数学变形的原则与方法

数学解题的实质是从已知条件出发,逐步寻求可知,进而求得结论达到未知的系列思维链.其呈现形式是一系列从条件或结论出发进行的命题转化过程——数学变形过程.文章从为什么要变形(变形目的),向什么方向变形(变形方向),用什么手段变形(变形手段)三个方面给出了思考分析的一般原则与方法.

9Ni钢的高温变形行为及其数学模型研究

在Gleeble-1500热模拟试验机上对低碳9Ni钢的高温变形行为进行了研究,并分析了变形温度、应变速率、变形量对变形抗力的影响规律,在此基础上采用Levenberg-Marquardt法对实测数据进行多元非线性回归。结果表明,回归方程有良好的曲线拟合特性,模型预报值与实测值吻合较好。

浅谈变形技巧在中职数学中的应用

数学变形是数学解题中求解、化简和证明的常用的一种解题方法.本文以举例的形式重点介绍了在中职数学三角函数、不等式、数列解题中变形的应用.

变形工艺对Q235钢热变形本构方程的影响

以Q235钢为对象,利用Gleeble-3500热模拟试验机研究其在不同变形工艺下的热变形本构方程。结果表明,Q235钢在不同变形工艺下的热变形本构方程受温度波动影响较大,较传统的方法测得的热变形本构方程,前者的计算结果更接近于实测值。

粗粒料湿化变形三轴试验研究

对小浪底斜心墙堆石坝的砂岩粗粒料采用单线法进行中型三轴湿化变形试验,研究了该种土料的湿化变形特性。通过对试验结果和湿化变形规律的分析,总结了湿化轴向应变、湿化体积应变与湿化应力水平、围压之间的关系。试验结果表明,湿化轴向应变与湿化应力水平呈双曲线关系,湿化轴向应变与围压呈线性关系;湿化体积应变与湿化应力水平和围压均为线性关系。根据对试验结果的分析以及计算湿化变形的单线法,提出了一个适用于计算粗粒料湿化变形的数学模型。该湿化变形模型参数共6个,并给出了通过室内常规试验确定参数的方法。对模型进行了验证,结果表明该湿化模型计算曲线与试验结果吻合较好,表明该模型能较好地反映粗粒料湿化变形的特征。

基于力学超材料的柔性机械臂设计技术

以力学超材料为基础结构的柔性机械臂可通过力学超材料的调配设计实现多重弯曲运动。为探究该类柔性机械臂的变形特性,在分析柔性机械臂结构及其驱动原理的基础上,通过分段常曲率假设建立胞元组变形的数学模型,同时根据柔性机械臂单元的弯曲特性进一步提出了单节柔性机械臂单元和多节柔性机械臂单元的变形预测模型,最后通过实物实验验证了变形预测模型的有效性,完成了超过±90°的弯曲并对末端周围的环境进行探查,可应用于复杂狭小空间的检视。

高速拉伸变形中的热传递

对高速拉伸变形加工中的短程高温加热器用集总容量方法建立了热传递数学模型,可预测变形加工中的纱线温度.

计算多因素定位误差微分法的改进

定位误差的分析和计算是进行工装设备设计必不可缺少的重要环节。文章针对机械制造工艺学和机床夹具设计中定位误差的计算,特别是多因素条件下定位误差的计算问题,根据普通微分法计算多因素条件下定位误差所遇到的矛盾,利用高等数学微分的近似计算,解释了全微分的数学变形这种方法的原理,同时提出并详细阐述了微分法的另一种改进即实体路程法,并通过具体实例对以上2种方法进行了验证,为正确、快速计算多因素条件下的定位误差提供了方法和依据。

印刷纸压缩特性实验研究

实验研究了印刷纸压缩变形特性,获得了压缩变形曲线,并得到印刷纸压缩变形规律的数学模型,利用实验数据及数学分析软件Matlab确定了印刷纸压缩变形数学模型的特性参量.其应力应变关系呈现出很强的非线性特性,结果表明所得方程能够如实反映印刷纸压缩变形规律.

Similar Single-Difference Model and Its Algorithm for Solving GPS Monitoring Deformation Directly at Single Epoch

A new similar single-difference mathematical model (SS-DM) and its corresponding algorithmare advanced to solve the deformationof monitoring point directly in singleepoch. The method for building theSSDM is introduced in detail, and themain error sources affecting the accu-racy of deformation measurement areanalyzed briefly, and the basic algo-rithm and steps of solving the deform-ation are discussed.In order to validate the correctnessand the accuracy of the similar single-difference model, the test with fivedual frequency receivers is carried outon a slideway which moved in plane inFeb. 2001. In the test,five sessions areobserved. The numerical results oftest data show that the advanced mod-el is correct.

A new mathematical model for predicting flow stress of X70HD under hot deformation

To realize numerical simulation of rolling and obtain the hot forming process parameters for X70 HD steel, the flow stress behaviors of X70 HD steel were investigated under different temperatures（820-1100 ℃ and strain rates（0.01-10 s-1） on a Gleeble-3500 thermo-simulation machine. A new flow stress model was established. The linear and exponential relationship methods were applied to the parameters with respect to temperature and deformation rates. The rise of curve ends under certain conditions was analyzed. The flow stress of X70 HD steel predicted by the proposed model agrees well with the experimental results. So, it greatly improves the precision of the metal thermoplastic processing through finite element method and practical application of engineering.

Computation of the Simplest Normal Forms for Resonant Double Hopf Bifurcations System Based on Lie Transform

The simplest normal form of resonant double Hopf bifurcation was studied based on Lie operator. The coefficients of the simplest normal forms of resonant double Hopf bifurcation and the nonlinear transformations in terms of the original system coefficients were given explicitly. The nonlinear transformations were used for reducing the lower- and higher-order normal forms, and the rank of system matrix was used to determine the coefficient of normal form which could be reduced. These make the gained normal form simpler than the traditional one. A general program was compiled with Mathematica. This program can compute the simplest normal form of resonant double Hopf bifurcation and the non-resonant form up to the 7th order.

Numerical Simulation of Shaped Charge Jet Using Multi-Phase SPH Method

Since the jets and detonation gaseous products are separated by sharp interfaces, the traditional smoothed particle hydrodynamics (SPH) method is difficult to avoid the computational instability at interfaces. The multi-phase SPH (MSPH) method was applied to improving the stabil-ity, which smoothes the particle density and makes pressure continuous at interfaces. Numericalexamples of jet forming process were used to test capability of the MSPH method. The results show that the method remains algorithm stability for large density gradient between the jets and gaseous products and has potential application to both the explosion and the jet problems. The effect of initiation ways of the shaped charge was discussed as well.

Long-term stability analysis of large-scale underground plant of Xiangjiaba hydro-power station

Numerical analysis of the optimal supporting time and long-term stability index of the surrounding rocks in the underground plant of Xiangjiaba hydro-power station was carried out based on the rheological theory. Firstly,the mechanical parameters of each rock group were identified from the experimental data; secondly,the rheological calculation and analysis for the cavern in stepped excavation without supporting were made; finally,the optimal time for supporting at the characteristic point in a typical section was obtained while the creep rate and displacement after each excavation step has satisfied the criterion of the optimal supporting time. Excavation was repeated when the optimal time for supporting was identified,and the long-term stability creep time and the maximum creep deformation of the characteristic point were determined in accordance with the criterion of long-term stability index. It is shown that the optimal supporting time of the characteristic point in the underground plant of Xiangjiaba hydro-power station is 5-8 d,the long-term stability time of the typical section is 126 d,and the corresponding largest creep deformation is 24.30 mm. While the cavern is supported,the cavern deformation is significantly reduced and the stress states of the surrounding rock masses are remarkably improved.

Plastic deformation behavior of Mg97Zn1Y2 extruded alloys

The mechanical properties of the Mg97ZnlY2 extruded alloy containing the long-period stacking ordered phase, the so-called LPSO-phase, with a volume fraction of 24%-25%, were examined by compression tests and cyclic tension-compression deformation tests. The plastic behavior of the extruded alloys with compositions of Mg99.2Zn0.2Y0.6 and Mg89Zn4Y7 （molar fraction, %）, which were almost the same compositions of Mg matrix phase and LPSO phase in Mg97Zn1Y2 Mg/LPSO two-phase alloy, respectively, were also prepared. By comparing their mechanical properties, the strengthening mechanisms operating in the Mg97Zn1 Y2 extruded alloy were discussed. Existence of the LPSO-phase strongly enhanced the refinement of Mg matrix grain size during extrusion, which led to a large increment of the strength of alloy. In addition, the LPSO-phases, which were aligned along the extrusion direction in Mg97Zn1Y2 extruded alloy, acted as hardening phases, just like reinforced fibers.

Numerical simulation of the effect of coupling support of bolt-mesh-anchor in deep tunnel

The mechanical effects of bolt-mesh-anchor coupling support in deep tunnels were studied by using a numerical method, based on deep tunnel coupling supporting techniques and non-linear deformation mechanical theory of rock mass at great depths.It is shown that the potential of a rigid bolt support can be efficiently activated through the coupling effect between a bolt-net support and the surrounding rock.It is found that the accumulated plastic energy in the surrounding rock can be sufficiently transformed by the coupling effect of a bolt-mesh-tray support.The strength of the surrounding rock mass can be mobilized to control the deforma-tion of the surrounding rock by a pre-stress and time-space effect of the anchor support.The high stress transformation effect can be realized by the mechanical coupling effect of the bolt-mesh-anchor support, whereby the force of the support and deformation of the surrounding rock tends to become uniform, leading to a sustained stability of the tunnel.

Equilibrium morphology of gas–liquid Janus droplets: A numerical analysis of buoyancy effect

In this article, a theoretical model for predicting the equilibrium morphology of gas–liquid Janus droplets was built. Based on this model, the effects of bubble radius and volume ratio on morphology change was systematically studied. The increase of bubble radius causes the two parts(bubble and oil drop) in Janus droplets tend to merge while the impact of volume ratio is complicated. When volume ratio increases, these two parts firstly tend to merge, then gradually separate. The accuracy of this model was verified by experimental results.

The Marine Dynamics and Changing Trend off the Modern Yellow River Mouth

Topography around the Yellow River mouth has changed greatly in recent years, but studies on the current state of ma- rine dynamics off the Yellow River mouth are relatively scarce. This paper uses a two-dimension numerical model （MIKE 21） to reveal the tidal and wave dynamics in 2012, and conducts comparative analysis of the changes from 1996 to 2012. The results show that M2 amphidromic point moved southeastward by 11 kin. It further reveals that the tides around the Yellow River mouth are relatively stable due to the small variations in the tidal constituents. Over the study period, there is no noticeable change in the distribution of tidal types and tidal range, and the mean tidal range off the river mouth during the period studied is 0.5-1.1 m. However, the tidal currents changed greatly due to large change in topography. It is observed that the area with strong tidal currents shifted from the old river mouth （1976-1996） to the modem river mouth （1996-present）. While the tidal current speeds decreased continually off the old river mouth, they increased off the modem river mouth. The Maximum Tidal Current Speed （MTCS） reached 1.4 m s-1, and the maximum current speed of 50-year return period reached 2.8 m s-1. Waves also changed greatly due to change in topography. The significant wave height （H1/3） of 50-year return period changed proportionately with the water depth, and the ratio of Hi/3 to depth being 0.4-0.6. H1/3 of the 50-year return period in erosion zone increased continually with increasing water depth, and the rate of change varied between 0.06 and 0.07myr-1. Based on the results of this study, we infer that in the future, the modem river mouth will protrude gradually northward, while the erosion zone, comprising the old river mouth and area between the modern river mouth and the old river mouth （Intermediate region） will continue to erode. As the modem river mouth protrudes towards the sea, there will be a gradual increase in the current speed and decrease in wave height. Conversely, the old river mouth will retreat, with gradual decrease in current speed and increase in wave height. As more coastal constructions spring up around the Yellow River mouth in the future, we recommend that variation in hydrodynamics over time should be taken into consideration when designing such coastal constructions.

Deformation of Superoperator's Kraus Representation Derived by Weyl Correspondence and Entangled State Representation

By virtue of the Weyl correspondence and based on the the technique of integration within an ordered product of operators, we show under what condition the superoperator＇s Kraus representation p^1=∑μAμpA^＋μ can be deformed as p＇= （1/π） ∫ d^2d^2α（α）D（α）D（α）pD^＋（α）, where D（α） is the displacement operator, B（α） is a probability density related to the classical Weyl correspondence of Aμ. An alternate discussion by using the entangled state representation and through a quantum teleportation process is also presented.

ELASTIC DEFORMATION ANALYSIS OF MULTILA YERED STRANDS

This paper describes a general model for the mechanical behavior studying of general wire rope strand. An exact solution of the deformation characteristics was given when the strands is under tensile and torsional loads. The theoretical results are useful in evaluating the extensional and torsional moduli of rigidity for the strands. Finally, a simple design criterion is establised for the nonrotating ropes.