Plastic shear deformation of a thin strain-hardening disc: variational principles

An analytical solution is derived for the problem of shearing of a thin disc of incompressible rigid, plastic strain-hardening material. The solution is obtained by a methodology introduced by the author in previous publications, relying fundamentally on continuity of the rotation-rate vector field. A variational theorem is derived which shows that the velocity vector field is unique if the boundary values are properly prescribed. The derived solution is compared to experiments, with which it shows good agreement.     

Laser cutting of thick sheet metals: Residual stress analysis

Laser cutting of tailored blanks from a thick mild steel sheet is considered. Temperature and stress field in the cutting sections are modeled using the finite element method. The residual stress developed in the cutting section is determined using the X-ray diffraction (XRD) technique and is compared with the predictions. The structural and morphological changes in the cut section are examined using the optical microscopy and scanning electron microscopy (SEM). It is found that temperature and von Mises stress increase sharply in the cutting section, particularly in the direction normal to the cutting direction. The residual stress remains high in the region close to the cutting section.     

Vibration characteristics of aluminum surface subjected to ultrasonic waves and their effect on wetting behavior of solder droplets

The vibration characteristics of an aluminum surface subjected to ultrasonic waves were investigated with a combination of numerical simulation and experimental testing. The wetting behavior of solder droplets on the vibrating aluminum surface was also examined. The results show that the vibration pattern of the aluminum surface is inhomogeneous. The amplitude of the aluminum surface exceeds the excitation amplitude in some zones, while the amplitude decreases nearly to zero in other zones. The distribution of the zero-amplitude zones is much less dependent on the strength of the vibration than on the location of the vibration source. The surface of the liquid solder vibrates at an ultrasonic frequency that is higher than the vibration source, and the amplitude of the liquid solder is almost twice that of the aluminum surface. The vibration of the surface of the base metal (liquid solder) correlates with the oxide film removal effect. Significant removal of the oxide film can be achieved within 2 s when the amplitude of the aluminum surface is higher than 5.4 μm or when the amplitude of the liquid solder surface is higher than 10.2 μm.     

自混合干涉效应的一般模型及其仿真

从自混合干涉效应的等效结构出发,建立了该效应的一般模型。该模型包含了多重光反馈和多模激光的自混合干涉效应等情况,并且可以转化为以往所报道的弱光反馈水平的弱光模型和单模条件下的一般激光自混合干涉模型,明确了模型中各个参数的物理意义,对自混合干涉理论的研究提供了很好的理论指导。对单模的几种情况分别进行了数值仿真,仿真结果很好地验证了模型的正确性。     

On discretization errors and subgrid scale model implementations in large eddy simulations

We analyze the impact of discretization errors on the performance of the Smagorinsky model in large eddy simulations (LES). To avoid difficulties related to solid boundaries, we focus on decaying homogeneous turbulence. It is shown that two numerical implementations of the model in the same finite volume code lead to significantly different results in terms of kinetic energy decay, time evolutions of the viscous dissipation and kinetic energy spectra. In comparison with spectral LES results, excellent predictions are however obtained with a novel formulation of the model derived from the discrete Navier–Stokes equations. We also highlight the effect of discretization errors on the measurement of physical quantities that involve scales close to the grid resolution.     

二元混合燃料在靶丸内壁形成均匀液体层的数学模型

 提出了一个数学模型,描述了二元混合燃料H-D和D-T在ICF低温靶丸内壁形成均匀液体层时,远端场的温度梯度和工作温度间的关系。在靶竖直方向施加一个温度梯度后,模型显示将在气液界面产生一个垂直向上的张力梯度,它将液体从靶丸底部拉到上部,适当的张力梯度抵消了重力对液层的作用,在靶丸的内壁形成了均匀的液体层。通过运用ANSYS软件对靶丸的导热情况进行了有限元分析,模型计算结果与Kim的实验数据吻合得较好,温度梯度的变化趋势也是相似的。     

Probabilistic approaches to compute uncertainty intervals and sensitivity factors of ultrasonic simulations of a weld inspection

For comprehension purpose, numerical computations are more and more used to simulate the propagation phenomena observed during experimental inspections. However, the good agreement between experimental and simulated data necessitates the use of accurate input data and thus a good characterization of the inspected material. Generally the input data are provided by experimental measurements and are consequently tainted with uncertainties. Thus, it becomes necessary to evaluate the impact of these uncertainties on the outputs of the numerical model. The aim of this study is to perform a probabilistic analysis of an ultrasonic inspection of an austenitic weld containing a manufactured defect based on advanced techniques such as polynomial chaos expansions and computation of sensitivity factors (Sobol, DGSM). The simulation of this configuration with the finite element code ATHENA2D was performed 6000 times with variations of the input parameters (the columnar grain orientation and the elastic constants of the material). The 6000 sets of input parameters were obtained from adapted statistical laws. The output parameters (the amplitude and the position of the defect echo) distributions were then analyzed and the 95% confidence intervals were determined.     

Spatial and temporal thermal analysis of acousto-optic deflectors using finite element analysis model

Thermal effects greatly influence the optical properties of the acousto-optic deflectors (AODs). Thermal analysis plays an important role in modern AOD design. However, the lack of an effective method of analysis limits the prediction in the thermal performance. In this paper, we propose a finite element analysis model to analyze the thermal effects of a TeO₂-based AOD. Both transducer heating and acoustic absorption are considered as thermal sources. The anisotropy of sound propagation is taken into account for determining the acoustic absorption. Based on this model, a transient thermal analysis is employed using ANSYS software. The spatial temperature distributions in the crystal and the temperature changes over time are acquired. The simulation results are validated by experimental results. The effect of heat source and heat convection on temperature distribution is discussed. This numerical model and analytical method of thermal analysis would be helpful in the thermal design and practical applications of AODs.     

超声辅助滚压系统的设计与研究*

鉴于风力发电机组主轴的复杂工作情况和疲劳断裂失效形式,提出一种基于表面强化技术的超声辅助滚压加工系统;首先基于运动合成原理,获得了滚轮接触线的运动轨迹特征,并应用ANSYS/LS-DYNA软件分析了加工过程的特点;之后,基于一维振动理论、等效波长理论与牛顿迭代理论,推导了并求解了复合变幅杆的频率方程,实现了该复合变幅杆的纵向振动。通过对该变幅杆进行有限元仿真分析与振动特性测试,结果表明二者相对设计频率的偏差仅在0.817％以内。最后,通过对40Cr主轴进行超声辅助滚压测试,结果获得了粗糙度Ra 0.085μm和表面硬度32.2HRC的加工表面,较普通滚压加工粗糙度降低了69.1％,显微硬度提高了60％。     

带有锥形孔的复合变幅杆设计及动态分析

在超声振动拉丝加工过程中,为了实现线材的顺利拉拔,需要应用带有锥形孔的复合变幅杆。为此,本文基于等效四端网络与传输矩阵法,建立了带锥形孔圆锥变幅杆的传输矩阵,推导出带锥形孔圆锥过渡复合变幅杆的频率方程的一般公式。根据推导出的频率方程,应用区间搜索法和牛顿迭代法获取了准确的数值解,实现了该复合变幅杆的纵向振动。之后,应用有限元软件Ansys对设计出的复合变幅杆分别进行模态分析和动力学特性分析,获得了各段不同长度下复合变幅杆谐振频率、放大系数以及最大应力值的变化规律。最后,对制造出的复合变幅杆进行阻抗与振动性能测试,结果表明其频率准确,且振幅比较稳定。     

Piano soundboard: structural behavior, numerical and experimental study in the modal range

The low frequency broadband vibrational behavior of a piano soundboard is considered. Attention is focused on the ability of finite element models and analytical models to predict precisely the behavior of such a complicated structure—especially with its orthotropy and rib effects. In order to validate these abilities, an experimental modal analysis, considered as the reference, is compared first with a numerical calculation and then with an analytical modeling of the modal basis of the same soundboard. The high structural complexity of the soundboard exceeds the analytical capabilities, but agreement is very good for the numerical model, in the frequency domain, and equally in the spatial one. The final aim is to generate a numerical tool for designing and optimizing piano soundboards.     

Determination of propagation constants in a Ti:LiNbO3 optical waveguide by using finite element and variational methods

The finite element and variational methods are used to determine the propagation constants in a titanium indiffused lithium niobate waveguide with the reconstructed refractive index profile (in depth) from the near field measurements. A subsequent second diffusion of magnesium affects the shape of the calculated electric field and we have defined an effective depth of the profile.     

Design and thermal analysis of electrically calibrated pyroelectric detector

A finite element model was set up by ANSYS to optimize the structure of an electrically calibrated detector and simulate the thermal diffusivity. High-performance relaxor-based ferroelectric crystals were selected as the detector materials. Gold-black was selected as the black coating on the surface of the calibrated pyroelectric detector. The finite element model was set up by ANSYS and the geometry model was meshed appropriately. The optimized structure stood out from the several feasible structures. The simulation results showed that the differences of ΔT on the top surface of PMN-PT crystal between radiant and electrical heating decrease with the increase of sensitive area. The sensitive area of the detector is 10 mm × 10 mm and the entrance aperture is ∅ 8 mm. In this condition, the differences of ΔT are 1.20%. An electrically calibrated pyroelectric detector was fabricated according to the simulation results.     

Fluid mechanics in rectangular cavities — analytical model and numerics

We present an analytical model of Stokes creeping flows in rectangular cavities. In the model, the fluid normal velocity at the wall is zero, while the fluid tangential velocity at the wall differs from the wall velocity. Numerical work is used to validate some of the ideas generated from this realizable model.     

Applicability of locally reacting boundary conditions to porous material layer backed by rigid wall: Wave-based numerical study in non-diffuse sound field with unevenly distributed sound absorbing surfaces

To clarify the applicability of locally reacting boundary conditions in wave-based numerical analyses of sound fields in rooms, we numerically analyzed a non-diffuse sound field in a room with unevenly distributed sound absorbing surfaces and investigated the differences between the extended and local reactions. Each absorbing surface was a porous material layer backed by a rigid wall. Simulations were performed by the fast multipole boundary element method, a highly efficient boundary element method using the fast multipole method. At low frequencies, the extended and local reactions yielded similar reverberation decay curves because of the influence of the room. However, when the random incidence absorption coefficients were small at low frequencies or frequencies were high, the difference was greater than expected from the corresponding Eyring decay lines. We conclude at high frequencies, the locally reacting boundary conditions lead to a longer reverberation time than that expected from the absorption coefficient differences between the extended and local reactions. These differences were similar in sound-pressure-level and sound-intensity-level distributions, and in the oblique incidence absorption coefficient of the absorbing surfaces, but were increased at low frequencies.     

Comparison of analytical and numerical analysis of the reference region model for DCE-MRI

This study compared three methods for analyzing DCE-MRI data with a reference region (RR) model: a linear least-square fitting with numerical analysis (LLSQ-N), a nonlinear least-square fitting with numerical analysis (NLSQ-N), and an analytical analysis (NLSQ-A). The accuracy and precision of estimating the pharmacokinetic parameter ratios K_R and V_R, where K_R is defined as a ratio between the two volume transfer constants, K^trans,TOI and K^trans,RR, and V_R is the ratio between the two extracellular extravascular volumes, v_e,TOI and v_e,RR, were assessed using simulations under various signal-to-noise ratios (SNRs) and temporal resolutions (4, 6, 30, and 60 s). When no noise was added, the simulations showed that the mean percent error (MPE) for the estimated K_R and V_R using the LLSQ-N and NLSQ-N methods ranged from 1.2% to 31.6% with various temporal resolutions while the NLSQ-A method maintained a very high accuracy (< 1.0×10^− 4 %) regardless of the temporal resolution. The simulation also indicated that the LLSQ-N and NLSQ-N methods appear to underestimate the parameter ratios more than the NLSQ-A method. In addition, seven in vivo DCE-MRI datasets from spontaneously occurring canine brain tumors were analyzed with each method. Results for the in vivo study showed that K_R (ranging from 0.63 to 3.11) and V_R (ranging from 2.82 to 19.16) for the NLSQ-A method were both higher than results for the other two methods (K_R ranging from 0.01 to 1.29 and V_R ranging from 1.48 to 19.59). A temporal downsampling experiment showed that the averaged percent error for the NLSQ-A method (8.45%) was lower than the other two methods (22.97% for LLSQ-N and 65.02% for NLSQ-N) for K_R, and the averaged percent error for the NLSQ-A method (6.33%) was lower than the other two methods (6.57% for LLSQ-N and 13.66% for NLSQ-N) for V_R. Using simulations, we showed that the NLSQ-A method can estimate the ratios of pharmacokinetic parameters more accurately and precisely than the NLSQ-N and LLSQ-N methods over various SNRs and temporal resolutions. All simulations were validated with in vivo DCE MRI data.     

Thermorefractive noise in whispering gallery mode microresonators: Analytical results and numerical simulation

We demonstrate numerical finite element simulation of thermorefractive noise in whispering gallery mode cavities and compare the results with known experimental data and analytical derivations. We show that thermal interaction of the microcavity with environment is very significant, making particular geometry significant for the noise spectral density at low frequencies.     

大口径薄型光学镜面支撑方案的优化设计

 针对薄型光学镜面支撑过程中的主动施力过程,建立了一个1维分析模型。利用该模型,采用有限元法对一个口径为300 mm、直径与厚度比为40的薄型光学镜面,利用离散支撑方案,针对4种镜面变形进行了计算,得到了实现变形要求所需施加力的大小。使用零阶优化方法中的子问题逼近法对施力位置、施力大小进行了具体优化。分析结果显示：优化后的镜面变形与目标形状更接近,最大平均差值比优化前减小了58%。     

Combined wave and ray based room acoustic simulations of audio systems in car passenger compartments,Part II: Comparison of simulations and measurements

The present series of papers summarizes the results of a three-year research project on the realistic simulation of sound fields in car passenger compartments using a combined Finite Element (FE) and Geometrical Acoustics (GA) approach. The simulations are conducted for the whole audible frequency range with the loudspeakers of the car audio system as the sound sources. The challenges faced during the project relate to fundamental questions regarding the realistic sound field simulation in small enclosures with strong modal and diffraction effects. While Part I of this series of papers focusses on the determination of the boundary and source conditions for the simulation model of the car compartment, the present paper, denoted here as Part II, presents extensive objective and subjective comparisons of the corresponding room acoustic measurement and simulation results.By applying the FE method to the low frequency part of the room transfer function (RTF) the study aims at the quantification of potential objective and subjective benefits with regard to the simulation quality in small rooms, when compared to a purely geometrical acoustics approach. The main challenges and limitations in the simulation domain are due to the very small volume, the difficult to determine source and boundary conditions and the considerable diffraction effects (especially at the seats) in the car passenger compartments. In order to keep the complexity of the FE simulations at a manageable level, all boundary conditions were described by acoustic surface impedances and no fluid-structural coupling was considered in the FE simulation model.While the results of the study reveal that an overall good agreement regarding the energy distribution in time and frequency domain is generally possible even in such complex enclosures, the results also clearly show the limitations of the impedance boundary approach in the FE domain as well as the strong sensitivity of the simulation results with regard to the uncertainty in the boundary and source conditions in both simulation domains. It can thus be concluded, that possible fields of application of the FE extension in room acoustic simulations lie in the prediction of the modally dominated low frequency part of the RTF of well defined rooms and in the prediction of sound fields that are strongly affected by near-field or diffraction effects as in the car passenger compartment. However, due to the considerable problems in the determination of realistic boundary conditions for the FE model, improved measurement techniques are urgently needed to further improve the overall simulation quality.     

Self-consistent Shaw optimized model potential: Application to the determination of structural and atomic transport properties of liquid alkali metals by molecular dynamics simulations

The ‘first-principles’ fully non-local and energy-dependent optimized model potential (OMP) derived by Shaw is developed further. In contrast to Shaw's original paper, OMP parameters are derived in a self-consistent manner that does not rely on knowledge of experimental values of the ionization and cohesive energies. To our knowledge, this is the first time that this method has been used for effective potential calculations. In an application to liquid Li, Na, and K alkali metals, we used OMP pseudopotential-based interactions between ions to carry out standard molecular dynamics simulations. In the calculations, the ionic structure for the liquid state was first checked at a temperature near the melting point. Similar accurate calculations, but for atomic transport properties, predict the temperature dependence of the self-diffusion coefficients. The theoretical results obtained are in overall agreement with available experimental measurements. Thus, one can have some confidence in the ability of the optimized model potential to give a good representation of the physical properties of these alkali ions in the liquid environment.