FUNDAMENTAL PROBLEMS IN FINITE ELEMENT SIMULATION OF WAVE MOTION

The transmitting boundary condition is written in a compact form, which can be direct-ly incorporated into finite elements. Basic characteristics of discretization are analyzed throughstudies on wave motion in a one-dimensional discrete model and their differences from those in thecorresponding continuum. Tbe analysis leads to identifying a frequency band within which thesimulation is possible, and to a suggestion of using the lumped-mass finite element model forthe simulation. Mechanism of the oscillation instability is then illuminated in the frequencydomain by amplification at the artificial boundary and multi-reflection of wave motion in afinite discrete model. Based on understanding of the mechanism, a modified transmittingboundary condition is devised for eliminating the instability. The special stability criterion forthe modified boundary is finally presented for the one-dimensional model.

Finite element simulation of steady state SH wave motion

A discrete local transmitting boundary is combined with a lumped-mass finite element technique for simulating steady SH wave motion in a layered and unbounded medium.The combination decouples any node of the finite element model from the others except those in its neighborhood,and an effective algorithm of the Gauss elimination in implementation of the method is then devised to reduce the main memory and computing time.The method and its accuracy are first analysed via simulating steady SH wave motion in layered elastic media,the effective algorithm is then introduced and illustrated by simple examples.

Simulation of near-fault bedrock strong ground-motion field by explicit finite element method

Based on presumed active fault and corresponding model, this paper predicted the near-fault ground motion filed of a scenario earthquake （Mw=6 3/4 ） in an active fault by the explicit finite element method in combination with the source time function with improved transmitting artificial boundary and with high-frequency vibration contained. The results indicate that the improved artificial boundary is stable in numerical computation and the predicted strong ground motion has a consistent characteristic with the observed motion.

Finite element equations and numerical simulation of elastic wave propagation in two-phase anisotropic media

Based on Biot theory of two-phase anisotropic media and Hamilton theory about dynamic problem,finite element equations of elastic wave propagation in two-phase anisotropic media are derived in this paper.Numerical solution of finite element equations is given.Finally,Properties of elastic wave propagation are observed and analyzed through FEM modeling.

Kinematic source model for simulation of near-fault ground motion field using explicit finite element method

This paper briefly reviews the characteristics and major processes of the explicit finite element method in modeling the near-fault ground motion field. The emphasis is on the finite element-related problems in the finite fault source modeling. A modified kinematic source model is presented, in which vibration with some high frequency components is introduced into the traditional slip time function to ensure that the source and ground motion include sufficient high frequency components. The model presented is verified through a simple modeling example. It is shown that the predicted near-fault ground motion field exhibits similar characteristics to those observed in strong motion records, such as the hanging wall effect, vertical effect, fling step effect and velocity pulse effect, etc.

IN-PLANE WAVE MOTION IN FINITE ELEMENT MODEL

The analysis method of lattice dynamics in classical physics is extended to study the properties of in-plane wave motion in the hybrid-mass finite element model in this paper. The dispersion equations of P and SV waves in the discrete model are first obtained by means of separating the characteristic equation of the motion equation, and then used to analyse the properties of P-and SV-homogeneous, inhomogeneous waves and other types of motion in the model. The dispersion characters, cut-off frequencies of P and SV waves, the polarization drift and appendent anisotropic property of wave motion caused by the discretization are finally discussed.

An explicit method for numerical simulation of wave equations: 3D wave motion

In this paper, an explicit method is generalized from 1D and 2D models to a 3D model for numerical simulation of wave motion, and the corresponding recursion formulas are developed for 3D irregular grids. For uniform cubic grids, the approach used to establish stable formulas with 2M-order accuracy is discussed in detail, with M being a positive integer, and is illustrated by establishing second order （M=1） recursion formulas. The theoretical results presented in this paper are demonstrated through numerical testing.

An explicit method for numerical simulation of wave equations

In this paper, a method to develop a hierarchy of explicit recursion formulas for numerical simulation in an irregular grid for scalar wave equations is presented and its accuracy is illustrated via 2-D and 1-D models. Approaches to develop the stable formulas which are of 2M-order accuracy in both time and space with Mbeing a positive integer for regular grids are discussed and illustrated by constructing the second order （M= 1） and the fourth order （M = 2） recursion formulas.

Numerical Simulation of Wave Forces on Seabed Pipelines

A three-step finite element method (FEM) together with Large Eddy Simulation (LES) is applied to incompressible turbulent flow around seabed pipelines at relatively high Reynolds numbers. Both two dimensional and three-dimensional numerical simulation is carried out to determine the three-dimensional effect. The results of numerical simulation agree quite well with the wave forces acting on pipeline models measured in physical model test.

Application of CLEAR-VOF method to wave and flow simulations

A two-dimensional numerical model based on the Navier-Stokes equations and computational Lagrangian-Eulerian advection remap-volume of fluid （CLEAR-VOF） method was developed to simulate wave and flow problems. The Navier-Stokes equations were discretized with a three-step finite element method that has a third-order accuracy. In the CLEAR-VOF method, the VOF function F was calculated in the Lagrangian manner and allowed the complicated free surface to be accurately captured. The propagation of regular waves and solitary waves over a flat bottom, and shoaling and breaking of solitary waves on two different slopes were simulated with this model, and the numerical results agreed with experimental data and theoretical solutions. A benchmark test of dam-collapse flow was also simulated with an unstructured mesh, and the capability of the present model for wave and flow simulations with unstructured meshes, was verified. The results show that the model is effective for numerical simulation of wave and flow problems with both structured and unstructured meshes.

Nonlinear Numerical Analysis of Vortex-Induced Vibration of A Three-Dimensional Deepwater Steep Wave Riser with Large Deformation Features

The cross-flow(CF)vortex-induced vibration(VIV)of a deepwater steep wave riser(SWR)subjected to uniform or shear flow loads is investigated numerically.The model is based on a three-dimensional(3D)nonlinear elastic rod theory coupled with a wake oscillator model.In this numerical simulation,the nonlinear motion equations of the riser with large deformation features are established in a global coordinate system to avoid the transformation between global and local coordinate systems,and are discretized with the time-domain finite element method(FEM).A wakeoscillator model is employed to study the vortex shedding,and the lift force generated by the wake flow is described in a van der Pol equation.A Newmark-βiterative scheme is used to solve their coupling equation for the VIV response of the SWR.The developed model is validated against the existing experimental results for the VIV response of the top-tension riser(TTR).Then,the numerical simulations are executed to determine VIV characteristics of the SWR.The effects of both flow velocity and the spanwise length of the flow field on the drag coefficient in the inline(IL)direction and the lift coefficient in the CF direction are investigated systematically.The results indicate that compared with TTR,the low frequency and multi-modal vibration are the main components of the SWR due to the large deformation and flexible characteristics.For shear flow,the multi-frequency resonance dominates the VIV response of the SWR,especially at the hang-off segment.

Defects detection in typical positions of bend pipes using low-frequency ultrasonic guided wave

In order to analyze the possibility of detecting defects in bend pipe using low-frequency ultrasonic guided wave, the propagation of T(0,1) mode and L(0,2) mode through straight-curved-straight pipe sections was studied. FE(finite element) models of bend pipe without defects and those with defects were introduced to analyze energy distribution, mode transition and defect detection of ultrasonic guided wave. FE simulation results were validated by experiments of four different bend pipes with circumferential defects in different positions. It is shown that most energy of T(0,1) mode or L(0,2) mode focuses on extrados of bend but little passes through intrados of bend, and T(0,1) mode or L(0,2) mode is converted to other possible non-axisymmetric modes when propagating through the bend and the defect after bend respectively. Furthermore, L(0,2) mode is more sensitive to circumferential notch than T(0,1) mode. The results of this work are beneficial for practical testing of pipes.

高载能超声骨刀的优化设计与性能评估

针对超声骨刀在手术过程中切割效率低和产生骨组织热损伤的问题,设计了具有二级放大结构的高载能超声骨刀。基于驻波理论的等效长度法,结合有限元仿真对其二级放大结构进行设计和优化,测试了其振动性能并进行了骨切割试验。结果表明:具有二级放大结构的超声骨刀的谐振频率为23306 Hz,振幅为140μm,骨切割表面平整且无损伤,满足临床手术需求。

STABILITY FOR IMPOSING ABSORBING BOUNDARY CONDITIONS IN THE FINITE ELEMENT SIMULATION OF ACOUSTIC WAVE PROPAGATION＊

It is well-known that artificial boundary conditions are crucial for the efficient and accurate computations of wavefields on unbounded domains. In this paper, we investigate stability analysis for the wave equation coupled with the first and the second order absorbing boundary conditions. The computational scheme is also developed. The approach allows the absorbing boundary conditions to be naturally imposed, which makes it easier for us to construct high order schemes for the absorbing boundary conditions. A thirdorder Lagrange finite element method with mass lumping is applied to obtain the spatial discretization of the wave equation. The resulting scheme is stable and is very efficient since no matrix inversion is needed at each time step. Moreover, we have shown both abstract and explicit conditional stability results for the fully-discrete schemes. The results are helpful for designing computational parameters in computations. Numerical computations are illustrated to show the efficiency and accuracy of our method. In particular, essentially no boundary reflection is seen at the artificial boundaries.

边缘空气层薄膜体声波谐振器的设计与制备

压电薄膜存在固有的对压电效应的非线性迟滞响应,并且声波有向边缘传播的横波分量,二者都会产生声波的能量损耗。该文设计了一种具有边缘空气层结构的单晶氮化铝薄膜体声波谐振器,可以减小非线性迟滞的机电损耗并阻止横波能量泄露,提高谐振器的品质因数。使用COMSOL对设计的器件进行有限元模拟仿真,并成功制备出具有边缘空气层结构的谐振器进行测试验证。

基于不同桩基模拟方式的大块式基础动力数值分析

为了更合理预测采用桩基的大块式基础的动力特性,建立桩基仿真模型并与桩-土动力试验相互验证,对组合桩基模型与大块式基础模型进行有限元数值分析,同时参考设计院所使用以弹簧单元模拟桩基的方式,建立数值模型并进行分析,探讨不同的桩基模拟方式对大块式基础动力特性的影响。研究结果表明:使用弹簧单元模拟桩基的方式忽略桩土质量、阻尼的影响,会造成大块式基础振型缺失、自振频率整体偏大、强迫振动响应被放大;使用桩基仿真模型更能反映大块式基础动力特性但计算成本增加。上述结论可为采用桩基的大块式基础动力特性研究提供参考。

基于车用永磁同步电机转子结构的电磁噪声优化仿真分析

针对目标电机低速加速段中存在明显类似“口哨”的高频噪声的问题及电机量产降本原则,将48槽8极峰值功率62 kW的乘用车前驱动电机作为案例进行电磁方案设计。基于设计指标及存在问题设计了定子结构相同内置式转子拓扑结构不同的优化方案,推导计算了两电机方案气隙磁场幅值波形时空分布方程及电磁力表达式,建立了两电机方案有限元模型及电磁-结构声场耦合模型,仿真分析比较两电机气隙磁密及径向电磁力谐波含量。基于仿真结果得到优化方案,在不牺牲电磁性能的前提下削弱了低速段加速过程的0阶6f1径向电磁力,并使磁钢用量从1.474 kg降低到了1.371 kg,实现了降本目的。最后分别制作样机进行实验验证,结果表明优化方案明显削弱了低速段径向振动,降低了24倍频电磁噪声,与仿真结果相吻合。

高过载下环氧树脂保护作用分析

为了研究环氧树脂在高过载环境下对弹体内关键零部件的保护作用,使用Ls-dyna有限元软件对同等外径下三种高度的灌封体在三种不同速度下的九种工况进行冲击过载仿真,用以确定应力波在高度范围内的传递衰减特性,选择所受应力最小的高度范围作为放置线路板的最佳高度。在最佳高度范围内加入线路板对整体灌封组进行冲击过载仿真实验,分析线路板周围应力分布及灌封胶对线路板的保护作用;之后通过冲击试验台对灌封组件进行了冲击过载试验,检测结果表明线路板遭受高过载后功能性完好。

A varying time-step explicit numerical inte-gration algorithm for solving motion equa-tion

If a traditional explicit numerical integration algorithm is used to solve motion equation in the finite element simulation of wave motion, the time-step used by numerical integration is the smallest time-step restricted by the stability criterion in computational region. However, the excessively small time-step is usually unnecessary for a large portion of computational region. In this paper, a varying time-step explicit numerical integration algorithm is introduced, and its basic idea is to use different time-step restricted by the stability criterion in different computational region. Finally, the feasibility of the algorithm and its effect on calculating precision are verified by numerical test.

椎管重建内固定术有限元模型的构建及稳定性分析

目的:构建椎管重建内固定术的有限元模型,并分析椎管重建内固定术对脊柱稳定性的影响,验证椎管重建内固定术在椎管内手术中的有效性和可靠性。方法:筛选1名30岁男性,身高172 cm,体重75 kg的健康志愿者并采集其腰椎CT资料,建立正常腰椎L3-L5的有限元模型,并与体外实体结果和已发表的有限元分析结果进行比较,以验证该模型的有效性。根据处理方式不同分为正常组、椎板切除组和椎管重建组。在相同边界固定和生理载荷条件下,实施前屈、后伸、左弯、右弯、左旋和右旋6种工况活动,分析6种工况活动下L3-L4和L4-L5观察节段的活动度(range of motion,ROM)和L3-L5整体最大ROM的变化情况。结果:构建的L3-L5有限元模型各节段ROM位移与体外实体结果和既往文献数据结果吻合,确认了该模型的有效性。在L3-L4中,椎管重建组仅在后伸时较正常组增加,ROM变化百分比>5%;其他工况下的ROM与正常组相近,变化百分比<5%;而椎板切除组在前屈、后伸、左旋和右旋时的ROM较正常组和椎管重建组增加,变化百分比>5%。在L4-L5中,椎管重建组,在各工况下的ROM与正常组相近,变化百分比<5%,而椎板切除组在6种工况下的ROM均大于正常组和椎管重建组,变化百分比>5%。在L3-L5的整体最大ROM中,椎管重建组仅在后伸时超过正常组,变化百分比>5%;而椎板切除在前屈、后伸、左旋和右旋时大于正常组和椎管重建组,变化百分比>5%。L3-L5各节段ROM及总体ROM的变化趋势为:椎板切除组>椎管重建组>正常组。结论:椎板切除会严重影响脊柱生物力学的稳定性,而应用椎管重建内固定的方式可有效减少脊柱责任节段的ROM位移并维持其生物力学稳定性。