Closed knight’s tour problem on some (m,n,k,1)-rectangular tubes

2020 ◽  
pp. 2150094
Author(s):  
Sirirat Singhun ◽  
Nathaphat Loykaew ◽  
Ratinan Boonklurb ◽  
Wasupol Srichote
Keyword(s):  
Middle Part ◽  
Two Dimensional ◽  
Rectangular Tube ◽  
Rectangular Tubes ◽  
Knight’S Tour

A closed knight’s tour of a normal two-dimensional chessboard by using legal moves of the knight has been generalized in several ways. One way is to consider a closed knight’s tour on a ringboard of width [Formula: see text], which is the [Formula: see text] chessboard with the middle part missing and the rim contains [Formula: see text] rows and [Formula: see text] columns. Another way is to stack [Formula: see text] copies of the [Formula: see text] chessboard to construct an [Formula: see text] rectangular chessboard and the closed knight’s tour can be on the surface or within the [Formula: see text] rectangular chessboard. This paper combines these two ideas by stacking [Formula: see text] copies of [Formula: see text] ringboard of width [Formula: see text], which we call the [Formula: see text]-rectangular tube. We explore the existence and the nonexistence of closed knight’s tours for [Formula: see text]-tube and [Formula: see text]-tube.

Modeling and Closed-Loop Control of Stretch Bending of Aluminum Rectangular Tubes

2003 ◽  
Vol 125 (1) ◽  
pp. 113-119 ◽  
Author(s):  
Hong Zhu ◽  
Kim A. Stelson
Keyword(s):  
Experimental Data ◽  
Real Time ◽  
Control Algorithm ◽  
Closed Loop ◽  
Strain History ◽  
Closed Loop Control ◽  
Loop Control ◽  
Stretch Bending ◽  
Rectangular Tube ◽  
Rectangular Tubes

During stretch bending, considerable springback will occur after a tube has been plastically bent. To predict the springback, a simplified two-flange model for stretch bending of a rectangular tube has been developed in which the strain history has been considered. A comparison has been made between the springback predicted by this model and experimental data, which shows rough agreement. Based on this model, a real time closed-loop control algorithm is developed.

Energy Absorption Analysis and Optimization Design of Local Surface Nanocrystallization Rectangular Tubes

2020 ◽  
Vol 975 ◽  
pp. 109-114
Author(s):  
Zhen Zhao ◽  
Wei Wang ◽  
Ying Li Chen ◽  
Zhen Huan Zhou ◽  
C.W. Lim ◽  
...  
Keyword(s):  
Energy Absorption ◽  
Optimization Design ◽  
Absorption Analysis ◽  
Local Surface ◽  
Buckling Modes ◽  
Surface Nanocrystallization ◽  
Rectangular Tube ◽  
Buckling Stability ◽  
Absorption Performance ◽  
Rectangular Tubes

A novel rectangular tube with circumferential anti-symmetric local self-surface nanocrystallization (CALSSN) layouts is designed for energy absorption. The effects of stripe numbers on the energy absorption performance is investigated. Results reveal that the 8-stripe CALSSN model exhibits the best buckling modes, which is more regular and stable than the untreated ones. It is also found that the stripe numbers highly depend on the structural sizes, unsuitable stripes number may reduce the buckling stability and periodicity. Besides, five CALSSN models with stripe numbers from 6 to 10 are selected to find the optimized size which has the highest specific energy absorption (SEA). A new 7-stripe CALSSN model which has optimal buckling modes and energy absorption performance is achieved.

Large-Deflection Bending of Clamped Metal Foam-Filled Rectangular Tubes

2017 ◽  
Vol 09 (03) ◽  
pp. 1750043 ◽  
Author(s):  
Jianxun Zhang ◽  
Qinghua Qin ◽  
Yan Yang ◽  
Xuehui Yu ◽  
Shangjun Chen ◽  
...  
Keyword(s):  
Analytical Model ◽  
Large Deflection ◽  
Metal Foam ◽  
Yield Criterion ◽  
Structural Response ◽  
Flat Punch ◽  
Plastic Yield ◽  
Rectangular Tube ◽  
Foam Filled ◽  
Rectangular Tubes

Large-deflection bending of fully clamped slender metal foam-filled rectangular tubes is investigated theoretically, experimentally and numerically. A plastic yield criterion for the foam-filled rectangular tube is proposed. Considering the filled foam strength effect and the interaction of bending and stretching, an analytical solution is proposed to predict the structural response of the foam-filled rectangular tubes transversely loaded by a flat punch. Clamped bending tests of aluminium alloy foam-filled rectangular tubes are conducted. The analytical model captures experimental results reasonably. Numerical calculations are carried out to predict the large-deflection behavior of the foam-filled tubes, and good agreement is achieved between the analytical solutions and numerical results. The effects of wall thickness of tube, punch size and filled foam strength are discussed in detail. It is demonstrated that the present analytical model can reasonably predict the post-yield behavior of the foam-filled rectangular tube.

scholarly journals Closed Knight’s Tours on (m,n,r)-Ringboards

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1217
Author(s):  
Wasupol Srichote ◽  
Ratinan Boonklurb ◽  
Sirirat Singhun
Keyword(s):  
Three Dimensional ◽  
Middle Part ◽  
Perpendicular Direction ◽  
Knight’S Tour

A (legal) knight’s move is the result of moving the knight two squares horizontally or vertically on the board and then turning and moving one square in the perpendicular direction. A closed knight’s tour is a knight’s move that visits every square on a given chessboard exactly once and returns to its start square. A closed knight’s tour and its variations are studied widely over the rectangular chessboard or a three-dimensional rectangular box. For m,n>2r, an (m,n,r)-ringboard or (m,n,r)-annulus-board is defined to be an m×n chessboard with the middle part missing and the rim contains r rows and r columns. In this paper, we obtain that a (m,n,r)-ringboard with m,n≥3 and m,n>2r has a closed knight’s tour if and only if (a) m=n=3 and r=1 or (b) m,n≥7 and r≥3. If a closed knight’s tour on an (m,n,r)-ringboard exists, then it has symmetries along two diagonals.

Three-dimensional analysis of soil – steel bridges

1995 ◽  
Vol 22 (6) ◽  
pp. 1155-1163 ◽  
Author(s):  
Youssef Girges ◽  
George Abdel-Sayed
Keyword(s):  
Plane Strain ◽  
Dimensional Analysis ◽  
Three Dimensional ◽  
Strain Analysis ◽  
Middle Part ◽  
Steel Bridges ◽  
Steel Shell ◽  
Live Load ◽  
Two Dimensional ◽  
Element Analysis

The present design of soil–steel bridges is based on plane-strain analysis by considering a slice of a unit width of the conduit wall and the surrounding soil. This two-dimensional analysis neglects the third-dimensional effect of the steel shell and the soil continuum which could be significant especially when the load varies in the longitudinal direction, as in the case of live load acting over a shallow cover. The structure is also subjected to a varying dead load due to the variation in the depth of cover from maximum at the middle part of the conduit to zero at the conduit edges. A three-dimensional finite element analysis is presented in this paper to examine the actual three-dimensional behaviour of soil-steel bridges. The thrust and bending moment around the conduit walls as well as the stability of a single conduit are presented and compared with the results obtained from plane-strain analysis. Also, the live load dispersion in the soil above the conduit is examined and compared with some present codes. The study leads to evaluation of the degree of approximation inherited with the practical approaches of the two-dimensional analysis. Key words: conduit, corrugated steel, three-dimensional analysis, stability, soil–steel bridges.

Distortion of Rectangular Tubes in Stretch Bending

2002 ◽  
Vol 124 (4) ◽  
pp. 886-890 ◽  
Author(s):  
Hong Zhu ◽  
Kim A. Stelson
Keyword(s):  
Internal Pressure ◽  
Energy Minimization ◽  
Stretch Bending ◽  
Rectangular Tube ◽  
Side Walls ◽  
Thin Walled ◽  
Analytical Expressions ◽  
Rectangular Tubes ◽  
Good Agreement

During stretch bending, considerable in-plane distortion occurs when a thin-walled rectangular tube is plastically bent. To minimize the distortion, fixed walls are used to limit the bulging of the side walls of the tube. Internal pressure can also be used to compensate for distortion. In this paper, analytical expressions for the amount of distortion and the needed internal pressure are derived based on energy minimization. The theory is in fairly good agreement with experiments.

scholarly journals Analyses on the effect of magnetic induction attenuation on the current distribution in a Faraday MHD generator

2013 ◽  
Vol 16 (2) ◽  
pp. 63-72
Author(s):  
Kien Chi Le
Keyword(s):  
Current Distribution ◽  
Magnetic Induction ◽  
Middle Part ◽  
Magnetic Flux Density ◽  
Two Dimensional ◽  
Electrical Parameters ◽  
Equilibrium Plasma ◽  
Exit Region ◽  
Mhd Generator ◽  
Non Equilibrium

This paper examines the dependence of the attenuation of magnetic induction on the current distribution etc. in the exit regions of the Faraday type non-equilibrium plasma MHD generator by a two-dimensional calculation. The numerical analyses are made for an example of the cesium-seeded helium. As a result, a reasonable magnetic induction attenuation can make the distribution of current very uniform near the exit region of generator channel and has little influence on the current distribution in the middle part of generator, and the output electrodes can be used without great ballast resistors. Also the inside resistance of the exit region and the current concentration at the exit electrode edges decrease with the attenuation of magnetic flux density. By the author's examination, it is made clear that the exit electrodes of the diagonal Faraday type non-equilibrium plasma MHD generator should be arranged in the attenuation region of the magnetic induction, since arranging them in this region becomes useful for the improvement of the electrical parameters of generator.

Spectrophotometric measurements of objective-prism spectra

1966 ◽  
Vol 24 ◽  
pp. 118-119
Author(s):  
Th. Schmidt-Kaler
Keyword(s):  
Progress Report ◽  
Two Dimensional ◽  
Objective Prism ◽  
Made In

I should like to give you a very condensed progress report on some spectrophotometric measurements of objective-prism spectra made in collaboration with H. Leicher at Bonn. The procedure used is almost completely automatic. The measurements are made with the help of a semi-automatic fully digitized registering microphotometer constructed by Hög-Hamburg. The reductions are carried out with the aid of a number of interconnected programmes written for the computer IBM 7090, beginning with the output of the photometer in the form of punched cards and ending with the printing-out of the final two-dimensional classifications.

Introductory paper

1966 ◽  
Vol 24 ◽  
pp. 3-5
Author(s):  
W. W. Morgan
Keyword(s):  
Line Intensity ◽  
Classification Scheme ◽  
Two Dimensional ◽  
Spectral Classification ◽  
Dimensional Array ◽  
Rr Lyrae ◽  
Metallic Line ◽  
Introductory Paper ◽  
Parameter Varying ◽  
Definition Of

1. The definition of “normal” stars in spectral classification changes with time; at the time of the publication of theYerkes Spectral Atlasthe term “normal” was applied to stars whose spectra could be fitted smoothly into a two-dimensional array. Thus, at that time, weak-lined spectra (RR Lyrae and HD 140283) would have been considered peculiar. At the present time we would tend to classify such spectra as “normal”—in a more complicated classification scheme which would have a parameter varying with metallic-line intensity within a specific spectral subdivision.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

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