用GeoGebra探究一类“果圆”问题的轨迹

将一个绳套套在两个定点上,拉紧并旋转一周可得到一个椭圆,若将绳套套在多个定点上拉紧并旋转,得到的轨迹是什么,有何规律？利用GeoGebra研究发现：当三个定点组成一个边长为2c的等边三角形时,周长为2a＋2c的绳套绕成的图形由六段椭圆弧组成,其中三个椭圆弧的长轴为2a,三个椭圆弧的长轴为2a-2c,当绳套绕n个定点旋转时,绕成的图形由2n段椭圆弧组成,进一步得出若干结论.当某个定点变化时,轨迹也发生变化.当绳套的长度变化时,轨迹也发生变化.

Chemical Constituents of Hedysarum gmelinii

To study the chemical constituents of Hedysarum gmelinii. Methods Theconstituents were separated and purified by different methods of chromatography, and theirstructures were elucidated by DR, MS and NMR. Results Eight compounds were isolated from Hedysarumgmelinii, including three triteipenoids, two flavonoids and two other compounds. Their structureswere identified as squasapogenol (1), soyasapogenol (2), lupeol (3), 3, 9-dihydroxy coumestan (4),3-hydroxy-9-me-thoxy pterocarpan (5), β-sitosterol (6), palmatic acid (7), and hexadecanoic acid 2,3-dihydroxypropyl ester (8). Conclusion All the compounds have been isolated from this plant forthe first time. Compounds 1 — 4 and 8 were obtained from this genus for the first time. The NMRdata of 1 are reported for the first time.

Influence of intermediate principal stress on failure mechanism of hard rock with a pre-existing circular opening

Based on particle flow theory, the influences of the magnitude and direction of the intermediate principal stress on failure mechanism of hard rock with a pre-existing circular opening were studied by carrying out true triaxial tests on siltstone specimen. It is shown that peak strength of siltstone specimen increases firstly and subsequently decreases with the increase of the intermediate principal stress. And its turning point is related to the minimum principal stress and the direction of the intermediate principal stress. Failure characteristic(brittleness or ductility) of siltstone is determined by the minimum principal stress and the difference between the intermediate and minimum principal stress. The intermediate principal stress has a significant effect on the types and distributions of microcracks. The failure modes of the specimen are determined by the magnitude and direction of the intermediate principal stress, and related to weakening effect of the opening and inhibition effect of confining pressure in essence: when weakening effect of the opening is greater than inhibition effect of confining pressure, the failure surface is parallel to the x axis(such as σ2=σ3=0 MPa); conversely, the failure surface is parallel to the z axis(such as σ2=20 MPa, σ3=0 MPa).

Analysis of complete plasticity assumption for solid circular shaft under pure torsion and calculation of shear stress

The distribution of shear stress on the cross-section of plastic metal solid circular shaft under pure torsion yielding, the applicability of complete plastic model assumption and the shear stress formula were researched. Based on the shear stress formula of circular shaft under pure torsion in elastic stage, the formula of torque in elastic stage and the definition of yield, it is obtained that the yielding stage of plastic metal shaft under pure torsion is only a surface phenomenon of torque-torsion angle relationship, and the distribution of shear stress is essentially different from that of tensile stress when yielding under uniaxial tension. The pure torsion platform-torsion angle and the shape of torque-torsion angle curve cannot change the distribution of shear stress on the shaft cross-section. The distribution of shear stress is still linear with the maximum shear stress ts. The complete plasticity model assumption is not in accordance with the actual situation of shaft under torsion. The experimental strength data of nine plastic metals are consistent with the calculated results of the new limiting strain energy strength theory （LSEST）. The traditional yield stress formula for plastic shaft under torsion is reasonable. The shear stress formula based on the plane assumption in material mechanics is applicable for all loaded stages of torsion shaft.

The Influence of Advection Schemes and Turbulence Closure Models on Drag Coefficient Calculation Around a Circular Cylinder at High Reynolds Number

Different advection schemes and two-equation turbulence closure models based on eddy viscosity concept are used to compute the drag coefficient around a circular cylinder at high Reynolds number (106).The numerical results from these simulations are compared with each other and with experimental data in order to evaluate the performance of different combinations of advection scheme and two-equation turbulence model.The separate contributions from form drag and friction drag are also ana-lyzed.The computational results show that the widely used standard k-ε turbulence closure is not suitable for such kind of study,while the other two-equation turbulence closure models produce acceptable results.The influence of the different advection schemes on the final results are small compared to that produced by the choice of turbulence closure method. The present study serves as a reference for the choice of advection schemes and turbulence closure models for more complex numerical simulation of the flow around a circular cylinder at high Reynolds number.

Study on the characteristics of grout permeation based on cylindrical diffusion

Permeation grouting is widely applied for its low grouting pressure and minor disturbance to the stratum in grouting engineering, especially in engineering with strict requirements on ground settlement. However, permeation grouting theory lags behind compared with other engineering disciplines, and the theoretical formulas now available cannot accurately be used to guide grouting engineering design and predict the cost and effects of grouting due to many factors affecting grout permeation in stratum. In this study, permeation grouting experiment devices were independently manufactured with the characteristics of easily controlling grouting pressure, simulating sandy strata grout, and detecting grouting effect. Using a uniform design, the sand consolidation agent, as grouting material, its spread in Shenyang sandy strata was tested with these experiment devices. The quantitative relations between grouting factors （grouting pressure, strata parameters, water-sand consolidation agent ratio） and grouting effects （grout spread radius, gell strength, grout amount） are obtained with regression analysis, and the influence degree of grouting factors on grouting effects is studied.

Influence of Non-Axisymmetric Terms on Circumferentially Averaged Method in Fan/Compressor

The governing equations are derived by circumferentially averaging the three-dimensional （3D） Navier-Stokes equations, which are solved using a time marching finite volume approach. Both Euler throughflow model and Navier-Stokes （N-S） throughflow model are employed to investigate the performance and flow fields of a highly loaded transonic single-stage fan ATS-2 and a four-stage fan. The results are compared with the experimental and three-dimensional computational results. It shows that the throughflow models can provide reasonable perform- ance characteristics and N-S throughflow model gives better predictions in endwall regions. A throughflow com- putation in which all the non-axisymmetric terms are included has been performed at off-design condition and the radial distributions of the flow field can be well described.

Active control of circular cylinder flow by affiliated rotating cylinders

This study puts forward an active control method for circular cylinder flow by placing two small affiliated rotating cylinders adjacent to the main cylinder, and their effects on the drag and lift forces acting on the main cylinder as well as the heat trans- fer effectiveness are numerically investigated. According to the diameter of the main cylinder the Reynolds number is chosen as Re=200. The well-proven finite volume method is employed for the calculation. The code is validated by comparing the present computed results of flow passing an isolated rotating cylinder with those available from the literature. To describe the present control model, two parameters are defined： the rotation direction of the two small cylinders （including co-current rota- tion and counter-current rotation） and the dimensionless rotation rate a. In the simulation, the rotation rate a varies from 0 to 2.4. The results indicate that the optimum rotation direction of the subsidiary cylinders, which is beneficial to both drag reduc- tion and beat transfer enhancement, is the co-current rotating （the upper affiliated cylinder spins clockwise and the lower affili- ated cylinder spins counter-clockwise）. We observe noticeable suppression of the vortex shedding and favorable reduction of the fluid forces acting on the main cylinder as the rotation rate increases. Besides, the pressure and viscous components of the drag force are analyzed. Energy balance between energy cost for activating the rotating cylinders and energy saving by the momentum injection is considered. In addition, the influence of the affiliated rotating cylinders on heat transfer is also investi- gated. The average Nusselt number is found to increase with the rotation rate.