用圆孔内单边裂纹平台巴西圆盘和实验-数值-解析法确定砂岩的动态起裂和扩展韧度

在I型(张开型)动态断裂实验中,利用大直径(?100 mm)分离式霍普金森压杆径向冲击圆孔内单边裂纹平台巴西圆盘试样。考虑了材料惯性效应和裂纹扩展速度对动态应力强度因子的影响,用实验-数值-解析法确定了高加载率和高裂纹扩展速度情况下,砂岩的动态起裂韧度和动态扩展韧度。由动态实验获取试样的动荷载历程,采用裂纹扩展计(Crack Propagation Gauge,CPG)测定试样断裂时刻和裂纹扩展速度,获得裂纹扩展速度对应的普适函数值。然后将动荷载历程带入到有限元软件中进行动态数值模拟,求出静止裂纹的动态应力强度因子历程,再用普适函数值对其进行近似修正。最后根据试样的起裂时刻和穿过CPG中点的时刻,由相应的动态应力强度因子历程分别确定砂岩的动态起裂和动态扩展韧度,它们分别随动态加载率和裂纹扩展速度的提高而增加。

用SHPB径向冲击边裂纹平台圆环(ECFR)的动态断裂实验

为了研究岩石的Ⅰ型动态断裂韧度测试方法,用大直径(100 mm)分离式霍普金森压杆(SHPB)对边裂纹平台圆环(edge cracked flattened ring,ECFR)砂岩试样进行径向冲击实验。分别用普通应变片和高精度裂纹扩展计2种测试元件监测试样起裂时刻和测定裂纹传播速度,比较了它们的准确性和合理性。用实验-数值结合普适函数分析测定了砂岩的动态起裂韧度和动态扩展韧度,初步探讨了动态加载率影响动态起裂韧度的原因,以及裂纹扩展速度对动态扩展韧度的影响,对ECFR试样裂纹扩展路径弯折现象也进行了理论分析。研究结果表明:裂纹扩展计测定比应变片更为灵敏、准确、合理。加载率在(0.74~4.48)×104MPa·m1/2/s范围内动态起裂韧度随动态加载率的增大而增大,裂纹扩展速度在(0.24~0.34)cR范围内动态扩展韧度随裂纹扩展速度的增大而提高。

Multi-Symplectic Splitting Method for Two-Dimensional Nonlinear Schrodinger Equation

Using the idea of splitting numerical methods and the multi-symplectic methods, we propose a multisymplectic splitting （MSS） method to solve the two-dimensional nonlinear Schrodinger equation （2D-NLSE） in this paper. It is further shown that the method constructed in this way preserve the global symplectieity exactly. Numerical experiments for the plane wave solution and singular solution of the 2D-NLSE show the accuracy and effectiveness of the proposed method.

Pseudo-spectral Approximations for a Class of the Kdv-Burgers Type Equation

In this paper, the pseudo-spectral approximations for a class of the Kdv-Burgers type equation is presented. Convergence and stability of the approximation have been proved by Sobolev's inequalities and the bounded extensive method of the nonlinear function. Finally, the numerical examples are proposed.

Benford's Law and β-Decay Half-Lives

The experimental values of 2059 β-decay half-lives are systematically analyzed and investigated. We have found that they are in satisfactory agreement with Benford＇s law, which states that the frequency of occurrence of each figure, 1-9, as the first significant digit in a surprisingly large number of different data sets follows a logarithmic distribution favoring the smaller ones. Benford＇s logarithmic distribution of β-deeay half-lives can be explained in terms of Neweomb＇s justification of Benford＇s law and empirical exponential law of β-decay half-lives. Moreover, we test the calculated values of 6721 β-decay half-lives with the aid of Benford＇s law. This indicates that Benford＇s law is useful for theoretical physicists to test their methods for calculating β-decay half-lives.

Strategies to Overcome Filter Divergence in the DRP-4-DVar Approach

This paper discusses an important issue related to filter divergence in the dimension-reduced projection,four-dimensional variational data assimilation(DRP-4-DVar) approach.Idealized experiments with the Lorenz-96 model over a period of 200 days showed that the amplitudes of the root mean square errors(RMSEs) reached the same levels as those of the state variables after approximately 100 days because of the accumulation of sampling errors following the cycle of assimilation.Strategies to reduce sampling errors are critical to ensure the quality of ensemble-based assimilation.Numerical experiments showed that localization and reducing observational errors can alleviate,but cannot completely overcome,the filter divergence in the DRP-4-DVar approach,while the method of perturbing observations and the inflation technique can efficiently eliminate the filter divergence problem.

用CSTBD试样确定砂岩的动态起裂和扩展韧度

利用大直径霍普金森压杆径向冲击中心直裂纹巴西圆盘(CSTBD)砂岩试样,完成Ⅰ型动态断裂实验。利用实验-数值方法确定了不同动态加载率下砂岩的动态起裂韧度;结合实验-数值法以及普适函数确定了不同裂纹扩展速度下砂岩的动态扩展韧度。为验证普适函数法和实验-数值法的有效性,将实验所得结果与其他学者的研究成果进行了对比分析,得到了相同的规律。所确定的岩石动态起裂韧度和动态扩展韧度分别随动态加载率的提高和裂纹扩展速度的提高而增加。

采用压缩单裂纹圆孔板确定岩石动态起裂、扩展和止裂韧度

爆炸、冲击、地震等人为或自然灾害不可避免,经常造成大量土木工程设施的破坏,因此岩石在动态载荷作用下的行为受到特别关注.岩石动态断裂韧度是评价岩石抵抗裂纹动态起裂、扩展和止裂性能的材料参数,开展岩石动态断裂韧度测试方法的研究对相关理论基础和实验技术的要求较高.岩石动态断裂韧度分为动态起裂、动态扩展、动态止裂三种,虽然关于动态起裂和动态扩展的研究已有一些成果,对岩石动态止裂的研究仍是一个难题,至今几乎无人问津.研究表明,在分离式霍普金森压杆撞击压缩单裂纹圆孔板岩石试样的I型动态断裂试验中,动态起裂、扩展、止裂的全过程可以由黏贴在压缩单裂纹圆孔板试样上的裂纹扩展计监测,岩石的动态起裂、扩展、止裂韧度可以用实验-数值-解析法确定.特别值得一提的是首次测出了岩石的动态止裂韧度.裂纹扩展计信号还显示,压缩单裂纹圆孔板在止裂后,停止的裂纹还会再次动态起裂、扩展并超出裂纹扩展计的检测范围.从能量的角度分析了动态止裂的过程,指出测试动态止裂韧度时要注意的一些问题.结果显示,岩石动态起裂韧度和动态扩展韧度分别随动态加载率和裂纹扩展速度的增大而增大,岩石动态起裂韧度略大于动态止裂韧度.

Influence of a Deflector or a Wall on Savonius Rotor Efficiency

The Savonius rotor is a vertical axis-wind machine composed of two half cylindrical blades presenting a central gap. It is a slow velocity machine compared with horizontal wind machines. Its efficiency is about twenty per cent. In this work experimental tests are presented using two kind of deflectors placed in front of the resistive blade. Such disposition allows to hide the resistant blade and to guide the flow toward the motrice blade. Two deflectors have been used： a short one and a long one. The results obtained in wind tunnel have shown that the long deflector is the more efficient, essentially for high values of the tip speed ratio. One has been interested, using a numerical approach, in the study of the influence of a wall on the aerodynamical field near the rotor.

Numerical Investigation of a New Method for Reducing Bends Erosion from Particles Impacts

The present paper intends to introduce a new method for reducingbends erosion from particles impacts: the ribbed bend erosionprotection method. Ribs are evenly fixed in the range of 20 deg-80deg on the inner-wall of inside 90 deg bend and the bend (includingribs) is made of medium carbon steel. Three-dimensional numericalworks is performed and the result shows satisfactory agreement withthe experimental measurement. Numerical simulation studies thecharacteristics of axial gas flow along the bend and secondary flowat cross section.

Numerical and experimental evaluation on methods for parameter identification of thermal response tests

Several parameter identification methods of thermal response test were evaluated through numerical and experimental study.A three-dimensional finite-volume numerical model was established under the assumption that the soil thermal conductivity had been known in the simulation of thermal response test.The thermal response curve was firstly obtained through numerical calculation.Then,the accuracy of the numerical model was verified with measured data obtained through a thermal response test.Based on the numerical and experimental thermal response curves,the thermal conductivity of the soil was calculated by different parameter identification methods.The calculated results were compared with the assumed value and then the accuracy of these methods was evaluated.Furthermore,the effects of test time,variable data quality,borehole radius,initial ground temperature,and heat injection rate were analyzed.The results show that the method based on cylinder-source model has a low precision and the identified thermal conductivity decreases with an increase in borehole radius.For parameter estimation,the measuring accuracy of the initial temperature of the deep ground soil has greater effect on identified thermal conductivity.

Accurate level set method for simulations of liquid atomization

Computational fluid dynamics is an efficient numerical approach for spray atomization study, but it is challenging to accurately capture the gas-liquid interface. In this work, an accurate conservative level set method is intro- duced to accurately track the gas-liquid interfaces in liquid atomization. To validate the capability of this method, binary drop collision and drop impacting on liquid film are investigated. The results are in good agreement with experiment observations. In addition, primary atomization （swirling sheet atomization） is studied using this method. To the swirling sheet atomization, it is found that Rayleigh-Taylor instability in the azimuthal direction causes the primary breakup of liquid sheet and complex vortex structures are clustered around the rim of the liq- uid sheet. The effects of central gas velocity and liquid-gas density ratio on atomization are also investigated. This work lays a solid foundation for further studvin~ the mechanism of s^rav atomization.

Dynamics of Anchor Last Deployment of Submersible Buoy System

Submersible buoy systems are widely used for oceanographic research,ocean engineering and coastal defense.Severe sea environment has obvious effects on the dynamics of submersible buoy systems.Huge tension can occur and may cause the snap of cables,especially during the deployment period.This paper studies the deployment dynamics of submersible buoy systems with numerical and experimental methods.By applying the lumped mass approach,a three-dimensional multi-body model of submersible buoy system is developed considering the hydrodynamic force,tension force and impact force between components of submersible buoy system and seabed.Numerical integration method is used to solve the differential equations.The simulation output includes tension force,trajectory,profile and dropping location and impact force of submersible buoys.In addition,the deployment experiment of a simplified submersible buoy model was carried out.The profile and different nodes' velocities of the submersible buoy are obtained.By comparing the results of the two methods,it is found that the numerical model well simulates the actual process and conditions of the experiment.The simulation results agree well with the results of the experiment such as gravity anchor's location and velocities of different nodes of the submersible buoy.The study results will help to understand the conditions of submersible buoy's deployment,operation and recovery,and can be used to guide the design and optimization of the system.

Experimental and Numerical Procedures of a Sonar Platform with a Sound Absorption Wedge

Experiments involving a sonar platform with a sound absorption wedge were carried out for the purpose of obtaining the low frequency acoustic characteristics. Acoustic characteristics of a sonar platform model with a sound absorption wedge were measured, and the effects of different wedge laid areas on platform acoustic characteristic were tested. Vibration acceleration and self-noise caused by model vibration were measured in four conditions: 0%, 36%, 60%, and 100% of wedge laid area when the sonar platform was under a single frequency excitation force. An experiment was performed to validate a corresponding numerical calculation. The numerical vibration characteristics of platform area were calculated by the finite element method, and self-noise caused by the vibration in it was predicted by an experiential formula. The conclusions prove that the numerical calculation method can partially replace the experimental process for obtaining vibration and sound characteristics.

霍普金森杆冲击压缩单裂纹圆孔板的岩石动态断裂韧度试验方法

对压缩单裂纹圆孔板（single cleavage drilled compression-SCDC）砂岩试样，利用分离式霍普金森压杆（SHPB）冲击加载，进行了岩石张开型（I型）动态断裂实验。分别采用2种方法确定砂岩的动态断裂韧度，第1种方法是实验一数值法：由SHPB弹性杆上应变片获得作用在试件上的加载力，然后输入有限元分析程序求得试样裂尖动态应力强度因子，对应于裂尖起裂时刻的动态应力强度因子即为材料动态断裂韧度值；第2种方法是准静态法：将载荷峰值代入静态应力强度因子公式确定动态断裂韧度。2种方法的结果差异较大，对无量纲裂纹长度α／R=0．64（A组）试样，准静态方法确定的断裂韧度值要比实验．数值法确定的断裂韧度值平均要小35％～62％；对无量纲裂纹长度α／R=1．61（B组）试样，准静态方法的计算结果比实验-数值法的计算结果平均要小72％～83％。从原理上讲，实验-数值法比准静态法能更合理地测定岩石的动态断裂韧度。

Experimental and Numerical Investigations on Vibration Characteristics of a Loaded Ship Model

In this paper, the vibration characteristics of the structure in the finite fluid domain are analyzed using a coupled finite element method. The added mass matrix is calculated with finite element method （FEM） by 8-node acoustic fluid elements. The vibration characteristics of the structure in the finite fluid domain are calculated combining structure FEM mass matrix. By writing relevant programs, the numerical analysis on vibration characteristics of a submerged cantilever rectangular plate in finite fluid domain and loaded ship model is performed. A modal identification experiment for the loaded ship model in air and in water is conducted and the experiment results verify the reliability of the numerical analysis. The numerical method can be used for further research on vibration characteristics and acoustic radiation problems of the structure in the finite fluid domain.

Numerical Homogenization of the Elliptic Problem with Rapidly Varying Tensor or Boundary Condition

Homogenization is concerned with obtaining the average properties of a material. The problem on its own has no easy solution, except in cases like the periodic case, when it can be obtained in closed form. In this paper we consider a numerical solution of the elliptic homogenization problem for the case of rapidly varying tensor or boundary conditions. The method makes use of an adaptive finite element method to correctly capture the rapid change in the tensor or boundary condition. In the numerical experiments we vary the mesh size and do a posteriori error analysis on test problems.

Simulation and experiment of starting transient flow field of the hydrostatic bearing based on dynamic mesh method

A new method is developed to assess and analyze the dynamic performance of hydrostatic bearing oil film by using an amulets-layer dynamic mesh technique. It is implemented using C Language to compile the UDF program of a single oil film of the hydrostatic bearing. The effects of key lubrication parameters of the hydrostatic bearing are evaluated and analyzed under various working conditions,i.e. under no-load,a load of 40 t,a full load of 160 t,and the rotation speed of 1r/min,2r/min,4r/min,8r/min,16r/min,32r/min. The transient data of oil film bearing capacity under different load and rotation speed are acquired for a total of 18 working conditions during the oil film thickness changing. It allows the effective prediction of dynamic performance of large size hydrostatic bearing. Experiments on hydrostatic bearing oil film have been performed and the results were used to define the boundary conditions for the numerical simulations and validate the developed numerical model. The results showed that the oil film thickness became thinner with the increase of the operating time of the hydrostatic bearing,both the oil film rigidity and the oil cavity pressure increased significantly,and the increase of the bearing capacity was inversely proportional to the cube of the change of the film thickness. Meanwhile,the effect of the load condition on carrying capacity of large size static bearing was more important than the speed condition. The error between the simulation value and the experimental value was 4.25%.

An adaptive time stepping method with efcient error control for second-order evolution problems

This work is concerned with time stepping finite element methods for abstract second order evolution problems. We derive optimal order a posteriori error estimates and a posteriori nodal superconvergence error estimates using the energy approach and the duality argument. With the help of the a posteriori error estimator developed in this work, we will further propose an adaptive time stepping strategy. A number of numerical experiments are performed to illustrate the reliability and efficiency of the a posteriori error estimates and to assess the effectiveness of the proposed adaptive time stepping method.

用边裂纹平台圆环试样测试岩石的Ⅰ型动态断裂韧度

用大直径(φ100 mm)分离式霍普金森压杆径向冲击边裂纹平台圆环试样,测试砂岩的Ⅰ型动态断裂韧度。使用裂纹扩展计(crack propagation gauge,CPG)测定试样起裂时刻和裂纹扩展速度,结果表明裂纹扩展计测定比传统电阻应变片更为灵敏,测定结果更接近裂纹破坏真实情况。用实验-数值法确定了试样的动态起裂韧度,采用实验-数值法并结合普适函数进一步求得砂岩的动态扩展韧度。研究发现在一定范围内动态起裂韧度随加载率的增加而增大,而动态扩展韧度随裂纹扩展速度的变大而略微增加。