梯度密度黏弹性材料的波传播研究

梯度密度黏弹性材料中波的传播比较复杂。为了研究其在冲击载荷作用下黏弹性响应特征,基于控制方程的Euler形式,利用Laplace变换,得到了这种材料中的波传播规律的一个理论公式;并据此分析了双层周期性黏弹性介质中的应力情况。选择具有梯度密度特性的钛-硼化钛（Ti-TiB₂）材料和碳纤维树脂材料,采用不同的叠合方向和方式,利用分离式霍普金森压杆（split Hopkinson pressure bar,SHPB）加载装置进行了动态冲击实验,并用三波法对得到的实验结果进行处理。同时,采用数值Laplace逆变换方法,结合SHPB测得的入射波与透射波数据,使用推导的理论公式计算出理论解,并与实验结果进行了比较。结果表明:（1）梯度钛-硼化钛材料由于内界面和叠层界面的存在,表现出一定的黏性特性;单层Ti-TiB₂材料的计算结果和三波法分析得到的结果基本一致,双层Ti-TiB₂材料叠合后的计算结果与三波法分析结果存在一定的差异。（2）双层碳纤维树脂材料表现出较强的黏弹性特征,应力波的衰减幅度较大,三波法分析结果与该材料的冲击性能有较大的差异。由此可知,无论是细微观结构特征产生的黏性,还是材料本身的黏性,对材料动力学行为的影响都不可忽略。。     

水下声波传播过程的时域间断Galerkin有限元方法

本文构建了声压波动方程的改进时域间断Galerkin有限元方法.传统时域连续有限元方法在计算高梯度、强间断特征水中声波传播问题时往往会出现虚假数值振荡现象,这些数值振荡会影响正常波动的计算精度.为了解决这一问题,本文通过引入人工阻尼的方式构建了改进的时域间断Galerkin有限元方法,并针对具有高梯度、强间断特征的多障碍物复杂边界和层合液体介质声传播问题进行了计算.计算结果表明,与传统时域连续方法如N ew mark方法计算结果对比,所发展方法能较好地消除高梯度和强间断声压力波传播过程中虚假的数值振荡,具有较高的计算精度.问题的求解为进一步流固声耦合问题的研究奠定了基础.     

Acoustic simulation using a novel approach for reducing dispersion error

It is well‐known that the traditional finite element method (FEM) fails to provide accurate results to the Helmholtz equation with the increase of wave number because of the ‘pollution error’ caused by numerical dispersion. In order to overcome this deficiency, a gradient‐weighted finite element method (GW‐FEM) that combines Shepard interpolation and linear shape functions is proposed in this work. Three‐node triangular and four‐node tetrahedral elements that can be generated automatically are first used to discretize the problem domain in 2D and 3D spaces, respectively. For each independent element, a compacted support domain is then formed based on the element itself and its adjacent elements sharing common edges (or faces). With the aid of Shepard interpolation, a weighted acoustic gradient field is then formulated, which will be further used to construct the discretized system equations through the generalized Galerkin weak form. Numerical examples demonstrate that the present algorithm can significantly reduces the dispersion error in computational acoustics. Copyright © 2016 John Wiley & Sons, Ltd.     

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…     

USING LAPLACE TRANSFORM TO SOLVE THE VISCOELASTIC WAVE PROBLEMS IN THE SHPB EXPERIMENTS

对分离式霍普金森压杆(split Hopkinson pressure bar, SHPB) 实验中试件的黏弹性波传播的控制方程组进行Laplace 变换,并结合恰当的初始-边界条件求解,得到变换域的应力、速度、应变等变量的像函数的精确表达式. 采用该方法处理SHPB 实验中涉及黏弹性试件内部应力非均匀性问题,并给出数值反变换解. 作为特例,对于弹性试件分别采用级数展开法和留数定理进行反Laplace 变换,从而给出弹性夹层介质中应力波传播问题的解析解.     

应力脉冲在SHPB实验中弥散效应的数值模拟与频谱分析

在评判不同材料的整形器对加载波形的改进效果的应用背景下,对比研究了不同形态的应力脉冲在霍普金森压杆(split Hopkinson pressure bar,SHPB)中的弥散效应。利用有限元软件LS-DYNA建立了杆件的三维有限元模型,在杆端分别施加矩形、三角形和半正弦形的应力脉冲,分析了波形振荡、前沿升时和应力峰值随传播距离的变化规律,并运用频谱分析的方法进行了理论解释。结果表明:三角应力脉冲和半正弦应力脉冲在各个方面都比传统的矩形应力脉冲表现出了更小的弥散效应;半正弦应力脉冲在传播过程中比三角应力脉冲更能控制其形态,能有效地减少弥散效应,提高Φ100mm SHPB实验精度,是岩石类非均质材料的理想加载波形;频谱分析的方法能从理论方面有效地解释应力脉冲信号在SHPB实验中的弥散现象。由此可见,波形整形设计的理想目标为具有较宽历时的半正弦应力脉冲。     

Laplace变换法研究SHPB实验中试件的黏弹性波传播问题

对分离式霍普金森压杆(split Hopkinson pressure bar, SHPB) 实验中试件的黏弹性波传播的控制方程组进行Laplace 变换,并结合恰当的初始-边界条件求解,得到变换域的应力、速度、应变等变量的像函数的精确表达式. 采用该方法处理SHPB 实验中涉及黏弹性试件内部应力非均匀性问题,并给出数值反变换解. 作为特例,对于弹性试件分别采用级数展开法和留数定理进行反Laplace 变换,从而给出弹性夹层介质中应力波传播问题的解析解.      

节点梯度光滑有限元配点法

配点法构造简单、计算高效, 但需要用到数值离散形函数的高阶梯度,而传统有限元形函数的梯度在单元边界处通常仅具有C$^{0}$连续性,因此无法直接用于配点法分析. 本文通过引入有限元形函数的光滑梯度,提出了节点梯度光滑有限元配点法. 首先基于广义梯度光滑方法,定义了有限元形函数在节点处的一阶光滑梯度值,然后以有限元形函数为核函数构造了有限元形函数的一阶光滑梯度,进而对一阶光滑梯度直接求导并用一阶光滑梯度替换有限元形函数的标准梯度,即完成了有限元形函数二阶光滑梯度的构造.文中以线性有限元形函数为基础的理论分析表明,其光滑梯度不仅满足传统线性有限元形函数梯度对应的一阶一致性条件,而且在均布网格假定下满足更高一阶的二阶一致性条件.因此与传统线性有限元法相比,基于线性形函数的节点梯度光滑有限元法的$L_{2}$和$H_{1}$误差均具有二次精度,即其$H_{1}$误差收敛阶次比传统有限元法高一阶, 呈现超收敛特性.文中通过典型算例验证了节点梯度光滑有限元配点法的精度和收敛性,特别是其$H_{1}$或能量误差的精度和收敛率都明显高于传统有限元法.      

大直径SHPB弥散效应的二维数值分析

采用轴对称动态有限元HONDO程序对大直径SHPB装置中压杆横向泊松效应引起的应力波弥散进行二维数值分析,并从以下三个方面讨论波形弥散的影响：（1）SHPB装置中压杆直径和杆长对弥散结果（主要是升时）的影响;（2）压杆中的波形弥散对试件应力-应变曲线的影响;（3）弥散对试件应变率的影响。分析表明,在直径SHPB弥散效应对实验结果的影响很大,必须考虑。     

固体中短波传播单位分解有限元法的解析积分

针对固体中短波传播数值模拟的单位分解有限元法中单元矩阵积分的被积函数的强烈振荡特性,应用直角坐标系下标准有限元形函数和单元内的波动方向知识提出了一种单元矩阵的解析积分方案。它对于平面三,六,四,八和九节点的直边单位分解有限单元是完全解析的,对于与这些单元相应的曲边单元则是半解析的。数值结果显示所提出的积分方案在计算效率上比高斯-勒让德积分有大幅度提高。     

A spectrally formulated finite element for wave propagation analysis in functionally graded beams

In this paper, spectral finite element method is employed to analyse the wave propagation behavior in a functionally graded (FG) beam subjected to high frequency impulse loading, which can be either thermal or mechanical. A new spectrally formulated element that has three degrees of freedom per node (based upon the first order shear deformation theory) is developed, which has an exact dynamic stiffness matrix, obtained by exactly solving the homogeneous part of the governing equations in the frequency domain. The element takes into account the variation of thermal and mechanical properties along its depth, which can be modeled either by explicit distribution law like the power law and the exponential law or by rule of mixture as used in composite. Ability of the element in capturing the essential wave propagation behavior other than predicting the propagating shear mode (which appears only at high frequency and is present only in higher order beam theories), is demonstrated. Propagation of stress wave and smoothing of depthwise stress distribution with time is presented. Dependence of cut-off frequency and maximum stress gradient on material properties and FG material (FGM) content is studied. The results are compared with the 2D plane stress FE and 1D Beam FE formulation. The versatility of the method is further demonstrated through the response of FG beam due to short duration highly transient temperature loading.     

高速列车穿越有竖井隧道流场的特性研究

给出了高速列车穿越隧道压力波的三维粘性流场数值模拟过程,控制方程为三维粘性、可压缩、等熵和非定常流的Navier-Stokes方程,空间离散采用了中心有限体积法格式,时间采用预处理二阶精度多步后差分格式进行离散,对隧道壁面采用壁面函数处理。在模拟中考虑了竖井的位置、竖井的断面积、竖井的数目等因素对隧道内压力及压力梯度的影响。计算结果表明,竖井的存在改变了压缩波的波前形状,从而使得隧道内的压力变化的最大值降低,因而能够降低隧道内的压力梯度最大值,但它并不能延长压力上升的时间。     

On the Plastic Wave Propagation Along the Specimen Length in SHPB Test

To observe the plastic wave propagation, an experimental setup is designed with a SHPB facility and a high speed digital camera. Two types of OFHC copper were selected as specimen materials: in the cold work condition and after total annealing, which represent non strain hardening and strain hardening material respectively. The rise time of incident impulse in the SHPB test is relevant to bar’s radius. A maximum allowable specimen length and a maximum allowable impact velocity (MAIV) of striker are proposed for the SHPB test. The propagation of plastic waves is observed along specimen length at the beginning of specimen’s plastic deformation in SHPB test. However, for both types of material, no plastic wave motion is caught along specimen length for large plastic strain level. Side confinement effect of friction is found to be significant, even with lubricant in the experiment.     

夹层聚能装药作用过程的数值模拟

基于凝聚炸药冲击起爆的Lee-Tarver模型,利用AUTODYN有限元计算软件对夹层聚能装药作用过程进行了数值模拟。分别对夹层聚能装药爆轰波形传播过程及其特性参数进行了数值计算,对典型聚能装药采用单一结构装药、夹层装药的射流成型过程进行了数值研究,最后对不同爆速炸药匹配关系的夹层聚能装药射流参数进行了计算分析。计算结果表明,相对于单一结构装药,夹层装药射流头部速度提高了20%,夹层聚能装药能有效提高聚能金属射流头部速度、提高侵彻深度、增加炸药装药的作功能力。     

921A钢纯剪切帽状试件在SHPB实验中的动态变形

应用ANSYS/LS-DYNA软件,开展了一系列基于921A钢纯剪切帽状试件的SHPB数值模拟.结合SHPB系统应力波理论,研究不同加载速率v0(或应力脉冲I(t))下,特别是高应变率(约106 s-1)下的压杆轴向应变波形以及相应的试件动态变形特性,并对高速撞击下压杆中应变波形的适用性作了相关讨论.     

Wave propagation analysis in anisotropic and inhomogeneous uncracked and cracked structures using pseudospectral finite element method

The work deals with the development of an effective numerical tool in the form of pseudospectral method for wave propagation analysis in anisotropic and inhomogeneous structures. Chebyshev polynomials are used as basis functions and Chebyshev–Gauss–Lobatto points are used as grid points. The formulation is implemented in the same way as conventional finite element method. The element is tested successfully on a variety of problems involving isotropic, orthotropic and functionally graded material (FGM) structures. The formulation is validated by performing static, free vibration and wave propagation analysis. The accuracy of the element in predicting stresses is compared with conventional finite elements. Free vibration analysis is carried out on composite and FGM beams and the computational resources saved in each case are presented. Wave propagation analysis is carried out using the element on anisotropic and inhomogeneous beams and layer structures. Wave propagation in thin double bounded media over long propagating distances is studied. Finally, a study on scattering of waves due to embedded horizontal and vertical cracks is carried out, where the effectiveness of modulated pulse in detecting small cracks in composites and FGMs has been demonstrated.     

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。     

有限元畸变单元离散模型中的SH波动

本文采用晶格动力学分析方法,研究了有限元畸变单元离散模型中的SH波的传播规律。结果表明单元畸变对波动规律影响显著,当单元畸变较小时,单元畸变对波动传播并不产生明显的不利影响,当单元畸变较大时,这一影响不可忽略。通过详细分析和对比集中质量、混合质量和一致质量模型中的波动规律,评价了不同有限元模型的抗畸变能力。文中还讨论了时域离散化与单元畸变联合作用对波动传播的影响。     

An investigation of the step-wise propagation of a mode-II fracture in a poroelastic medium

In this paper we use an eXtended Finite Element Method based model for the simulation of shear fracture in fully saturated porous materials. The fracture is incorporated as a strong discontinuity in the displacement field by exploiting the partition of unity property of finite element shape functions. The pressure is assumed to be continuous across the fracture. However, the pressure gradient, i.e. the fluid flow, can be discontinuous. The failure process is described by the cohesive zone approach and a Tresca fracture condition without dilatancy. We investigate the propagation of a shear fracture under compression asking the question whether or not a Tresca criterion can result in stepwise propagation in a poroelastic medium. In order to evaluate possible numerical artefacts, we also look at the influence of the element size and the magnitude of a time increment. The performance of the X-FEM model and the influence of the pore pressure on the fracture propagation are addressed. Our simulations do not show evidence for step wise progression in mode II failure.     

Crashworthiness design of density-graded cellular metals

Crashworthiness of cellular metals with a linear density gradient was analyzed by using cell-based finite element models and shock models. Mechanisms of energy absorption and deformation of graded cellular metals were explored by shock wave propagation analysis. Results show that a positive density gradient is a good choice for protecting the impacting object because it can meet the crashworthiness requirements of high energy absorption, stable impact resistance and low peak stress.