Equations of Deformation of an Elastic Inhomogeneous Laminated Body of Revolution

Equations governing deformation of an elastic inhomogeneous laminated body of revolution are proposed. Each layer is a domain bounded by convex equidistant surfaces of revolution.     

Stress singularities in an anisotropic body of revolution

To fill the gap in the literature on the application of three-dimensional elasticity theory to geometrically induced stress singularities, this work develops asymptotic solutions for Williams-type stress singularities in bodies of revolution that are made of rectilinearly anisotropic materials. The Cartesian coordinate system used to describe the material properties differs from the coordinate system used to describe the geometry of a body of revolution, so the problems under consideration are very complicated. The eigenfunction expansion approach is combined with a power series solution technique to find the asymptotic solutions by directly solving the three-dimensional equilibrium equations in terms of the displacement components. The correctness of the proposed solution is verified by convergence studies and by comparisons with results obtained using closed-form characteristic equations for an isotropic body of revolution and using the commercial finite element program ABAQUS for orthotropic bodies of revolution. Thereafter, the solution is employed to comprehensively examine the singularities of bodies of revolution with different geometries, made of a single material or bi-materials, under different boundary conditions.     

Influence of the Direction of the Principal Anisotropy Axes in a Rectilinearly Orthotropic Material on the Stress State of a Compound Solid of Revolution Subject to Nonaxisymmetric Heating

A technique for analysis of the temperature fields and the stress state of isotropic and orthotropic laminated bodies of revolution under nonaxisymmetric loading is described. The influence of the direction of the principal anisotropy axes in a rectilinearly orthotropic material on the stress state of a three-layer body of revolution under nonaxisymmetric loading is studied     

平头锥型回转体高速入水结构强度数值分析

为探究回转体在高速入水过程中的结构强度，基于非线性有限元LS-DYNA软件中流固耦合任意拉格朗日-欧拉(arbitrary Lagrangian-Eulerian, ALE)方法，分析了不同壁厚的回转体以100 m/s的初速度入水过程中的冲击力特性和结构强度。结果表明:数值计算得到的入水冲击压强峰值和速度衰减曲线与相应的理论值吻合较好，从而验证了数值方法的有效性；入水冲击载荷峰值出现在结构入水瞬间，结构入水后冲击载荷急剧变小且微小震荡；回转体的结构形式对其在高速入水过程中的结构强度有重要影响，尤其回转体头部厚度影响回转体结构强度，当回转体头部厚度为8 mm、后体壁厚大于2.5 mm时，可以保证回转体强度要求。     

Onset of separation in hydrodynamic impact on a floating body

The vertical impact problem is considered for a body of revolution immersed in an ideal incompressible fluid bounded from below by a bottom in the shape of a surface of revolution. For a certain class of bodies it is proved that separation begins on the intersection between the wetted surface of the body and the meridional plane in which the shock impulse is located. As shown by the examples of spindle-shaped surfaces of revolution and an ellipsoid of revolution, separation can take place at one of two points on the boundary of the wetted surface of the body, one farther from and the other nearer to the point of application of the impulse.Rostov-on-Don. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 99–104, November–December, 1996.     

Analytical computation of aerodynamic characteristics of bodies of revolution under locality law conditions

An analytical method of computing the aerodynamic forces acting on a convex body of revolution whose motion satisfies locality law conditions. i.e., the force pulse acting on a surface element depends only on the flow mode and the local angle between the velocity and the normal to the surface, is elucidated. The solution is represented in a form where the influence of the parameters characterizing the shape of the streamlined body, the angle of attack, and the flow mode are explicitly extracted. Universal expressions are obtained for a number of coefficients, which are valid for any body of revolution. The aerodynamic characteristics of a four-parameter family of bodies of revolution in the hypersonic-flow mode are computed in a gas with a different degree of rarefaction.     

Determining the stress state of flexible orthotropic shells of revolution in magnetic field

A two-dimensional nonlinear magnetoelastic model of a current-carrying orthotropic shell of revolution is constructed taking into account finite orthotropic conductivity, permeability, and permittivity. It is assumed that the principal axes of orthotropy are aligned with the coordinate axes and that the orthotropic body is magnetically and electrically linear. The coupled nonlinear differential equations derived describe the stress-strain state of flexible current-carrying orthotropic shells of revolution that have an arbitrarily shaped meridian and orthotropic conductivity and are in nonstationary mechanical and electromagnetic fields. A method to solve this class of problems is proposed Translated from Prikladnaya Mekhanika, Vol. 44, No. 8, pp. 64–76, August 2008.     

回转体高速倾斜入水的流场特性及结构响应

回转体高速入水过程涉及液体和固体的耦合作用，是一个复杂的非线性、非定常过程。为研究回转体高速入水的结构动响应及流场演变规律，本文中基于STAR-CCM+和ABAQUS平台，建立了回转体高速入水的双向流固耦合数值模型，开展了不同入水速度的回转体高速倾斜入水流固耦合数值计算。结果表明:数值计算的入水速度、位移曲线和空泡形态与实验结果良好吻合，验证了流固耦合方法的有效性；回转体倾斜高速入水的载荷先集中在触水部分边缘处，后集中于回转体底部中心处；流固耦合方法的入水冲击载荷峰值小于刚体的，弹性回转体的载荷曲线产生明显波动；撞水阶段，回转体空泡呈现不对称形态，随着入水加深，空泡不对称性变弱；入水速度60 m/s下，空泡发生表面闭合，回转体入水初速度越快，空泡表面闭合越晚；冲击载荷与入水速度有关，入水速度越大，峰值出现越早，震荡越明显，速度超过100 m/s时，回转体产生塑性形变。     

Bodies of revolution with minimal drag coefficient and low heat transfer at high supersonic speeds

On the basis of modified Newtonian theory and the theory of selfsimilar hypersonic flows we study the form of the optimal contour of a body of revolution with minimal drag coefficient at hypersonic speeds. It is shown that bodies of optimal form also have a small heat transfer coefficient, much smaller than for a conical body. It is established experimentally that the optimal properties of these bodies of revolution are also retained for moderate supersonic flight speeds.In concluslion the author wishes to thank V. V. Sychev for valuable discussions of this problem.     

Slender bodies of revolution with minimum wave drag in nonequilibrium supersonic flow

We examine the problem of finding the generatrix shape of a body of revolution which travels at supersonic speed and has minimum wave drag. We assume that any number of nonequilibrium processes can take place in the flow. The pressure distribution over the body surface is taken in the linear approximation [1, 2]. A survey of studies using linear theory to find bodies of revolution of optimal form in supersonic perfect gas flow can be found in [3]. The solution of the problem of finding the form of two-dimensional slender bodies of minimum wave drag in nonequilibrium supersonic flow was obtained in [4]. In the following we examine the optimization of only those bodies of revolution for which the leading point lies on the axis of symmetry.The author wishes to thank A. N. Kraiko for his helpful comments.     

Optimal Axisymmetric Noses of Bodies in a Flow. Calculations and Experiments

The distinctive features of directmethods for contouring axisymmetric noses of bodies in a supersonic flow are discussed. The nose of a body of revolution in a supersonic flow, optimal with respect to the wave drag, includes a forward-looking flat face adjoining through a bend a sloping region of given aspect ratio (length-to-base-radius ratio), which, in turn, adjoins, again through a bend, the main part of the body. The above-mentioned sloping region can have, depending on its length, some additional internal bends. The presence of bends in a contoured configuration can often be undesirable, owing to strength, thermal, or others restrictions. For this reason, in solving the optimal contouring problems by means of direct methods analytical approximations of the unknown contour are often used, which leads to an increase in the drag of the optimized configuration. The degree of the increase in the drag of the nose part of a body of revolution in the cases of the local smoothing of bends in the optimal configuration and the global variation of its shape on the basis of an analytical approximation is investigated. It is shown that an increase in the drag of the nose part of a body of revolution owing its ineffective approximation can be many times greater than the gain due to optimization. The results of calculations are confirmed by the experimental data obtained.     

On the stress-strain state of a transversally isotropic body with a paraboloidal inclusion

A closed solution is presented for the three-dimensional problem of the stress-strain state of an unbounded elastic body with a soldered-in transversally isotropic inclusion in the form of a paraboloid of revolution. Here, it is assumed that the body is under axisymmetric tension (compression). A solution of the corresponding problem for a paraboloidal recess is obtained as a special case. Podil’chuk [2, 3] has investigated similar problems for isotropic bodies with an inclusion assuming the form of a paraboloid of revolution or an elliptical paraboloid. Translated from Prikladnaya Mekhanika, Vol. 34, No. 11, pp. 16–22, November, 1998.     

Stability of spatial motion of a body of revolution in an elastoplastic medium

A previously constructed model that describes the spatial motion of a body of revolution in an elastoplastic medium (without flow separation and with nonsymmetric separation of the medium flow taken into account) is used to study the Lyapunov stability of rectilinear motion of a body in the case of frozen axial velocity on a half-infinite time interval. Some stability criteria are obtained and the influence of tangential stresses is analyzed.     

Three-dimensional hypersonic rarefied gas flow round bodies of revolution

A proposed method of studying three-dimensional rarefied gas flow around a body of revolution is based on the numerical solution of model kinetic equations. By way of example, the problem is considered of hypersonic flow round an ellipsoid of revolution whose velocity vector forms an angle of ₀ with the axis of symmetry of the body and is located in the plane of symmetry. A study is made of the effect of the angle of attack, surface temperature and Knudsen number on the aerodynamic characteristics of the body.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti 1 Gaza, No. 1, pp. 184–186, January–February, 1986.     

Decomposition of teflon heat protective coatings at hypersonic flight velocities

We consider the decomposition of a teflon thermal protective coating along the generatrix of a blunted solid of revolution for various Mach numbers and pressures of the incident flow. On the basis of preliminary parametric study of the equations of a laminar boundary layer with pressure gradient, calculation of the teflon decomposition parameters is reduced to solution of a system of nonlinear and transcendental equations. It is shown that the temperature distribution and decomposition rate along the generatrix of the solid of revolution have a monotonie character, and that the effective enthalpy of the material remains constant along the body. A simple approximate formula is proposed for calculation of the teflon decomposition rate.     

A new kind of mixed elements for shells of revolution subjected to arbitrary loads

In this paper a generalized variational principle with two-field variables is derived from the Reissner principle of elasticity in the curvilinear coordinates of a revolution shell, based on which, a new kind of mixed elements with independent transverse rotations is formulated for revolution shells subjected to harmonic external loads. The resultant-stress interpolations are carefully selected so that the shear part of the element stiffness contains the Kirchhoff hypothesis for thin shells and element stiffness matrices have correct ranks. The elements are free from shear locking and spurious kinematic modes. Numerical examples show that the new elements have good generality and high accuracy for thin and moderately-thick revolution shells.     

Radiation and scattering from loaded bodies of revolution

The problem of electromagnetic radiation and scattering from loaded bodies of revolution of arbitrary shape is considered. The analysis assumes the existence of an impedance function relating the tangential electric field to the surface current on the body. A solution is obtained by the method of moments applied to the potential integral formulation of the problem. The results are expressed in terms of generalized network parameters, using formulas previously obtained for unloaded bodies. Representative computations are given for plane-wave scattering and radiation from apertures in loaded cylinders and hemispheres. A general computer program for arbitrary bodies of revolution is available.     

Aerodynamic characteristics of a body of revolution with gas-permeable surface areas

Results of experimental studies and numerical calculations of aerodynamic characteristics of a supersonic flow around a body of revolution with a gas-permeable porous nose cone and an internal duct are presented. At a flow velocity corresponding to the Mach number M = 3, the body considered is found to have a lower drag coefficient (approximately by 9%) than a similar body impermeable for the gas and a lower streamwise static stability.     

Stability in a case of motion of a paraboloid over a plane

We solve a nonlinear orbital stability problem for a periodic motion of a homogeneous paraboloid of revolution over an immovable horizontal plane in a homogeneous gravity field. The plane is assumed to be absolutely smooth, and the body–plane collisions are assumed to be absolutely elastic. In the unperturbed motion, the symmetry axis of the body is vertical, and the body itself is in translational motion with periodic collisions with the plane.The Poincare´ section surfacemethod is used to reduce the problemto studying the stability of a fixed point of an area-preserving mapping of the plane into itself. The stability and instability conditions are obtained for all admissible values of the problem parameters.     

Numerical study of Navier-Stokes equations

The problem of a viscous incompressible fluid flow around a body of revolution at incidence, which is described by Navier-Stokes equations, is considered. For low Reynolds numbers, the solutions of these equations are smooth functions. A numerical algorithm without saturation is constructed, which responds to solution smoothness. The calculations are performed on grids consisting of 900 (10 × 10 × 9) and 700 (10 × 10 × 7) nodes. On the grid consisting of 900 nodes, a system of 3600 nonlinear equations is solved by a standard code. The pressures on the shaded side of the body of revolution are compared. It is found that a numerical study (on this grid) is feasible for problems with Re ≈ 1. For high Reynolds numbers, the number of grid nodes has to be increased. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 43–52, September–October, 2007.