GENERAL FORM OF MATCHING EQUATION OF ELASTIC-PLASTIC FIELD NEAR CRACK LINE FOR MODE I CRACK UNDER PLANE STRESS CONDITION

Crack line field analysis method has become an independent method for crack elastic-plastic analysis, which greatly simplifies the complexity of crack elastic-plastic problems and overcomes the corresponding mathematical difficulty. With this method, the precise elastic-plastic solutions near crack lines for variety of crack problems can be obtained. But up to now all solutions obtained by this method were for different concrete problems, no general steps and no general form of matching equations near crack line are given out. With crack line analysis method, this paper proposes the general steps of elastic plastic analysis near crack line for mode I crack in elastic-perfectly plastic solids under plane stress condition, and in turn given out the solving process and result for a specific problem.

EXACT SOLUTIONS OF NEAR CRACK LINE FIELDS FOR MODE I CRACK UNDER PLANE STRESS CONDITION IN AN ELASTIC－PERFECTLY PLASTIC SOLID

The near crack line analysis method has been used in the present paper,The classical small scale yielding conditions have been completely abandoned in the analyses and one inappropriate matching condition used to be used at the elasticplastic boundary has been corrected.The reasonable solution of the plastic stresses near the crack line region has been established.By matching the plastic stresses with the exact elastic stresses at the elastic-plastic boundary,the plastic stresses the length of the plastic zone and the unit normal vector of the elastic-plastic boundary near the crock line region have been obtained for a mode I crack under uniaxial tension,as well as a mode I crack under biaxial tension,which shows that for both conditions the plastic stress componentsσy, and σsy.he length of the plastic zone and the unit normal vector of the elastic-plastic boundary are quite the same while the plastic stress σs is different.

A New Method for Locating Calculation of Arbitrary Spatial Straight Line or Plane in NC Machining

In the manufacturing process, we often encounter so me location machining of space arbitrary straight lines and planes that are not on ly unparalleled but also not vertical with the machine tool spindle or the cutti ng tool. In the past, we can do the location machining through the methods of dr awing line and making level in the ordinary machine tool. In the numerical contr ol machining of the CNC machine tool and manufacturing center, however, the spac e location and angle of the arbitrary straight lines and planes must be precisel y calculated in advance. So that precisely locating can be guaranteed in machini ng. Therefore, how to work out the space location angle of the arbitrary straigh t lines and planes to be machined both conveniently and precisely, turns out to be the must-be-solved chief problem in the numerical control machining. In thi s paper, through the deeply research of this problem, a new kind of calculating formula that calculates and defines the space location angle of the arbitrary st raight lines and planes by using the methods of analytic calculating. The formul a has been applied in the practical manufacturing calculation. It is proved that the new space angle calculating methods of arbitrary straight lines and planes is convenient in calculating and precise in locating. And it provides us a n ew, brief and precise calculating method in the numerical control machining of t he numerical control machine tool and manufacturing center.

The detailed characteristics of positive corona current pulses in the line-to-plane electrodes

The corona current pulses generated by corona discharge are the sources of the radio interference from transmission lines and the detailed characteristics of the corona current pulses from conductor should be investigated in order to reveal their generation mechanism.In this paper,the line-to-plane electrodes are designed to measure and analyze the characteristics of corona current pulses from positive corona discharges.The influences of inter-electrode gap and line diameters on the detail characteristics of corona current pulses,such as pulse amplitude,rise time,duration time and repetition frequency,are carefully analyzed.The obtained results show that the pulse amplitude and the repetition frequency increase with the diameter of line electrode when the electric fields on the surface of line electrodes are same.With the increase of inter-electrode gap,the pulse amplitude and the repetition frequency first decrease and then turn to be stable,while the rise time first increases and finally turns to be stable.The distributions of electric field and space charges under the line electrodes are calculated,and the influences of inter-electrode gap and line electrode diameter on the experimental results are qualitatively explained.

Analysis of Distribution Generation Influences on the Vol-tage Limit Violation Probability of Distribution Line

Considering the time-sequence characteristic and randomness of load and natural resources, ?this paper studies on the distributed generation (DG) impacts on voltage limit violation probability of distribution lines. The time-sequence characteristic and randomness of load, wind and photovoltaic (PV) generation are analyzed;the indices and risk levels of voltage limit violation probability of node and distribution line are proposed. By using probabilistic load flow based on semi-invariant method, the impact degrees of voltage limit violation are calculated with different distributed power penetration levels, different seasons, different time periods, different allocation ratio between the wind power and PV power. Voltage limit violation laws of distribution line, which are concluded by IEEE33 bus system simulation, are very helpful to guide the voltage?regulation of distribution line including distributed generation.

Instantaneous Point, Line, and Plane Motions Using a Clifford Algebra

The motions of points, lines, and planes, embedded in a rigid body are expressed in a unified algebraic framework using a Clifford algebra. A Clifford algebra based displacement operator is addressed and its higher derivatives from which the coordinate-independent characteristic numbers with simple geometric meaning are defined. Because of the coordinate independent feature, no tedious coordinate transformation typically found in the conventional instantaneous invariants methods is needed.

Teaching method for reading views by analyzing lines and planes

This paper deals with the teaching method in reading engineering drawing. It introduces the basic theory and fundamental ideas as well as the approach of reading views by analyzing lines and planes. It gives out the steps for completing the third view based on the other two views. As it is easy and quick for students to read and understand views by this method, it is welcome by students in teaching practice.

Crossing Limit Cycles of Planar Piecewise Hamiltonian Systems with Linear Centers Separated by Two Parallel Straight Lines

In this paper, we have studied several classes of planar piecewise Hamiltonian systems with three zones separated by two parallel straight lines. Firstly, we give the maximal number of limit cycles in these classes of systems with a center in two zones and without equilibrium points in the other zone (or with a center in one zone and without equilibrium points in the other zones). In addition, we also give examples to illustrate that it can reach the maximal number.

THE INTEGRAL AS A FUNCTION OF THE UPPER LIMIT AND AN ANALYTICAL SOLUTION TO PLANE STRAIN DRAWING AND EXTRUSION

A kinematically admissible velocity field which is different from Avitzur's is established in Cartesian Coordinates. An upper-bound analytical solution to strip drawing andextrusion is obtained by using the integral as a function of the upper limit in this paper.

“Naturally in Love” Fashion Night in Beijing Launching Limited Edition Line of Handkerchiefs

January 7, 2010, Beijing China–The COTTON USATM "Naturally in Love" Fashion Night was officially launched tonight at the

Sub-pixel extraction of laser stripeand itsapplication in laser plane calibration

For calibrating the laser plane to implement 3D shape measurement, an algorithm for extracting the laser stripe with sub-pixel accuracy is proposed. The proposed algorithm mainly consists of two stages： two-side edge detection and center line extraction. First, the two-side edge of laser stripe is detected using the principal component angle-based progressive probabilistic Hough transform and its width is calculated through the distance between these two edges. Secondly, the center line of laser strip is extracted with 2D Taylor expansion at a sub-pixel level and the laser plane is calibrated with the 3D reconstructed coordinates from the extracted 2D sub-pixel ones. Experimental results demonstrate that the proposed method can not only extract the laser stripe at a high speed, nearly average 78 ms/frame, but also calibrate the coplanar laser stripes at a low error, limited to 0.3 mm. The proposed algorithm can satisfy the system requirement of two-side edge detection and center line extraction, and rapid speed, high precision, as well as strong anti-jamming.

Identifying the limiting factors driving the winter wheat yield gap on smallholder farms by agronomic diagnosis in North China Plain

North China Plain(NCP) is the primary winter wheat production region in China, characterized by smallholder farming systems. Whereas the winter wheat average yield of smallholder farmers is currently low, the yield potential and limiting factors driving the current yield gap remain unclear. Therefore, increasing the wheat yield in NCP is essential for the national food security. This study monitored wheat yield, management practices and soil nutrient data in 132 farmers’ fields of Xushui County, Baoding City, Hebei Province during 2014–2016. These data were analyzed using variance and path analysis to determine the yield gap and the contribution of yield components(i.e., spikes per hectare, grain number per spike and 1 000-grain weight) to wheat yield. Then, the limiting factors of yield components and the optimizing strategies were identified by a boundary line approach. The results showed that the attainable potential yield for winter wheat was 10 514 kg ha^–1. The yield gaps varied strongly between three yield groups(i.e., high, middle and low), which were divided by yield level and contained 44 farmers in each group, and amounted to 2 493, 1 636 and 814 kg ha^–1, respectively. For the three yield components, only spikes per hectare was significantly different(P<0.01) among the three yield groups. For all 132 farmers’ fields, correlation between yield and spikes per hectare(r=0.51, P<0.01), was significantly positive, while correlations with grain number per spike(r=–0.16) and 1 000-grain weight(r=–0.10) were not significant. The path analysis also showed that the spikes per hectare of winter wheat were the most important component to the wheat yield. Boundary line analysis showed that seeding date was the most limiting factor of spikes per hectare with the highest contribution rate(26.7%), followed by basal N input(22.1%) and seeding rate(14.5%), which indicated that management factors in the seeding step were the most important for affecting spikes per hectare. For desired spikes per hectare(>6.598×10^6 ha^–1),the seeding rate should range from 210–300 kg ha^–1, seeding date should range from 3th to 8th October, and basal N input should range from 90–180 kg ha^–1. Compared to these reasonable ranges of management measures, most of the farmers’ practices were not suitable, and both lower and higher levels of management existed. It is concluded that the strategies for optimizing yield components could be achieved by improving wheat seeding quality and optimizing farmers’ nutrient management practices in the NCP.

A New Approach to Plane Failure of Rock Slope Stability Based on Water Flow Velocity in Discontinuities for the Latian Dam Reservoir Landslide

The stability of slopes is always of great concern in the field of rock engineering. The geometry and orientation of pre-existing discontinuities show a larger impact on the behavior of slopes that is often used to describe the measurement of the steepness, incline, gradient, or grade of a straight line. One of the structurally controlled modes of failure in jointed rock slopes is plane failure. There are numerous analytical methods for the rock slope stability including limit equilibrium, stress analysis and stereographic methods. The limiting equilibrium methods for slopes under various conditions against plane failure have been previously proposed by several investigators. However, these methods do not involve water pressure on sliding surfaces assessments due to water velocity and have not yet been validated by case study results. This paper has tried to explore the effects of forces due to water pressure on discontinuity surfaces in plane failure through applying the improved equations. It has studied the effect of water flow velocity on sliding surfaces in safety factor, as well. New equations for considering water velocity (fluid dynamics) are presented. To check the validity of the suggested equations, safety factor for a case study has been determined. Results show that velocity of water flow had significant effect on the amount of safety factor. Also, the suggested equations have higher validity rate compared to the current equations.

Critical State Sedimentation Line of Soft Marine Clays

The compression behavior responsible for unity sensitivity is very valuable in quantitative assessment of the effects of soil structure on the compression behavior of soft marine sediments. However, the quantitative assessment of such effects is not possible because of unavailability of the formula for the compression curve of marine sediments responsible for unit sensitivity. In this study, the relationship between the remolded state and the conventional critical state line is presented in the deviator stress versus mean effective stress plot. The analysis indicates that the remolded state is on the conventional critical state line obtained at a relatively small strain. Thus, a unique critical state sedimentation line for marine sediments of unit sensitivity is proposed. The comparison between the critical state sedimentation line proposed in this study and the existing normalized consolidation curves obtained from conventional oedometer tests on remolded soils or reconstituted soils explains well the

A HALF PLANE CRACK UNDER THREE-DIMENSIONAL COMBINED MODE IMPACT LOADING

The dynamic stress intensity factor history for a half plane crack in an otherwise unbounded elastic body, with the crack faces subjected to a traction distribution consisting of two pairs of suddenly-applied shear line loads is consid- ered. The analytic expression for the combined mode stress intensity factors as a function of time is obtained. The method of solution is based on the application of integral transforms and the Wiener-Hopf technique. Some features of the solutions are discussed and graphical numerical results are presented.

Calibration method for multi-line structured light vision sensor based on Plücker line

For the rapid calibration of multi-line structured light system,a method based on Plücker line was proposed.Most of the conventional line-structured light calibration methods extract the feature points and transform the coordinates of points to obtain the plane equation.However,a large number of points lead to complicated operation which is not suitable for the application scenarios of multi-line structured light.To solve this issue,a new calibration method was proposed that applied the form of Plücker matrix throughout the whole calibration process,instead of using the point characteristics directly.The advantage of this method is that the light plane equation can be obtained quickly and accurately in the camera coordinate frame.Correspondingly a planar target particularly for calibrating multi-line structured light was also designed.The regular lines were transformed into Plücker lines by extending the two-dimensional image plane and defining a new image space.To transform the coordinate frame of Plücker lines,the perspective projection mathematical model was re-expressed based on the Plücker matrix.According to the properties of the line and plane in the Plücker space,a linear matrix equation was efficiently constructed by combining the Plücker matrices of several coplanar lines so that the line-structured light plane equation could be furtherly solved.The experiments performed validate the proposed method and demonstrate the significant improvement in the calibration accuracy,when the test distance is 1.8 m,the root mean square(RMS)error of the three-dimensional point is within 0.08 mm.

Calibration of line structured light vision system based on camera’s projective center

Based on the characteristics of line structured light sensor, a speedy method for the calibration was established. With the coplanar reference target, the spacial pose between camera and optical plane can be calibrated by using of the camera’s projective center and the light’s information in the camera’s image surface. Without striction to the movement of the coplanar reference target and assistant adjustment equipment, this calibration method can be implemented. This method has been used and decreased the cost of calibration equipment, simplified the calibration procedure, improved calibration efficiency. Using experiment, the sensor can attain relative accuracy about 0.5%, which indicates the rationality and effectivity of this method.

Nonlinearity and periodic solution of a standard-beam balance oscillation system

We present the motion equation of the standard-beam balance oscillation system, whose beam and suspensions, compared with the compound pendulum, are connected flexibly and vertically. The nonlinearity and the periodic solution of the equation are discussed by the phase-plane analysis. We find that this kind of oscillation can be equivalent to a standard-beam compound pendulum without suspensions; however, the equivalent mass centre of the standard beam is extended. The derived periodic solution shows that the oscillation period is tightly related to the initial pivot energy and several systemic parameters： beam length, masses of the beam, and suspensions, and the beam mass centre. A numerical example is calculated.

A Discusion on Limited Load-Carrying Capacity of Rectangular Plates

The elastic-plastic method is often used in designing the inner flat bulkhead plates of submarines, and the upper structure of ships and drilling platforms. Such bulkhead plates can bear the load only once. For the improvement of the load-carrying capacity or the reduction of the weight of plates, the yield line analytical method is employed in this paper to design the bulkhead plate to improve economy and increase the effiective load. Besides, a further sutdy of this method has been made theoretically and experimentally, and the data of the limited load-carrying capacity of the plate have been obtained. Furthermore, the safety coefficients for such a method are presented, which can be used as reference for related departments and staffs.

Plane extraction for navigation of humanoid robot

In order to make the humanoid robot walk freely in complicated circumstance, the reliable capabilities for obtaining plane information from its surroundings are demanded. A system for extracting planes from data taken by stereo vision was presented, After the depth image was obtained, the pixels of each line were scanned and split into straight line segments. The neighbouring relation of line segments was kept in link structure. The groups of three line segments were selected as seed regions. A queue was maintained for storing seed regions, and then the plane region was expanded around the seed region. The process of region growing continued until the queue of seed regions was empty. After trimming, the edges of the planes became smooth. In the end, extracted planes were obtained. In the experiment, two models were used： pipe and stairs. Two planes in pipe mode/and six planes in stairs model were extracted exactly. The speed and precision of algorithm can satisfy the demands of humanoid robot＇s navigation.