都是数值计算,这样对使用其结果时深感不便.本文提供了全部分析解,并对其结果进行了讨论.本文对冲量计算进行了修正,修正理论的分析解指出,其结果比泰勒理论的解更加符合实验[2].     

Wave propagation in the soil due to a falling chimney

This paper describes a simulation of wave propagation in the soil as a result of an impact. In this specific case, the dynamic load is the velocity of a falling chimney. The impacting parts of the chimney transfer their dynamic forces to the adjacent continuum. This causes vibrations in the surrounding area. In this paper, measurements of velocities in the soil caused by a falling chimney are compared with numerical solutions using a two-dimensional FEM-SBFEM model. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Updated Lagrangian Taylor-SPH method for large deformation in dynamic problems

In this paper, the updated Lagrangian Taylor-SPH meshfree method is applied to the numerical analysis of large deformation and failure problems under dynamic conditions. The Taylor-SPH method is a meshfree collocation method developed by the authors over the past years. The governing equations, a set of first-order hyperbolic partial differential equations, are written in mixed form in terms of stress and velocity. This set of equations is first discretized in time by means of a Taylor series expansion in two steps and afterwards in space using a corrected form of the SPH method. Two sets of particles are used for the computation resulting on the elimination of the classical tensile instability. In the paper presented herein the authors propose an updated Lagrangian Taylor-SPH approach to address the large deformations of the solid, and therefore the continuous re-positioning of the particles. In order to illustrate the performance and efficiency of the proposed method, some numerical examples based on elastic and viscoplastic materials involving large deformations under dynamic conditions are solved using the proposed algorithm. Results clearly show that the updated Lagrangian Taylor-SPH method is an accurate tool to model large deformation and failure problems under dynamic loadings.     

Suppressing grazing chaos in impacting system by structural nonlinearity

In this note we investigate the influence of structural nonlinearity of a simple cantilever beam impacting system on its dynamic responses close to grazing incidence by a means of numerical simulation. To obtain a clear picture of this effect we considered two systems exhibiting impacting motion, where the primary stiffness is either linear (piecewise linear system) or nonlinear (piecewise nonlinear system). Two systems were studied by constructing bifurcation diagrams, basins of attractions, Lyapunov exponents and parameter plots. In our analysis we focused on the grazing transitions from no impact to impact motion. We observed that the dynamic responses of these two similar systems are qualitatively different around the grazing transitions. For the piecewise linear system, we identified on the parameter space a considerable region with chaotic behaviour, while for the piecewise nonlinear system we found just periodic attractors. We postulate that the structural nonlinearity of the cantilever impacting beam suppresses chaos near grazing.     

Blast Damage Simulation With the Discontinuous Galerkin Finite Element Method of Bond⁃Based Peridynamics北大核心CSCD

近场动力学是一种积分型非局部的连续介质力学理论,已广泛应用于固体材料和结构的非连续变形与破坏分析中,其数值求解方法主要采用无网格粒子类的显式动力学方法.近年来,弱形式近场动力学方程的非连续Galerkin有限元法得到发展,该方法不仅可以描述考察体的非局部作用效应和非连续变形特性,还可以充分利用有限单元法高效求解的特点,并继承了有限元法能直接施加局部边界条件的优点,可有效避免近场动力学的表面效应问题.该文阐述了键型近场动力学的非连续Galerkin有限元法的基本原理,导出了计算列式,给出了具体算法流程和细节,计算模拟了脆性玻璃板动态开裂分叉问题,并对爆炸冲击荷载作用下混凝土板的毁伤过程进行了计算分析.研究结果表明,该方法能够再现爆炸冲击荷载作用下结构的复杂破裂模式和毁伤破坏过程,且具有较高的计算效率,是模拟结构爆炸冲击毁伤效应的一种有效方法.     

用白光散斑方法测量动态变形

本文提出一个简便的,用多火花动光弹仪进行动态变形测量的白光散斑方法,用此方法不但可以进行动态大变形测量[1],也可动态小变形测量.如果和动光弹等色线结合,可以同时获得被测材料的弹性模量、泊松比、材料条纹值参数.     

A higher-order Godunov method for modeling finite deformation in elastic-plastic solids

In this paper we develop a first-order system of conservation laws for finite deformation in solids, describe its characteristic structure, and use this analysis to develop a second-order numerical method for problems involving finite deformation and plasticity. The equations of mass, momentum, and energy conservation in Lagrangian and Eulerian frames of reference are combined with kinetic equations of state for the stress and with caloric equations of state for the internal energy, as well as with auxiliary equations representing equality of mixed partial derivatives of the deformation gradient. Particular attention is paid to the influence of a curl constraint on the deformation gradient, so that the characteristic speeds transform properly between the two frames of reference. Next, we consider models in rate-form for isotropic elastic-plastic materials with work-hardening, and examine the circumstances under which these models lead to hyperbolic systems for the equations of motion. In spite of the fact that these models violate thermodynamic principles in such a way that the acoustic tensor becomes nonsymmetric, we still find that the characteristic speeds are always real for elastic behavior, and essentially always real for plastic response. These results allow us to construct a second-order Godunov method for the computation of three-dimensional displacement in a one-dimensional material viewed in the Lagrangian frame of reference. We also describe a technique for the approximate solution of Riemann problems in order to determine numerical fluxes in this algorithm. Finally, we present numerical examples of the results of the algorithm.