ANALYTICAL SOLUTIONS FOR THE LAYERED GEO-MATERIALS SUBJECTED TO AN ARBITRARY POINT LOAD IN THE CARTESIAN COORDINATE

This paper presents analytical solutions for the stress and displacement field in elastic layered geo-materials induced by an arbitrary point load in the Cartesian coordinate system. The point load solutions can be obtained by referring to the integral transform and the transfer matrix technique. However, former solutions usually exist in the cylindrical coordinate system subjected, to axisymmetric loading. Based on the proposed solutions in the Cartesian coordinate, it is very easy to solve asymmetric problems and consider the condition with internal loads in multi-layered geo-materials. Moreover, point load solutions can be used to construct solutions for analytical examination of elastic problems and incorporated into numerical schemes such as boundary element methods. The results discussed in this paper indicate that there is no problem in the evaluation of the point load solutions with high accuracy and efficiency, and that the material non-homogeneity has a significant effect on the elastic field due to adjacent loading.

A Hybrid Model to Predict Cartesian Planimetric Coordinates

Coordinates are basic needs for both geospatial and non-geospatial professionals and as a result, geodesists have the responsibility to develop methods that are applicable and practicable for determining cartesian coordinates either through transformation, conversion or prediction for the geo-scientific community. It is therefore necessary to implement mechanisms and systems that can be employed to predict coordinates in either two dimensional （2D） or three dimensional （3D） spaces. Artificial Intelligence （AI） techniques and conventional methods within the last decade have been proposed as an effective tool for modeling and forecasting in various scientific disciplines for solving majority of problems. The primary objective of this work is to compare the efficiency of artificial intelligence technique （Feed Forward Back propagation Neural Network （FFBPNN）） and conventional methods （Ordinary Least Squares （OLS）, General Least Squares （GLS）, and Total Least Squares （TLS）） in cartesian planimetric coordinate＇s prediction. In addition, a hybrid approach of conventional and artificial intelligence method thus, TLS-FFBPNN has been proposed in this study for 2D cartesian coordinates prediction. It was observed from the results obtained that FFBPNN performed significantly better than the conventional methods. However, the TLS-FFBPNN when compared with FFBPNN, OLS, GLS and TLS gave stronger and better performance and superior predictions. To further confirm the superiority of the TLS-FFBPNN the Bayesian Information Criterion was introduced. The BIC selected the TLS-FFBPNN as the optimum model for prediction.

Intelligent Sensing and Control of Road Construction Robot Scenes Based on Road Construction

Automatic control technology is the basis of road robot improvement,according to the characteristics of construction equipment and functions,the research will be input type perception from positioning acquisition,real-world monitoring,the process will use RTK-GNSS positional perception technology,by projecting the left side of the earth from Gauss-Krueger projection method,and then carry out the Cartesian conversion based on the characteristics of drawing;steering control system is the core of the electric drive unmanned module,on the basis of the analysis of the composition of the steering system of unmanned engineering vehicles,the steering system key components such as direction,torque sensor,drive motor and other models are established,the joint simulation model of unmanned engineering vehicles is established,the steering controller is designed using the PID method,the simulation results show that the control method can meet the construction path demand for automatic steering.The path planning will first formulate the construction area with preset values and realize the steering angle correction during driving by PID algorithm,and never realize the construction-based path planning,and the results show that the method can control the straight path within the error of 10 cm and the curve error within 20 cm.With the collaboration of various modules,the automatic construction simulation results of this robot show that the design path and control method is effective.

Expression of strain tensor in orthogonal curvilinear coordinates

Based on an analysis of connotation and extension of the concept of the orthogonal curvilinear coordinates, we have deduced a platform of strain tensor expression of Cartesian coordinates, which turns out to be a function of Lame coefficient and unit vector. By using transform matrix between Cartesian coordinates and orthogonal eurvilinear coordinates, we have deduced a mathematical expression for correcting displacement vector differential in orthogonal curvilinear coordinates, and given a general expression of strain tensor in orthogonal curvilinear coordinates.

Analysis for the Deployment of Single-Point Mooring Buoy System Based on Multi-Body Dynamics Method

Deployment of buoy systems is one of the most important procedures for the operation of buoy system. In the present study, a single-point mooring buoy system which contains surface buoy, cable segments with components, anchor and so on is modeled by applying multi-body dynamics method. The motion equations are developed in discrete node description and fully Cartesian coordinates. Then numerical method is used to solve the ordinary differential equations and dynamics simulations are achieved while anchor is casting from board. The trajectories and velocities of different nodes without current and with current in buoy system are obtained. The transient tension force of each part of the cable is analyzed in the process of deployment. Numerical results indicate that the transient payload increases to a peak value when the anchor is touching the seabed and the maximum tension force will vary with different floating configuration. This work is helpful for design and deployment planning of buoy system.

Study on accuracy of casting flow simulation

In the field of casting flow simulation, the application of body-fitted coordinate(BFC) has not been widely used due to the difficulty and low efficiency of grid generation, despite the availability of good quality analysis results. Cartesian coordinates, on the other hand, have been used predominantly in casting process simulations because of their relatively easy and fast grid generation. However, Cartesian grid systems cannot obtain accurate results because they cannot express the geometries properly. In this study, Cut Cell method was applied to solve this problem. The three-dimensional incompressible viscous governing equation was analyzed using a function defined for the volume and area of the casting in the cutting cell. Using the Cut Cell method, accurate flow analysis results were also obtained in the Cartesian grid systems. The tests of simple shape and the applications of actual casting product have been tried with Cut Cell method.

The Algebra of Projective Spheres on Plane, Sphere and Hemisphere

Numerous authors studied polarities in incidence structures or algebrization of projective geometry [1] [2]. The purpose of the present work is to establish an algebraic system based on elementary concepts of spherical geometry, extended to hyperbolic and plane geometry. The guiding principle is: “The point and the straight line are one and the same”. Points and straight lines are not treated as dual elements in two separate sets, but identical elements within a single set endowed with a binary operation and appropriate axioms. It consists of three sections. In Section 1 I build an algebraic system based on spherical constructions with two axioms: ab = ba and (ab)(ac) = a, providing finite and infinite models and proving classical theorems that are adapted to the new system. In Section Two I arrange hyperbolic points and straight lines into a model of a projective sphere, show the connection between the spherical Napier pentagram and the hyperbolic Napier pentagon, and describe new synthetic and trigonometric findings between spherical and hyperbolic geometry. In Section Three I create another model of a projective sphere in the Cartesian coordinate system of the plane, and give methods and techniques for using the model in the theory of functions.

APPLICATIONS OF FRACTIONAL EXTERIOR DIFFERENTIAL IN THREE-DIMENSIONAL SPACE

A brief survey of fractional calculus and fractional differential forms was firstly given.The fractional exterior transition to curvilinear coordinate at the origin were discussed and the two coordinate transformations for the fractional differentials for three-dimensional Cartesian coordinates to spherical and cylindrical coordinates are obtained, respectively. In particular, for v=m=1 ,the usual exterior transformations, between the spherical coordinate and Cartesian coordinate, as well as the cylindrical coordinate and Cartesian coordinate, are found respectively, from fractional exterior transformation.

Comparative eye-tracking evaluation of scatterplots and parallel coordinates

We investigate task performance and reading characteristics for scatterplots(Cartesian coordinates)and parallel coordinates.In a controlled eye-tracking study,we asked 24 participants to assess the relative distance of points in multidimensional space,depending on the diagram type(parallel coordinates or a horizontal collection of scatterplots),the number of data dimensions(2,4,6,or 8),and the relative distance between points(15%,20%,or 25%).For a given reference point and two target points,we instructed participants to choose the target point that was closer to the reference point in multidimensional space.We present a visual scanning model that describes different strategies to solve this retrieval task for both diagram types,and propose corresponding hypotheses that we test using task completion time,accuracy,and gaze positions as dependent variables.Our results show that scatterplots outperform parallel coordinates significantly in 2 dimensions,however,the task was solved more quickly and more accurately with parallel coordinates in 8 dimensions.The eye-tracking data further shows significant differences between Cartesian and parallel coordinates,as well as between different numbers of dimensions.For parallel coordinates,there is a clear trend toward shorter fixations and longer saccades with increasing number of dimensions.Using an area-of-interest(AOI)based approach,we identify different reading strategies for each diagram type:For parallel coordinates,the participants’gaze frequently jumped back and forth between pairs of axes,while axes were rarely focused on when viewing Cartesian coordinates.We further found that participants’attention is biased:toward the center of the whole plot for parallel coordinates and skewed to the center/left side for Cartesian coordinates.We anticipate that these results may support the design of more effective visualizations for multidimensional data.

An Enlarged Canonical Quantization Scheme and Quantization of a Free Particle on Two-Dimensional Sphere

For a non-relativistic particle that freely moves on a curved surface, the fundamental commutation relations between positions and momenta are insufficient to uniquely determine the operator form of the momenta. With introduc- tion of more commutation relations between positions and Hamiltonian and those between momenta and Hamiltonian, our recent sequential studies imply that the Cartesian system of coordinates is physically preferable, consistent with Dirae＇s observation. In present paper, we study quantization problem of the motion constrained on the two-dimensional sphere and develop a discriminant that can be used to show how the quantization within the intrinsic geometry is im- proper. Two kinds of parameterization of the spherical surface are explicitly invoked to investigate the quantization problem within the intrinsic geometry.