Numerical modelling of cavities on axisymmetric bodies at zero and non-zero angle of attack

The flow about submerged, fully cavitating axisymmetric bodies at both zero and non-zero angle of attack is considered in this paper. A cavity closure model that relates the point of detachment, the angle that the separating streamline makes with the body and the cavity length is described. The direct boundary element method is used to solve the potential flow problem and to determine the cavity shape. A momentum integral boundary layer solver is included in the formulation so that shear stresses can be incorporated into the drag calculations. The numerical predictions based on the proposed closure model are compared with water tunnel measurements and photographs.     

Three-dimensional turbulent boundary layers on bielliptic bodies in a stream of compressible gas at an angle of attack

The results are given of a numerical investigation of the three-dimensional turbulent boundary layer formed on bielliptic bodies in a stream of compressible gas at an angle of attack. The investigation was made on the basis of the finite-difference method of calculation. The influence of a number of determining parameters on the development of the three-dimensional flows is analyzed. The characteristic flow regions in the boundary layer are found: lines of flow divergence and convergence, the region of “separation,” and flow division surfaces. The positions of the maximal values of the heat flux and the friction on the surface are determined, and the behavior of the limiting streamlines on the body is described.     

Shape control of thin rigid inclusions and cracks in elastic bodies

The paper is concerned with a control of thin rigid inclusion and crack shapes in elastic bodies. It is assumed that rigid inclusions are delaminated; thus, cracks are located on the boundary of inclusions as well as outside of inclusions. We provide the problem formulations and analyze the shape sensitivity with respect to geometrical perturbations in the frame of free boundary models. Inequality type boundary conditions are considered at the crack faces to guarantee a mutual non-penetration between crack faces. Inclusion and crack shapes are considered as control functions. The cost functional, which is based on the Griffith rupture criterion, characterizes the energy release rate and provides the shape sensitivity with respect to a change of the geometry of the structure. We prove an existence of optimal shapes in the problems considered.     

The determination of an equivalent elastic modulus for bodies with cracks by boundary element method

The equivalent elastic modulus of cracked bodies with orderly distributed cracks was computed with the boundary element method. A practical self-consistent scheme has been proposed in consideration of the mutual interaction effects of the cracks. The influence of friction coefficients and orientation of cracks has been investigated. Some computational examples have been given, and the results show that the proposed method is adequate and the scheme is efficient.This project is supported by the National Natural Science Foundation of China.     

Asymptotic modelling of an elastic roller crossing a scratch

The paper presents asymptotic modelling of the generalized Greenwood problem for an elastic cylinder (considered as a bounded two-dimensional elastic body) pressed between two rigid punches one of them with the dented surface having a scratch. The method of matched asymptotic expansions is used to obtain analytic approximations for the mutual displacement of the punches and the relative displacement of the roller's center.     

Solution for dissimilar elastic inclusions in a finite plate using boundary integral equation method

This paper studies the boundary value problem for a finite plate containing two dissimilar inclusions. The matrix and the two inclusions have different elastic properties. The loadings applied along the outer boundary are in equilibrium. The mentioned problem is decomposed into three boundary value problems (BVPs). Two of them are interior BVP for the elastic inclusions, while the other is a BVP for the triply-connected region. Three problems are connected together through the common displacements and tractions along the interface boundaries. Explicit form for the complex variable boundary integral equation (CVBIE) is derived. After discretization of relevant BIEs, the solutions are evaluated numerically. Three numerical examples for different elastic constant combinations are provided.     

Shape and topology sensitivity analysis for cracks in elastic bodies on boundaries of rigid inclusions

We consider an elastic body with a rigid inclusion and a crack located at the boundary of the inclusion. It is assumed that nonpenetration conditions are imposed at the crack faces which do not allow the opposite crack faces to penetrate each other. We analyze the variational formulation of the problem and provide shape and topology sensitivity analysis of the solution in two and three spatial dimensions. The differentiability of the energy with respect to the crack length, for the crack located at the boundary of rigid inclusion, is established.     

Stability of axisymmetric annular fluid interfaces at zero contact angle

We study the stability of liquid configurations in axisymmetric containers when the liquid-vapor interface is annular and meets the container walls at zero contact angle. Necessary and sufficient conditions for stability, as the contact angle tends to zero, are formulated in terms of the Jacobi accessory differential equations. The stability of the configuration is then shown to depend crucially on whether the equilibrium liquid-vapor interface stays inside the container or not, when continued analytically past the three-phase contact lines.     

Stress-strain state of an elastic half-plane with rectangular inclusions

Conclusions As is seen from Fig. 5, elevated stress zones are formed for small distances d<0.2a between the inclusions. In practice there is no mutual influence between the inclusions for distances d>2.5a since the distribution of the stress along the line x₁=0 for d=5a is the same as for the case of a half-plane without inclusions.Kiev University. Translated from Prikladnaya Mekhanika, Vol. 26, No. 5, pp. 56–61, May, 1990.     

A boundary element solution to scattering of elastic SH wave by arbitrarily shaped inclusions embedded in an infinite anisotropic medium

Scattering problems for inhomogeneous bodies are investigated by the integral equation method. The boundary integral equation (BIE) for the scattered displacement field associated with finite inhomogeneities in an anisotropic medium are derived with the help of the generalized Green's identity. The discretization of BIE is based upon the constant element, linear element and quadratic element. Several numerical examples for calculating the scattering displacement, stress and scattering cross section from a cylinder, an interface crack, and two elliptic cylinders are given. Results show that the present method can be advantageously applied to a wide range of scattering problems of elastic waves.     

A row of external cracks in an elastic half-plane

The plane-strain solution of the problem of a row of external cracks in an elastic half-plane whose faces are uniformly pressurized, is obtained. The stress intensity factor and the strain energy per crack are calculated and their variations with the distance of separation of the cracks are shown.

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Résumé On obtient la solution pour la contrainte simple du problème d'une suite de fissures extérieures dans un demiplan élastique dont les surfaces sont à pression uniforme. On calcule le facteur d'intensité de contrainte et l'energie de déformation pour chaque fissure et on montre leurs variations avec la distance entre les fissures.

     

Laminar boundary layer on swept-back wings of infinite span at an angle of attack

A study is made of the flow of a compressible gas in a laminar boundary layer on swept-back wings of infinite span in a supersonic gas flow at different angles of attack. The surface is assumed to be either impermeable or that gas is blown or sucked through it. For this flow and an axisymmetric flow an analytic solution to the problem is obtained in the first approximation of an integral method of successive approximation. For large values of the blowing or suction parameters, asymptotic solutions are found for the boundary layer equations. Some results of numerical solution of the problem obtained by the finite-difference method are given for wings of various shapes in a wide range of angles characterizing the amount by which the wings are swept back and also the blowing or suction parameters. A numerical solution is obtained for the equations of the three-dimensional mixing layer formed in the case of strong blowing of gas from the surface of the body. The analytic and numerical solutions are compared and the regions of applicability of the analytic expressions are estimated. On the basis of the solutions obtained in the present paper and studies of other authors a formula is proposed for the calculation of the heat fluxes to a perfectly catalytic surface of swept-back wings in a supersonic flow of dissociated and ionized air at different angles of attack. Flow over swept-back wings at zero angle of attack has been considered earlier (see, for example, [1–4]) in the theory of a laminar boundary layer. In [5], a study was made of flow over swept-back wings at nonzero angle of attack at small and moderate Reynolds numbers in the framework of the theory of a hypersonic viscous shock layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 27–39, May–June, 1980.We thank G. A. Tirskii for a helpful discussion of the results.     

Study of laminar boundary layer separation on a cone at an angle of attack

Experimental data are obtained on the position of the line of separation as a function of angle of attack, cone apex angle, and flow Mach number.     

Stability of elastic bodies with nonmonotone multivalued boundary conditions of the quasidifferential type

Necessary conditions for the stability of elastic bodies subjected to nonmonotone multivalued boundary conditions are derived. These conditions are assumed to be derived from nonconvex and nonsmooth, quasidifferentiable energy functions. A difference convex approximation of the potential energy function is written based on an appropriate quasidifferential formulation. Under appropriate assumptions for the convex and the concave parts we prove the existence of at least one nontrivial solution to the nonlinear eigenvalue problem.