有限元离散模型中的出平面波动

采用分离变量技术,将二维出平面(Anti-Plane)波动问题的有限元运动方程化为两个联立的一维方程,获得了这一离散模型中波动的解析解,由此对有限元离散模型中出平面波动问题进行了深入的研究。分析了出平面弹性波的频散、截止频率、寄生振荡和有限元离散化引起的波传播的附加的各向异性性质等,同时讨论了时域离散化对出平面波动规律的影响。     

三维离散网格中的弹性波动

本文采用形式解法研究三维有限元离散模型中波动的传播规律。文中由波动方程得到它的特征方程，进而给出了三维离散网格中波的频散关系，分析了三维网格中平面波、非匀匀波、寄生振荡及其它可能存在的运动形式的基本特点；详细讨论了平面波的频散、截止频率及偏振漂移等重要的不同于连续介质中的波动传播性质的特点，提示了其中不同于低维网格中 波动的现象。     

弹性半空间二维出平面自由波场的一维化时域算法

提出了一种计算出平面SH波斜入射时弹性半空间自由波场时域计算的一维化有限元方法。首先利用Snell定律确定平面波沿水平方向的传播规律,在用有限元法对弹性半空间进行离散化时,竖向单元尺寸根据波动有限元模拟精度要求确定,而水平向有限元网格尺寸根据水平向波的传播规律和采用的离散时间步长确定,使得有限元离散模型中任意节点的运动可以用水平向相邻节点的运动表示,从而将二维有限元节点运动方程组化为一维的形式。求解此一维方程组,可得到弹性半空间中一列节点的运动,再根据行波的传播规律,可确定全空间自由波场。理论分析和数值算例表明,该方法具有较高的精度和良好的稳定性。     

针对有砟道床动力特性分析的嵌入式离散元-有限元耦合方法

在离散元-有限元耦合方法中,离散元和有限元交界面处的耦合方式对整体有砟道床的力学行为影响显著.采用基于球形单元的镶嵌单元或粘结单元模拟有砟道床时,由于球形单元和有限单元表面的自锁能力较差,使道砟层在列车载荷作用下容易产生侧向滑移,导致数值模型不稳定.此外,在实际铁路道床中,底部道砟均不同程度地嵌入路堤.为此,发展了一种嵌入式离散元-有限元耦合方法,通过设置一层嵌入地基有限元模型中的球形颗粒传递离散元域和有限元域间的力学参数,实现离散元和有限元方法的耦合.数值结果表明,嵌入式离散元-有限元耦合模型能够有效降低有砟道床的侧向位移,数值结果更加稳定,在处理与有砟道床类似的连续介质与散体介质的耦合问题时推荐采用嵌入式耦合算法.     

局部透射边界和叠加边界的精度分析与比较

本文研究了出平面和平面内波动在局部透射边界和叠加边界的反射系数，在研究中考虑了时空离散化的影响及反射波本身对反射系数的影响．采用一维有限元离散模型讨论了两种边界的阶数对反射系数的影响．通过比较这两种边界的反射系数得出以下结论：局部透射边界在有限元波动模拟中的精度高于叠加边界，且其优越性随着边界阶数的增加而提高。     

二维波动方程的动态有限元离散化的频散研究

本文利用二维波动方程，推导出波在单元内行进的动态形函数，在此基础上，得到了波在离散体内传播的频散关系，利用这一关系式，绘出了频谱曲线，分析表明：波在离散体内传播的频散程度不仅与波的传播方向有关而且与单元的质量分布，网格划分有密切的关系。     

构造几何不敏感四边形膜元的广义协调方法

许多有限元模型在规则网格下具有很高的精度，但当网格畸变程度增大时，其计算精度也随之迅速下降．如何构造出对网格畸变不敏感的单元，长期以来是人们十分关注的课题．本文应用作者早期提出的广义协调方法，构造出具有平面内旋转自由度的任意四边形膜元．该单元不仅列式简洁，而且具有对网格畸变极不敏感的优异性能，为构造对网格畸变不敏感的优质单元提供了一个通用方法     

二维波动方程的动态有限元离散化的频散研究

本文利用二维波动方程，推导出波在单元内行进的动态形函数，在此基础上，得到了波在离散体内传播的频散关系，利用这一关系式，绘出了频谱曲线．分析表明：波在离散体内传播的频散程度不仅与波的传播方向有关而且与单元的质量分布、网格划分有密切的关系．     

三维自适应FE-SPH耦合算法在多层间隔金属靶侵彻问题中的应用

鉴于有限元算法不能有效地模拟侵彻过程所产生的金属碎片, 本文中基于三维自适应FE-SPH耦合算法的基本理论, 自主开发了模拟多层间隔金属靶侵彻问题的三维FE-SPH耦合计算程序。该程序采用四面体单元对多层间隔金属靶侵彻模型进行初始离散, 计算过程中, 当四面体单元等效塑性应变超过某一设定值时, 单元自动转化为SPH粒子, 并引入有限单元-粒子接触算法和耦合算法, 实现大变形和破碎区域采用SPH方法计算, 克服有限元法单元畸变存在的问题。多层间隔靶侵彻算例分析表明, 三维FE-SPH耦合计算程序采用等效塑性应变作为转化判据计算结果较稳定, 并且能够有效地再现侵彻过程中所产生的碎片, 能够模拟侵彻碎片对后层靶的毁伤效应。     

滞后细观模型在岩石力学中的应用

对以砂岩为代表的所谓``NME材料'的力学行为研究方面的一些新的概念和模型进行了评介.首先介绍了一种基于所谓``滞后单元'的描述滞后现象的物理模型------Preisach-Mayergoyz(P-M)模型,然后详细阐述了P-M模型应用于模拟岩石的非线性滞后应力应变关系的过程和结果.这种唯象模型很好地描述了宏观上的滞后表现和``离散记忆'效应.接着本文对应变能耗散的力学机制进行了简单分析. 最后,介绍了一种描述弹性波在``NME材料'中传播规律的数学方法, 该方法从一般的弹性波传播规律出发,分析了``NME材料'特殊的力学性质给弹性波传播带来的影响,揭示了产生特殊的弹性波传播规律的原因.      

An efficient RPIM for simulating wave motions in saturated porous media

An efficient meshless technique for simulating wave motions in saturated porous media is introduced in this paper. Using radial point interpolation method (RPIM) and considering the precision requirement in wave motion simulation, a lumped-mass RPIM for saturated porous media with clear physical concepts is derived. Combining explicit time integration with the lumped-mass RPIM leads to a decoupled radial point interpolation method (decoupled RPIM) for dynamic analysis without solving algebra equation set. A two-dimensional problem is calculated by the proposed decoupled RPIM, the ordinary RPIM, and the finite element method (FEM). The accuracy and efficiency of these methods are compared, which demonstrate that the proposed decoupled RPIM has comparable accuracy with the ordinary RPIM and the finite element method, but has high efficiency in simulating wave motions in saturated porous media.     

ELASTIC WAVES IN 3-D DISCRETE GRIDS

Wave motion in finite element models presents some characteristics different from thoseof wave motion in continuum,which leads to the errors and other special phenomena in finite elementsimulation of wave motion.The wave propagation in a 3-D finite element model is studied by utilizingthe formal solution in the paper,and the corresponding dispersion relations are derived.Then the mainproperties of wave motion in 3-D grids such as dispersion,cut-off frequency and polarization drift arediscussed.Characteristics different from those of wave motion in 2—D grids are revealed.     

成层半空间出平面自由波场的一维化时域算法

提出了一种计算出平面SH波斜入射时弹性水平成层半空间中自由波场时域计算的一维化有 限元方法. 在进行有限元网格划分时，竖向单元取满足有限元模拟精度的任意尺寸，水平向 网格尺寸由时间离散步长和水平视波速确定，并自动进行虚拟网格划分. 基底设置人工边界， 并将波动输入转化为等效荷载施加在边界节点上. 然后将集中质量有限元法和中心差分法相 结合建立节点运动方程，并将水平方向相邻节点的运动用该节点相邻时刻的运动表示，从而 将求解节点运动的二维方程组转化为一维方程组. 求解此方程组，即得到自由场中竖向一列 节点的运动. 最后根据行波传播的特点，可方便地确定全部自由波场. 理论分析和数值算例 表明，该方法具有较高的精度和良好的稳定性.     

Free vibration characteristics of sectioned unidirectional/bidirectional functionally graded material cantilever beams based on finite element analysis

Advancements in manufacturing technology, including the rapid development of additive manufacturing (AM), allow the fabrication of complex functionally graded material (FGM) sectioned beams. Portions of these beams may be made from different materials with possibly different gradients of material properties. The present work proposes models to investigate the free vibration of FGM sectioned beams based on onedimensional (1D) finite element analysis. For this purpose, a sample beam is divided into discrete elements, and the total energy stored in each element during vibration is computed by considering either the Timoshenko or Euler-Bernoulli beam theory. Then, Hamilton's principle is used to derive the equations of motion for the beam. The effects of material properties and dimensions of FGM sections on the beam's natural frequencies and their corresponding mode shapes are then investigated based on a dynamic Timoshenko model (TM). The presented model is validated by comparison with three-dimensional (3D) finite element simulations of the first three mode shapes of the beam.     

PARTITION OF UNITY FINITE ELEMENT METHOD FOR SHORT WAVE PROPAGATION IN SOLIDS

IntroductionIt is known that standard finite element procedure is unable to simulate the wavepropagation with high oscillations or gradients in space in the media with reasonableefficiency and accuracy due to the nature of polynomial interpolation approxi…     

Synthesis of highly convergent 2D and 3D finite elements for short acoustic wave simulation

New higher-order finite elements of enhanced convergence properties for acoustic wave simulation are presented in the paper. The element matrices are obtained by combining modal synthesis and optimization techniques in order to achieve minimum errors of higher modes of the computational domain. As a result, simulation models of propagating wave pulses require a smaller number of finite element divisions per wavelength compared to the conventional element model thus significantly reducing computational costs. Though finite element matrices are obtained in optimization, the resulting patterns of the matrices are versatile and further can be used in any wave propagation model. The mass matrices of the elements are diagonal, so explicit time integration schemes are applicable. The usage of new elements is especially efficient in situations where wavelengths of the simulated signal are much shorter than the dimensions of the computational domain. This is referred to as short wave propagation analysis. The results of wave propagation simulation for ultrasonic measurements are presented as application examples. The B-scans and computed dispersion curves are provided for visual interpretation of the results.