Optimum Shapes of Spatial Bodies with a Minimum Total Radiative Flux to the Surface

A solution of a variational problem of a slender body with a minimum total radiative heat flux, moving in a gas with a constant velocity, is constructed. It is found that there are three types of the transverse contour of the optimum body: a circumference, a starshaped contour, and a contour consisting of circle arcs and sectors of straight lines. The radiation parameter affects only the shape of the longitudinal contour and does not affect the optimum shape of the transverse contour. It is shown that the use of optimum spatial bodies allows a significant (more than 50%( decrease in the radiative heat flux to the body surface as compared to bodies of revolution with similar geometric characteristics.     

On the optimum shape of apertures for a perforated plate subject to bending

The problem of finding the optimum shape of the holes in a perforated plate weakened by a triangular or square lattice of holes and subject to bending is considered by methods based on the theory of functions of a complex variable. The criterion determining the optimum shape of the hole is based on the condition that no stress concentration should occur on the hole contour or, alternatively, that a plastic region should be created around the whole contour of the hole at exactly the same instant.     

Solution of some problems of particle motion in a gas stream

The problem of designing the contour of an optimum nozzle for particle acceleration is considered in the one-dimensional formulation. In [1] a similar problem was solved in the general formulation using a numerical method. Here, in contrast to [1], the solution is obtained in analytic form for the particular case of low particle concentration. The problem of the motion of a particle in a uniform stream is solved in the same form. Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 86–90, September–October, 1988.     

Thin flat bodies of minimum wave drag in nonequilibrium supersonic flow

In [1] the problem of optimal profiling of the contours of plane and axisymmetric bodies in supersonic nonequilibrium flow without the formation of a shock wave (these bodies include, in particular, the contours of base sections and nozzles) is reduced to the boundary value problem for a hyperbolic system of equations, which includes the flow equations and the equations for the Lagrange multipliers (there is an error in Eq. (4.5) of [1]; there should be a minus sign in front of the third term in the braces). In view of the solution complexity, in [2] the construction of the optimum nozzle contour is based on the one-dimensional approximation. Although this approach does permit establishing the order of the possible gain, the conclusions concerning the contour shape which result from this approach are basically qualitative. In the following the construction of thin plane bodies of minimal wave drag in a nonequilibrium supersonic flow is carried out in the linear approximation, which leads to a more complete picture of the form of the optimum contours. Numerous examples of the use of linear theory for optimizing body shape in supersonic perfect gas flow are given in [3].The authors wish to thank L. E. Sternin for continued support.     

Optimization of the shape of a body with respect to two criteria: Radiation heat flux and wave drag

The numerical solution of the two-criteria variational problem of the body contour with minimum radiation heat flux and wave drag is obtained in the class of axisymmetric and plane slender bodies in hypersonic flow. Solutions obtained using the Pareto, ideal point and minimax methods are compared. It is shown that in the class of axisymmetric slender bodies the optimum body gives a decrease in the radiation heat flux as compared with a cone of up to 15% for the Pareto method, up to 13% for the ideal point method, and up to 5% for the minimax method. A solution is also obtained in the subclass of power-law slender bodies and it is shown that the optimum power-law bodies are inferior, as compared with the optimum bodies from the general class of such bodies, in reducing both radiation heating and resistance.     

Biomechanical research of joint III. An experimental biomechanical research on the Femur's articular surface of knee of pongidae

In this paper, moiré contour fringes is applied to study the femur's articular surface of the knee of Pongidae. The preliminary division of the femur's articular surface of knee into three types is proposed. The moiré contour fringes ofthe medial condyle is taken as a mark according to the references. Owing to the fact that the moiré contour fringes obtained from experiments after the 2nd order of fringe basically follow a certain rule, an investigation is made on the distribution of the angle α which is defined as the angle of the major axis of the 2nd order's near-oval shaped moiré contour fringe on the medial condyle with the horizontal axis. Preliminary distribution graphs are given in the paper.     

Effect of surface and internal waves on the hydrodynamic characteristics of a contour in the linear approximation

A method of solving the problem of the motion of an elliptic contour in a three-layer fluid is developed within the framework of the linear theory. The results of calculating the hydrodynamic contour loads and the shape of the interfaces are presented for the following problems: the motion of a contour beneath an interface between two media and in a two-layer fluid both beneath a rigid lid and a free surface. On the basis of the numerical experiment it is concluded that surface and internal waves have a significant effect on the hydrodynamic characteristics of the contour. Omsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 121–127, May–June, 1998. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 96-01-00093).     

岩石钻爆开挖中预裂缝的隔震效果分析

通过应力波与由节理刚度系数描述的预裂缝的相互作用分析，考虑预裂缝在爆炸应力波作用下的闭合效应及预裂缝充水等条件下，研究了预裂缝的隔震机制与隔震效果，从而为岩石开挖过程中周边控制爆破方式的优选提供了理论依据。     

Global and local fuzzy energy-based active contours for image segmentation

This paper proposes a novel active contour model for image segmentation based on techniques of curve evolution. The paper introduces an energy functional including a local fuzzy energy and a global fuzzy energy to attract the active contour and stop it on the object boundaries. The local term allows the method to deal with intensity inhomogeneity in images. The global term, aside from driving the contour toward the desired objects, is used to avoid unsatisfying results led by unsuitable initial contour position, a common limitation of models using local information solely. In addition, instead of solving the Euler–Lagrange equation, the paper directly calculates the alterations of the fuzzy energy. By this way, the contour converges quickly to the object boundary. Experimental results on both 2D and 3D images validate the effectiveness of the model when working with intensity inhomogeneous images.     

Effect of ideal-gas flow swirl on the optimum supersonic contour of an axisymmetric nozzle with break

The effect of swirling the flow at the nozzle inlet on the shape of the optimum supersonic section with a break at the point of intersection of the limiting characteristic and the contour is investigated within the framework of the ideal (inviscid and non-heat-conducting) gas model. A direct method based on reduction to a problem of nonlinear programming is used for the numerical solution of the corresponding variational problem.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 155–160, May–June, 1989.In conclusion, the authors wish to thank N. I. Tillyaeva and A. N. Kraiko for participating in the discussions and A. A. Glazunov for assisting with the work.     

Contouring by moiré interferometry

A double-exposure moiré-interferometry technique for topographic contour measurement of an arbitrarily curved object is presented. A curved surface coated with light-sensitive material is exposed twice in a volume of virtual gratings formed by the interference of two coherent light beams split from a laser. An adequate rotation of the curved surface relative to the virtual grating between the two exposures produces moiré fringes which reveal topographic contour, or contour under some conditions, of the surface. The advantage of the present method in comparison with others is that it offers both reasonably good fringe quality and easily adjustable high sensitivity. The sensitivity of the technique is shown to be from the order of micrometer to that of millimeter depending on the frequency of the virtual grating and the amount of the relative rotation. This technique was successfully applied to the topographic contour measurement of a cylindrical shell with and without a diametrical point loading.The principle of this paper and some early results were presented at the SPIE conference held at Dearborn, MI on June 27–30, 1988 and appeared in its proceeding.¹     

The lifting force action on a contour in a plane homogeneous vortex flow of an incompressible ideal fluid

The plane problem of homogeneous vortex flows of an incompressible inviscid fluid around a contour is considered. A method is developed for contours having a center or an axis of symmetry for calculating the lifting force acting on the contour which reduces the problem of determining the lifting force to an ordinary problem of a potential flow of a fluid around the given contour.     

On the Green's Functions and Boundary Integral Formulation of Elastic Planes with Cutouts

ABSTRACT

The problem of an infinite elastic plane that contains a hole of arbitrary shape and is subjected to a concentrated unit load is considered. The Green's function (influence function) for the problem is formulated by means of two complex potential functions. This is accomplished by mapping the region that is exterior to the hole onto a unit circle. A class of closed contour hole shapes is analyzed. Green's functions for an elliptical hole and a class of triangular holes are determined. Green's functions for a class of rectangular holes are also discussed. In order to determine stress and displacement fields for the finite plane problem, Green's function is employed and an indirect boundary integral equation is formulated, with the integrand of the integral equation incorporating the effect of the hole. The contour of the hole is no longer considered a part of the boundary and only the contour of the region that is exterior to the hole is subdivided into boundary elements. Examples for elliptical and triangular holes are solved.     

Force acting on a deformable contour moving in an arbitary fluid stream

A solution is given for the plane nonstationary motion of an arbitary deformable contour in the potential flow of an ideal incompressible fluid. The problem was solved by conformal mapping. A simple formula is obtained for the force acting on a small size contour.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 4–8, January–February, 1973.The author is grateful to L. I. Sedov and Yu. L. Yakimov for formulating the problem and supervising the research.     

A numerical implementation using mid-node collocation for the hypersingular boundary contour method

A variant of the boundary element method, called the boundary contour method (BCM), offers a further reduction in dimensionality. Consequently, boundary contour analysis of two-dimensional problems does not require any numerical integration at all. In another development, a boundary contour implementation of a regularized hypersingular boundary integral equation (HBIE) using quadratic elements and end-node collocation was proposed and the technique is termed the hypersingular boundary contour method (HBCM). As reported in that work, the approach requires highly refined meshes in order to numerically enforce the stress continuity across boundary contour elements. This continuity requirement is very crucial since the regularized HBIE is only valid at collocation points where the stress tensor is continuous, while the computed stress at the endpoints of a boundary contour element, which is a non-conforming element, is generally not. This paper presents a new implementation of the HBCM for which the regularized HBIE is collocated at the mid-node of a boundary contour element. As the computed stress tensor is continuous at these mid-nodes, there is no need for unusually refined meshes. Some numerical tests herein show that, for the same mesh density, the HBCM using mid-node collocation has a comparable accuracy as the BCM.     

Variational problem of optimum side wall design for a narrow three-dimensional nozzle

The optimum design of the side walls of the supersonic section of a three-dimensional nozzle with two planes of symmetry is considered in the narrow channel model approximation, which reduces three-dimensional to two-dimensional flow. This nozzle realizes maximum thrust for given sonic or supersonic inlet flow, upper and lower walls, maximum permissible length and pressure outside the nozzle. In general, an approximate solution of the variational problem can be obtained by the indeterminate control contour method [1]. For nozzles with nonexpanding end sections of the upper and lower walls this is a rigorous solution. Numerical algorithms, based on the method of characteristics, for constructing the optimum, side walls and calculating the flow in narrow channels are developed in the formulation adopted using the optimality conditions found, which generalize the wellknown conditions for plane and axisymmetric configurations [1]. In addition, the three-dimensional supersonic flow in the nozzles thus designed has been calculated in accordance with a shock-capturing marching scheme [2], which for the uniform grids employed in the calculations gives a second-order approximation. A rather complex relation is established between the thrust of the optimum configurations constructed and the shape of their inlet cross sections.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 102–112, March–April, 1992.The authors are grateful to L. E. Sternin for drawing their attention to the problem and to V. A. Vostretsova for assisting with the work.     

磨粒磨损中磨粒几何外形参数的分析方法

根据Ｆｏｕｒｉｅｒ级数的频域分析方法，并且运用快速Ｆｏｕｒｉｅｒ变换的算法，在ＩＢＭ－ＰＣ机上通过自编程序进行了不同磨粒几何外形参数的数值计算，利用这种计算方法，可以获得磨粒尖锐度、粗糙度和轮廓的角形特征等信息，是对不同磨粒外部几何形状进行比较判别的一种有效方法。     

A new representation for the dynamic green's tensor of an elastic half-space or layered medium

A method for inverting the transforms of the terms in generalized ray series representations for disturbances in layered media is presented. It differs from the Cagniard reduction in that the solution of algebraic equations depending upon position x and time t is not required. This step is, in effect, replaced by contour integration of relatively simple functions. The method is applicable to anisotropic layers but it simplifies when applied to isotropic layers, for which any term in the ray series is represented as a single contour integral, around a fixed contour, of the product of a function that embodies material properties and a simple explicit function of x and t. The ‘material function’ can be tabulated and used repeatedly when the integral is evaluated for a range of values of x and t, so that the procedure is computationally quite efficient. It is illustrated by a computation of Green's function for an isotropic half-space, either free or overlaid by a fluid. Wave-front singularities are obtained explicitly from the representation and are given in an appendix.     

Measuring Inaccessible Residual Stresses Using Multiple Methods and Superposition

The traditional contour method maps a single component of residual stress by cutting a body carefully in two and measuring the contour of the cut surface. The cut also exposes previously inaccessible regions of the body to residual stress measurement using a variety of other techniques, but the stresses have been changed by the relaxation after cutting. In this paper, it is shown that superposition of stresses measured post-cutting with results from the contour method analysis can determine the original (pre-cut) residual stresses. The general superposition theory using Bueckner’s principle is developed and limitations are discussed. The procedure is experimentally demonstrated by determining the triaxial residual stress state on a cross section plane. The 2024-T351 aluminum alloy test specimen was a disk plastically indented to produce multiaxial residual stresses. After cutting the disk in half, the stresses on the cut surface of one half were determined with X-ray diffraction and with hole drilling on the other half. To determine the original residual stresses, the measured surface stresses were superimposed with the change stress calculated by the contour method. Within uncertainty, the results agreed with neutron diffraction measurements taken on an uncut disk.     

Design of a wing airfoil in a flow with a separated turbulent boundary layer

The problem of designing the contour of an airfoil in a viscous (incompressible and compressible) flow with a separated turbulent boundary layer from a pressure distribution given on the separationless part of the contour is solved using the boundary layer theory together with the separated flow model proposed in [1]. Numerical calculations are carried out to demonstrate the possibilities of the method.Kazan'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 83–91, May–June, 1994.