Symmetric cavitation flow past a wedge in the presence of a source on the wedge or in the flow

A solution is found to the problem of symmetric cavitation flow over a wedge by an ideal incompressible fluid (in accordance with Efros's scheme [1]) in the presence of a point source in the flow or on the wedge. Expressions are obtained for the forces exerted on the source and the wedge by the fluid, the conditions under which there is a negative resistance (thrust) are indicated, and the profiles of the free streamlines are constructed for different values of the flow parameters.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Shidkosti i Gaza, No. 6, pp. 137–141, November–December, 1979.We thank L. I. Sedov for his interest in the work.     

Delaminations induced by constrained transverse cracking in symmetric composite laminates

Transverse ply cracking and its induced delaminations at the φ/90° interfaces in [. . . /φ_i/φ_m/90_n] _s laminates are theoretically investigated. Three cracked and delaminated model laminates, one five-layer model (FLM) laminate [S^L/φ_m/90_2n/φ_m/S^R] _T and two three-layer model (TLM) laminates I and II, [φ_m/90_2n/φ_m] _T and [S′^L/90_2n/S′^R] _T, are designed to examine constraining mechanisms of the constraining plies of the center 90°-ply group on transverse crack induced delaminations, where S^L, S^R, S′^L and S′^R are sublaminates [. . ./φ_i] _T, [φ_i/. . .] _T, [. . ./φ_i/φ_m] _T and [φ_m/φ_i/. . .] _T, respectively. A sublaminate-wise first-order shear laminate theory is used to analyze stress and strain fields in the three cracked and delaminated laminates loaded in tension. The extension stiffness reduction of the constrained 90°-plies and the strain energy release rate for a local delamination normalized by the square of the laminate strain are calculated as a function of delamination length and transverse crack spacing. The constraining effects of the immediate neighboring plies and the remote plies are identified by conducting comparisons between the three model laminates. It is seen for the examined laminates that the nearest neighboring ply group of the 90°-plies primarily affects the stiffness reduction and also the normalized strain energy release rate, whereas the influences of the remote constraining layers are negligible.     

Diffraction of surface waves by a wedge

This paper presents a study of diffraction of surface waves by a wedge with angle . (2–n/m), where n and m are natural numbers and n/m2. The infinitely deep heavy liquid is considered ideal. Two cases are considered: 1) there is a source within the liquid which acts periodically with the frequency and maximal intensity Q; 2) at some point of the liquid surface at the initial instant of time there is a concentrated elevation of volume S. For both cases the exact solution is obtained and asymptotic estimates are made.The author wishes to thank S. S. Voit for guidance and assistance in carrying out the present Investigation.     

Plastic deformation of a wedge by a sliding punch

We present a self-similar solution of the problem of deformation of an ideally plastic wedge by a sliding punch with regard to contact friction; such a solution generalizes the well-known solutions of the problem of wedge penetration into a plastic half-space and of compression of an ideally plastic wedge by a plane punch. The problem is of interest for modeling the processes of plastic deformation of rough surfaces of metal pieces by a rigid tool.     

Diffraction of a solitary wave by a thin wedge

The diffraction of a solitary wave by a thin wedge with vertical walls is studied when the incident solitary wave is directed along the wedge axis. The method of multiple scales is extended to this problem and reduces the task to that of solving the two-dimensional KdV equation with proper boundary and initial conditions. The finite-difference numerical procedure is carried out with the fractional step algorithm in which difference schemes are all implicit. Except the maximum run-up at the wall, the results in this paper are found to corroborate the Melville's experiments not only qualitatively but also quantitatively. The maximum run-up of our results agrees well with Funakoshi's numerical one but it is considerably larger than that in Melville's experiment. An important reason for this discrepancy is believed to be the effect of viscous boundary layer on the vertical side wall.     

Delamination crack originating from transverse cracking in cross-ply composite laminates under extension

Based upon the Stroh formalism for anisotropic elastic materials and upon the method of eigenfunction expansion, the stress redistribution due to delamination cracks originating from transverse cracking is examined from [90/0], and [0/90], laminates under extension. The structure of the solution, in the form of a series expansion, is determined from the eigenvalue equation resulting from appropriate near-field conditions. To complete the solution, use is made of a boundary collocation technique in conjunction with the eigenfunction series that includes a large number of terms, enough to represent the elastic state throughout the appropriate domain concerned. The fracture mechanics parameters, such as stress intensity factors and energy release rates, are calculated and the major characteristics of stress distribution are discussed. The stability of delamination cracks is examined for varying ratios of ply thickness in terms of the energy release rate.     

Virtual testing applied to transverse multiple cracking of tows in woven ceramic composites

The present paper proposes a method of virtual testing with a view to investigating the local response of tows within textile ceramic matrix composite (CMC) under various loading conditions. The method was developed on 2D woven SiC/SiC composites. It capitalizes on knowledge on mechanical damage phenomenology and data established in previous works. It is applied to isolated transverse tows subjected to uniaxial loading by parallel longitudinal tows. The transverse tows contain heterogeneities like matrix voids, fibres and interphases. Mesh for finite element analysis is constructed from micrographs of composite cross section. Cracks were introduced into the mesh for simulation of multiple cracking. Transverse tow tensile behavior and data on distributions of flaw populations were derived from finite element computations of stress-state. Results were compared to experimental observations.     

Virtual testing applied to transverse multiple cracking of tows in woven ceramic composites

The present paper proposes a method of virtual testing with a view to investigating the local response of tows within textile ceramic matrix composite (CMC) under various loading conditions. The method was developed on 2D woven SiC/SiC composites. It capitalizes on knowledge on mechanical damage phenomenology and data established in previous works. It is applied to isolated transverse tows subjected to uniaxial loading by parallel longitudinal tows. The transverse tows contain heterogeneities like matrix voids, fibres and interphases. Mesh for finite element analysis is constructed from micrographs of composite cross section. Cracks were introduced into the mesh for simulation of multiple cracking. Transverse tow tensile behavior and data on distributions of flaw populations were derived from finite element computations of stress-state. Results were compared to experimental observations.     

Scattering of a Rayleigh wave by an elastic wedge

We study the two-dimensional, steady-state problem of the scattering of waves in a homogeneous, isotropic, linear-elastic wedge where the wedge angel is less than 180°. For incidence of a Rayleigh surface wave, we plot the amplitudes and phases of the surface waves reflected and transmitted by the corner.     

Cohesive modeling of transverse cracking in laminates under in-plane loading with a single layer of elements per ply

This study aims to bridge the gap between classical understanding of transverse cracking in cross-ply laminates and recent computational methods for the modeling of progressive laminate failure. Specifically, the study investigates under what conditions a finite element model with cohesive X-FEM cracks can reproduce the in situ effect for the ply strength. It is shown that it is possible to do so with a single element across the thickness of the ply, provided that the interface stiffness is properly selected. The optimal value for this interface stiffness is derived with an analytical shear lag model. It is also shown that, when the appropriate statistical variation of properties has been applied, models with a single element through the thickness of a ply can predict the density of transverse matrix cracks.     

Diffraction by a metallic wedge covered with a dielectric material

In the literature, the usual formulation which assumes a constant impedance boundary condition does not permit one to express both the value of the geometrical optics field and the actual excited surface wave, since the impedance associated with the material for the reflection and for the surface wave are generally different. To obtain these elements in the field expression, we replace the notion of constant impedance by a differential operator. The general solution presented here preserves enough degrees of freedom to satisfy the continuity of fields at the internal junction of the two materials which cover each face of the wedge. The numerical calculations are based upon a function, related to the Maliuzhinets function, in a form which is easily computable.     

Vertical displacements of a Wave-Riding buoy

The influence of water waves on the free vertical oscillations of a spar buoy with an attached line of measuring instruments is investigated. The equations of motion of such a system are derived on the basis of the Lagrangian approach. Local parametric splines are used to reduce the problem to a system of second-order nonlinear ordinary differential equations, which is solved numerically by Geer's method. The period of free oscillations of the buoy is plotted as a function of its waterline area and the elasticity of the dropline, and the amplitude of the buoy oscillations is plotted as a function of the period and amplitude of the water waves and the elasticity of the dropline.S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 31, No. 7, pp. 83–88, July, 1995.     

Structure of an oblique detonation wave induced by a wedge

The structure of an oblique detonation wave (ODW) induced by a wedge is investigated via numerical simulations and Rankine–Hugoniot analysis. The two-dimensional Euler equations coupled with a two-step chemical reaction model are solved. In the numerical results, four configurations of the Chapman–Jouguet (CJ) ODW reflection (overall Mach reflection, Mach reflection, regular reflection, and non-reflection) are observed to take place sequentially as the inflow Mach number increases. According to the numerical and analytical results, the change of the CJ ODW reflection configuration results from the interaction among the ODW, the CJ ODW, and the centered expansion wave.     

The criterion of the existence or inexistence of transverse shock wave at wedge supported oblique detonation wave

A simplified theoretic method and numerical simulations were carried out to investigate the characterization of propagation of transverse shock wave at wedge supported oblique detonation wave.After solution validation,a criterion which is associated with the ratio Φ (u 2 /u CJ) of existence or inexistence of the transverse shock wave at the region of the primary triple was deduced systematically by 38 cases.It is observed that for abrupt oblique shock wave (OSW)/oblique detonation wave (ODW) transition,a transverse shock wave is generated at the region of the primary triple when Φ < 1,however,such a transverse shock wave does not take place for the smooth OSW/ODW transition when Φ > 1.The parameter Φ can be expressed as the Mach number behind the ODW front for stable CJ detonation.When 0.9 < Φ < 1.0,the reflected shock wave can pass across the contact discontinuity and interact with transverse waves which are originating from the ODW front.When 0.8 < Φ < 0.9,the reflected shock wave can not pass across the contact discontinuity and only reflects at the contact discontinuity.The condition (0.8 < Φ < 0.9) agrees well with the ratio (D ave /D CJ) in the critical detonation.     

Numerical solution of the problem of wave diffraction by a wedge

The systematic development of the theory of shock reflection from a solid wall started in [1]. Regular reflection and a three-shock configuration originating in Mach reflection were considered there under the assumption of homogeneity of the domains between the discontinuities and, therefore, of rectilinearity of these latter. The difficulties of the theoretical study include the essential nonlinearity of the process as well as the instability of the tangential discontinuity originating during Mach reflection. Analytic solutions of the problem in a linear formulation are known for a small wedge angle or a weak wave (see [2–4], for example). The solution in a nonlinear formulation has been carried out numerically in [5, 6] for arbitrary wedge angles and wave intensities. Since the wave was nonstationary, the internal flow configuration is difficult to clarify by means of the constant pressure and density curves presented. A formulation of the problem for the complete system of gasdynamics equations in self-similar variables is given in [7] and a method of solution is proposed but no results are presented. Difficulties with the instability of the contact discontinuity are noted. The problem formulation in this paper is analogous to that proposed in [7]. However, a method of straight-through computation without extraction of the compression shocks in the flow field is selected to compute the discontinuous flows. The shocks and contact discontinuities in such a case are domains with abrupt changes in the gasdynamics parameters. The computations were carried out for a broad range of interaction angles and shock intensities. The results obtained are in good agreement with the analytical solutions and experimental results. Information about the additional rise in reflection pressure after the Mach foot has been obtained during the solution.