求解等圆Packing问题的完全拟物算法

沿着拟物的思路进一步研究了具有NP难度的等圆Packing问题.提出了两个拟物策略,第一个是拟物下降算法,第二是让诸圆饼在某种物理定律下做剧烈运动.结合这两个策略,提出了一个统一的拟物算法.当使用N(N=1,2,3,…,100)等圆最紧布局的国际记录对此算法进行检验时,发现对于N=66,67,70,71,77,89这6个算例,本算法找到了比当前国际纪录更优的布局.     

Axisymmetric deformation of cylinders made of homogeneous and fiber-reinforced elastic materials in butt-end torsion

The equations of axisymmetric deformation of a circular cylinder made of homogeneous and weakly fiber-reinforced materials in a macroscopically two-dimensional problem statement are presented. The fibers are placed in the axial, circumferential, and radial directions and along spirals in the cylinder wall. They also can lie along opposite spirals in adjacent cylindrical layers, forming an angle-ply reinforcement scheme. At a low content of fibers, it is assumed that they are in the uniaxial stress state, determined by the axial tension or constraint compression in the deformed cylinder. Based on this mathematical model, the deformation of homogeneous and fiber-reinforced elastic cylinders of various length, with free outer surfaces, in butt-end torsion is investigated. The effect of length of the cylinders on their deformation character in torsion is evaluated. The torsion of the cylinders under the conditions of sliding fit along the inner surface and under the action of pressure on the surface, when the initial and deformed configurations are practically congruent, is considered.     

Modelling two-dimensional flow past arbitrary cylindrical bodies using boundary element formulations

This paper presents an efficient method of solving Queen's linearized equations for steady plane flow of an incompressible, viscous Newtonian fluid past a cylindrical body of arbitrary cross-section. The numerical solution technique is the well known direct boundary element method. Use of a fundamental solution of Oseen's equations, the ‘Oseenlet’, allows the problem to be reduced to boundary integrals and numerical solution then only requires boundary discretization. The formulation and solution method are validated by computing the net forces acting on a single circular cylinder, two equal but separated circular cylinders and a single elliptic cylinder, and comparing these with other published results. A boundary element representation of the full Navier-Stokes equations is also used to evaluate the drag acting on a single circular cylinder by matching with the numerical Oseen solution in the far field.     

Extension of the Lamé–Gadolin problem for large deformations and its analytical solution

The formulation and solution of the axisymmetric static problem of the stress-strain state of two hollow circular elastic cylinders, one of which is predeformed and inserted into the other cylinder, is considered in the case of large plane deformations (an extension of the Lamé–Gadolin problem to large deformations). Using the theory of the superposition of large deformations, an exact analytical solution of the static problem for cylinders made of incompressible Treloar and Bartenev–Khazanovich materials is obtained, including the case when the cylinders are made of dissimilar materials. An analytical solution is obtained in parametric form for a compressible Blatz–Ko material. Non-linear effects are investigated.     

Optimizing the packing of cylinders into a rectangular container: A nonlinear approach

The container loading problem has important industrial and commercial applications. An increase in the number of items in a container leads to a decrease in cost. For this reason the related optimization problem is of economic importance. In this work, a procedure based on a nonlinear decision problem to solve the cylinder packing problem with identical diameters is presented. This formulation is based on the fact that the centers of the cylinders have to be inside the rectangular box defined by the base of the container (a radius far from the frontier) and far from each other at least one diameter. With this basic premise the procedure tries to find the maximum number of cylinder centers that satisfy these restrictions. The continuous nature of the problem is one of the reasons that motivated this study. A comparative study with other methods of the literature is presented and better results are achieved.     

Torsional vibrations of piezoceramic hollow cylinders with circular polarization

A problem of natural torsional vibrations of hollow piezoceramic cylinders is considered. The piezoceramic is polarized in the circular direction. The lateral surfaces of the cylinder are covered with shortcircuited thin electrodes. The method of solution of the problem is based on the combination of the spline collocation methods along the longitudinal coordinate and the stepwise search method along the radial coordinate. We present results of a numerical analysis of a cylinder made from PZT 4 ceramic in a wide range of change in the geometrical characteristics of the cylinder.     

On the hydrodynamic interaction of two circular cylinders oscillating in a viscous fluid

The present paper deals with the plane flow fields induced by two parallel circular cylinders with radiia andb oscillating in a direction which is i) parallel or ii) perpendicular to the plane containing their axes. The effect of the cylinders' hydrodynamic interaction on steady streaming has been studied analytically at high frequency by the method of matched asymptotic expansions.It is found that ifa=b the steady streaming is directed symmetrically to the cylinders while whenab (in the case i)) the secondary steady flow is directed towards the larger cylinder and one of the outer steady vortices disappears.It is shown in case i) that the drag force acting on each cylinder is smaller than the same force experienced on a single cylinder with the same radius which is placed in an unbounded oscillating flow. When the cylinder radii are equal, the drag is greater on the forward cylinder than on the rear one.In contrast, in case ii), wherea=b, it is shown that the drag on each of the two cylinders is greater than the drag acting on a single cylinder with the same radius placed in an unbounded oscillating stream and also each of the cylinders experiences a repulsive force in a direction perpendicular to the oscillating flow.     

Natural convection between horizontal heated concentric circular cylinders

Natural convection between infinitely long, horizontal, heated, concentric circular cylinders is considered. It is assumed that the temperature difference between the cylinders is small and also that the radius of the inner cylinder is small. It is shown that the problem is mainly conduction dominated provided thatR, the ratio of the radius of the outer cylinder to the radius of the inner cylinder, is not too large. The criterion derived for a conduction dominated problem is a relation betweenR and the Grashof number.

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Zusammenfassung Die freie Konvektion zwischen zwei unendlichen, horizontalen, geheizten, konzentrischen Zylindern wird untersucht. Der Temperaturunterschied zwischen den Zylindern sowohl wie der Radius des inneren Zylinders, wird klein angenommen. Es wird gezeigt, dass das Problem vom Wärmedurchgang beherrscht ist, fallsR, das Verhältnis zwischen dem Radius des äusseren und inneren Zylinders, nicht zu gross ist. Das abgeleitete Kriterium für diesen Fall ist eine Beziehung zwischenR und der Grashof-Zahl.

     

Thermal effects in orthotropic porous elastic beams

This paper is concerned with the linear theory of anisotropic porous elastic bodies. The extension and bending of orthotropic porous elastic cylinders subjected to a plane temperature field is investigated. The work is motivated by the recent interest in the using of the orthotropic porous elastic solid as model for bones and various engineering materials. First, the thermoelastic deformation of inhomogeneous beams whose constitutive coefficients are independent of the axial coordinate is studied. Then, the extension and bending effects in orthotropic cylinders reinforced by longitudinal rods are investigated. The three-dimensional problem is reduced to the study of two-dimensional problems. The method is used to solve the problem of an orthotropic porous circular cylinder with a special kind of inhomogeneity.      

Investigation of the effect of rheological factors on the magnitude of the circular zone of plasticity in a cylinder of elastoplastic material

The problem of the effect of rheological factors on the magnitude of the circular zone of plasticity in a cylinder of elastoplastic material was solved for two cases: for a cylinder of material reinforced with concentric fibers and for an isotropic cylinder under conditions of plane axisymmetric strain. The displacements and stresses arising in the investigated cylinders were obtained. In each case bilateral estimates were obtained for the time-variable unknown radii of plasticity.Dnepropetrovsk State University. Translated from Mekhanika Polimerov, No. 1, pp. 118–123, January–February, 1972.     

含裂纹的圆柱体的弯曲

含裂纹的圆柱体弯曲的研究有十分重要的意义。文献[1]～[4]研究过含径向裂纹或裂纹系的情形,[5]研究过有同心圆弧裂纹的圆柱体的弯曲。本文继续[6]对内部出现在任意位置的直线裂纹的圆柱体在力与裂纹垂直时的弯曲问题,用弹性理论复变函数方法进行了讨论;得到了位移、应力和应力强度因子用级数表示的表达式;对Ah小的这种弯曲问题的应力强度因子给出了好的近似式,分析了它们随裂纹中心的变化规律。最后对裂纹的一个尖端在原点的径向裂纹圆柱体的扭转率和弯曲中心进行了计算,其结果与[1]几乎完全相同。     

The virtual mass coefficients of a circular cylinder moving in an ideal fluid between parallel walls

A modification of the method of successive approximations to find the dependence of the virtual mass coefficients of a circular cylinder, moving perpendicular to its axis at an arbitrary point between parallel walls, on the dimensionless distances to both walls, is proposed. The velocity field of the corresponding plane problem is modelled by an infinite sequence of dipoles, situated along a line passing through the centre of the cylinder and perpendicular to the walls. The relations obtained are approximated by simple continuous functions. In special cases, the results obtained are compared with well-known solutions of the problem of the motion of the cylinder near one wall and transverse in rotational flow around an array of cylinders.     

Sound transmission into a thick hollow cylinder with the fixed-end boundary condition

In this paper sound transmission through the air filled finite thick cylinders exposed to the different incident acoustic wave is studied. The effect of end boundary conditions on the noise reduction of finite cylinders is evaluated. The uniform incident wave and the wave radiated from monopole and dipole sources are used in this study. Three positions are considered for the dipole source. Every position for the dipole source causes symmetric or antisymmetric pressure distributions on the external surface of the cylinder in tangential or axial direction. For the purpose of sound transmission analysis the linear three-dimensional theory of elasticity utilizing the technique of variables separation for the infinite circular cylinders is used to analyze the vibration of finite circular cylinder. In these analyzes the stress continuity condition on the inner and outer surfaces of the cylinder is satisfied using orthogonalization technique and velocity continuity condition is exactly satisfied on the interfacial surfaces. The sound transmission evaluation is carried out for cylinders with various half-length to outer-radius ratios. The results show that in the case of the fixed-end cylinder, the effect of boundary conditions on the noise reduction can be neglected for the half-length to outer-radius ratio of more than 10. Comparing between the obtained results from different acoustic sources shows that the obtained noise reductions from the uniform acoustic wave are less than those obtained from the monopole and dipole sources.     

Analysis of natural convection from a column of cold horizontal cylinders using Artificial Neural Network

Artificial Neural Networks (ANNs) offer an alternative way to tackle complex problems. They can learn from the examples and once trained can perform predictions and generalizations at high speed. They are particularly useful in behavior or system identification. According to the above advantages of ANN in the present paper ANN is used to predict natural convection heat transfer and fluid flow from a column of cold horizontal circular cylinders having uniform surface temperature. Governing equations are solved in a few specified cases by finite volume method to generate the database for training the ANN in the range of Rayleigh numbers of 10⁵–10⁸ and a range of cylinder spacing of 0.5, 1.0, and 1.5 diameters, thereafter a Multi-Layer Perceptron (MLP) network is used to capture the behavior of flow and temperature fields and then generalized this behavior to predict the flow and temperature fields for any other Rayleigh numbers. Different training algorithms are used and it is found that the resilient back-propagation algorithm is the best algorithm regarding the faster training procedure. To validate the accuracy of the trained network, comparison is performed among the ANN and available CFD results. It is observed that ANN can be used more efficiently to determine cold plume and thermal field in lesser computational time. Based on the generalized results from the ANN new correlations are developed to estimate natural convection from a column of cold horizontal cylinders with respect to a single horizontal cylinder.     

Oscillatory flow about a cylinder pair

Oscillatory flow about a pair of circular cylinders is considered.The distance between the cylinders can be varied as can theangle that the undisturbed oscillatory flow makes with the linejoining the cylinder centres. In common with other fluid flowsdominated by oscillatory flow, a time-independent, or steadystreaming, motion develops. Attention is focused on the caseof high streaming Reynolds numbers and the resulting jets thaterupt from the surfaces of the cylinders.     

Torsional wave dispersion relations in a pre-stressed bi-material compounded cylinder with an imperfect interface

This paper studies the influence of the imperfectness of the contact condition on the torsional wave propagation in the initially stressed (stretched) bi-material compounded circular cylinder. The investigation is carried out within the scope of the piecewise homogeneous body model with the use of the Three-dimensional Linearized Theory of Elastic Waves in Initially Stresses Bodies. The mathematical formulation of the corresponding eigen-value problem is formulated and the solution method for that is developed. The two cases considered are the bi-material compounded cylinder consists of the solid inner and surrounding hollow outer cylinders (Case 1); the bi-material compounded cylinder consists of the hollow inner and surrounding hollow outer cylinders (Case 2). The mechanical relations of the cylinders’ materials are written through the Murnaghan potential. It is proven that the imperfectness of the contact condition does not influence the asymptotic-limit values of the wave propagation velocity. Moreover, the numerical results on the effects of the imperfectness of the boundary condition on the influence of the initial stresses on the wave propagation velocity are presented and discussed.     

Temperature stresses in an inhomogeneous cylinder of finite length

An analytic method of determining the temperature stresses in circular cylinders is described. In the solution of the problem, based on a collocation method, together with the finite length of the cylinder its arbitrary inhomogeneity is also taken into account. In a particular case this may be caused by the effect of temperature on the mechanical constants of the material, which is especially typical of polymers at negative temperatures. The results of a calculation of the stresses in a hollow cylinder of finite length with a variable modulus of elasticity are presented as an example.Dzherzhinskii Military Engineering Academy. Translated from Mekhanika Polimerov, Vol. 4, No. 4, pp. 710–715, July–August, 1968.     

Thermal effects in orthotropic porous elastic beams

This paper is concerned with the linear theory of anisotropic porous elastic bodies. The extension and bending of orthotropic porous elastic cylinders subjected to a plane temperature field is investigated. The work is motivated by the recent interest in the using of the orthotropic porous elastic solid as model for bones and various engineering materials. First, the thermoelastic deformation of inhomogeneous beams whose constitutive coefficients are independent of the axial coordinate is studied. Then, the extension and bending effects in orthotropic cylinders reinforced by longitudinal rods are investigated. The three-dimensional problem is reduced to the study of two-dimensional problems. The method is used to solve the problem of an orthotropic porous circular cylinder with a special kind of inhomogeneity.     

The volume of a solid of revolution in calculus

<正>On the last time,you have known what a right circular cylinder is in calculus.Right circular cylinders are just a part of solids of revolution.Today you will learn solids of revolution arent right circular cylinders.In general way,a solid is bounded by the region under the curve y=f(x)by rotating a-     

Interaction of a hollow cylinder of finite length and a plate with a cylindrical cavity with a rigid insert

Two problems of the interaction of a hollow circular cylinder with load-free ends and an unbounded plate with a cylindrical cavity and a symmetrically imbedded rigid insert are considered. Homogeneous solutions are found and the generalized orthogonality of these solutions is used when the modified boundary conditions are satisfied. As a result, we have a system of two integral equations in functions of the displacements of the outer and inner surfaces of the hollow cylinder. These functions are sought in the form of sums of a trigonometric series and a power function with a root singularity. The ill-posed infinite systems of linear algebraic equations obtained are regularized by the introduction of small positive parameters. Since the elements of the matrices of the systems as well as the contact stresses are defined by poorly converging numerical and functional series, an efficient method for calculating of the remainders of the above-mentioned series is developed. Formulae are found for the contact pressure distribution function and the integral characteristic. Examples of the calculation of the interaction of the cylinder and the plate with an insert are given.The method of solving contact problems described here has been used earlier1, 2 and the generalized orthogonality of the solutions found for bodies of finite dimensions, that is, for a rectangle and cylinders of finite length, is its basis. Problems for hollow cylinders with a band ² and an insert reduce to a system of two integral equations, and the problem for a rectangle¹ reduces to one integral equation. Solving these integral equations, ill-posed systems of linear algebraic equations are obtained which are subject to regularization³.