Stress analysis near the tips of a transverse crack in an elastic semi-strip

The plane elastic problem for a semi-strip with a transverse crack is investigated. The initial problem is reduced to a one-dimensional continuous problem by use of an integral transformation method with a generalized scheme. The one-dimensional problem is first formulated as a vector boundary problem, and then reduced to a system of three singular integral equations(SIEs). The system is solved by use of an orthogonal polynomial method and a special generalized method. The contribution of this work is the consideration of kernel fixed singularities in solving the system. The crack length and its location relative to the semi-strip's lateral sides are investigated to simplify the problem's statement. This simplification reduces the initial problem to a system of two SIEs.     

Motion of a variable-volume sphere in an ideal fluid near a plane surface

The motion of a spherical cavity in a fluid is investigated. The radius of the sphere varies under the action of a constant pressure at infinity. The problems of the collapse of a cavity moving in an unbounded fluid and of the collapse of a cavity near a plane are solved in the exact formulation. The occurrence of an initial translational velocity or the presence of a solid surface, by contrast with the collapse of a sphere at rest in an unbounded fluid [1], yields a limiting radius at which the process of collapse ceases. A sphere initially at rest near a plane always comes into contact with the plane as a result of collapse. The radius and velocities at which the sphere arrives the plane are calculated for various initial distances from the latter. The possible mechanism of the action of a cavitation bubble on a solid surface is discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 94–103, September–October, 1971.     

Singular perturbation analysis of dynamic fields in a thermoelastic solid with a small surface-breaking crack

An asymptotic analysis is presented for a dynamic problem of a semi-infinite isotropic thermoelastic solid with a small surface breaking crack. The exterior surface of the solid is subjected to a series of short thermal pulses. The crack surface is traction free and an ideal thermal contact is assumed across the crack. The stress intensity factor is asymptotically evaluated as a function of the crack depth and time. The effect of a boundary layer associated with the diffusive term is identified. The theoretical model is supplied with numerical simulations.     

A Control Algorithm for a 3D Hopping Machine

The paper addresses several control problems for a three-dimensional hopping machine. The machine consists of a ponderable torso and an imponderable leg. The leg is a kinematic chain with joints allowing rotation and translation. The leg is attached at the torso's center of mass. The force in the leg is developed by a linear spring. A control system is synthesized within the framework of a periodic linear quadratic problem. The efficiency of the controller is exemplified by a case where the hopper changes the direction of its motion     

Numerical prediction of flow in a model of a (potential) soft acting peristaltic blood pump

This paper presents a numerical study of the flow field in a novel ‘soft’ acting peristaltic pump. The pump has potential applications wherever pumping of biological or sensitive fluids with reduced damage is required. The application of the device presented is as a blood pump. The model of the pump comprises a cylindrical tube that forms three chambers. The walls of these chambers move radially as a function of time. The pumping action is initiated by applying phased movement between the chambers. The flow is treated as laminar, unsteady, incompressible, Newtonian, and with a moving boundary. The governing equations are solved using a finite element method (FEM). An operating speed of 60 cycle min⁻¹ has been chosen. The results show that a periodic solution can be achieved after four cycles. The velocity field, streamline and shear stress are presented and discussed. The flow has generally a two‐way pulsatile nature, moving forwards and backwards. However, at the outlet, there is a net outflow over one cycle against a zero pressure head. Net flow linearly decreases to zero with increasing pressure head. Copyright © 2000 John Wiley & Sons, Ltd.     

Hydrodynamic Solution to the Problem of Water Permeability of a Screen with Damaged Continuity

The problem of water permeability of a thin impervious screen made of a polymeric geomembrane with flaws (damages) is considered. The screen consists of a covering layer and a ground base underlaid by a drainage bed. The solution is implemented using methods of theory of flow through a porous medium by means of the conformal mapping and velocity hodograph methods. The characteristic feature of this solution is the study of free pressurized–pressureless flow in a porousmediumthrough a continuous slit in the plane formulation. The basic computational dependences are presented and the calculations of the water permeability are carried out by means of the formulas obtained in comparison with the well-known dependences for a particular case.     

Interaction of a shock wave with a high-speed vortex ring

This is a detailed experimental study of the behavior of diffraction and refraction of a shock front resulting from the interaction of a shock wave and a vortex ring. A spherical shock wave impinges on a vortex ring which is traveling at a high speed in the opposite direction. The configuration of the wave front is visualized by a shadowgraph technique using a pulse dye laser. The shock front is influenced by the non-uniform flow induced by the vortex and diffracted around the vortex core. The shock front passing through the inside of the ring is decelerated by the counter-flow, and the density behind it increases. The diffracted front over the vortex ring expands spirally around the core and intersects the front passing through the inside of the ring. The intersecting circular curve converges toward the central axis of the ring. The diffracted shock in the inner part of the core forms branching waves. The branching points also focus on the central axis of the ring.     

On the theory of reflection from a wire grid parallel to an interface between homogeneous media

Summary The reflection from a wire grid parallel to a plane interface is considered. The respective media are homogeneous and either or both can be dissipative. The grid is composed of thin equi-spaced wires of finite conductivity. The plane wave solution for arbitrary incidence is then generalized for cylindricalwave excitation. The energy absorbed from a magnetic line source by a grid situated on the surface of a dissipative half-space is treated in some detail. This latter problem is a two-dimensional analogy of a vertical antenna with a radial wire ground system.     

Study of gas recirculation in the base region of a model launcher

The technique and the results of a study of gas recirculation in the base region of a launcher are described. The investigation is based on the measurement of the concentrations of chemical substances on a model in a wind tunnel. The engine jets are modeled by the combustion products of a solid fuel.     

Control of separation phenomena in a high-speed flow by means of the surface electric discharge

The results of an experimental and theoretical investigation of the interaction between a surface electric discharge and a supersonic air flow in a constant cross-section channel are given. The features of the generation of the surface discharge in the flow are described. A model of the interaction is proposed. The regime of gasdynamic screening of a mechanical obstacle on the channel wall is investigated. Data on the change in the main flow parameters as a result of the generation of a surface discharge are given. The experimental results are compared with the results of calculations based on a simplified model of the interaction.     

Interaction of a rigid punch and a circular plate with a fixed side and a stress-free face

The axisymmetric contact problem of a rigid punch indentation into an elastic circular plate with a fixed side and a stress-free face is considered. The problem is solved by a method developed for finite bodies which is based on the properties of a biorthogonal system of vector functions. The problem is reduced to a Volterra integral equation (IE) of the first kind for the contract pressure function and to a system of two Volterra IE of the first kind for functions describing the derivative of the displacement of the plate upper surface outside the punch and the normal (or tangential) stress on the plate lower fixed surface. The last two functions are sought as the sum of a trigonometric series and a power-law function with a root singularity. The obtained ill-conditioned systems of linear algebraic equations are regularized by introducing small parameters and have a stable solution. A method for solving the Volterra IE is given. The contact pressure functions, the normal and tangential stresses on the plate fixed surface, and the dimensionless indentation force are found. Several examples of a plane punch computation are given.     

Detonation combustion of hydrogen in a Laval nozzle under rarefied atmosphere conditions

Detonation combustion of a hydrogen-air mixture entering an axisymmetric convergent-divergent nozzle at a supersonic velocity is considered under atmospheric conditions at altitudes up to 24 km. The investigation is carried out on the basis of the two-dimensional gasdynamic Euler equations for a multicomponent reacting gas. The limiting altitude ensuring detonation combustion in a Laval nozzle of given geometry is numerically established for freestream Mach numbers 6 and 7. The possibility of the laser initiation of detonation in a supersonic flow of a stoichiometric, preliminarily heated hydrogen-air mixture is experimentally studied. The investigation is carried out in a shock tube under conditions simulating a supersonic flow in the nozzle throat region.     

Finite inflation of a hyperelastic toroidal membrane over a cylindrical rim

The present paper is devoted to the study of finite inflation of a hyperelastic toroidal membrane on a cylindrical rim under uniform internal pressure. Both compliant and rigid frictionless rims have been considered. The compliant cylindrical rim is modeled as a linear distributed stiffness. The initial cross-section of the torus is assumed to be circular, and the membrane material is assumed to be a homogeneous and isotropic Mooney–Rivlin solid. The problem is formulated as a two point boundary value problem and solved using a shooting method by employing the Nelder–Meads search technique. The optimization function is constructed on a two (three) dimensional search space for the compliant cylinder (rigid cylinder). The effect of the inflation pressure, material properties and elastic properties of the rim on the state of stretch and stress, and on the geometry of the inflated torus have been studied, and some interesting results have been obtained. The stability of the inflated configurations in terms of occurrence of the impending wrinkling state in the membrane has also been studied.     

Fracture behavior of brittle plates and cylindrical shells subjected to concentrated impulse loading

The influence of impact velocity and geometry in the fracture patterns produced by a concentrated impulse loading on brittle plates and cylindrical shells has been studied both experimentally and theoretically. The experiments were performed by impacting plates and cylindrical shells made of plaster with a steel ball. The fracture behavior was photographed by a camera with a flash. The crack-initiation time was measured using a memoriscope. The fracture behavior is explained using the theory of flexural motion of a plate and a cylindrical shell. With the addition of impact-fracture criteria to these theories, the fracture patterns of brittle plates and cylindrical shells are predicted and the resemblance is discussed.     

Digital image correlation and biaxial test on composite material for anisotropic damage law identification

The purpose of the work is to extend the use of non-conventional tests and full field measurements to the identification of an anisotropic damage law. A Digital Image Correlation technique based on a finite element discretization is used to extract planar displacement fields. The reconditioned Equilibrium Gap Method is then used to retrieve a damage law that accounts for shear softening, a specific form suited to the present application. The identification is shown to reduce to a linear system. The example of a biaxial shear test performed on a cruciform specimen is considered. The approach is first qualified by using displacement fields resulting from a non-linear computation with a known damage law. A good agreement is observed between the prescribed and identified laws for distinct parameter settings, even when significant noise is added to the displacement fields. The reconstructed displacement fields coincide perfectly with the measurements. The complete scheme is finally tested considering images taken during an experiment performed on a carbon/carbon composite. The identified damage pattern and the corresponding damage values are similar to post-processed maps using classically identified parameters. The reconstructed displacement field accounts for 95% of the fluctuations observed in the measurements.     

Large Eddy Simulation of Turbulent Confined Highly Swirling Annular Flows

The present paper discusses the Large Eddy Simulation of a confined non-reacting annular swirling jet. The configuration corresponds to a well investigated flow studied experimentally by Sheen (1993). The flow field is characterised by a high swirl number resulting in relatively complex features. The challenging behaviour of the flow is governed by the interaction of several recirculation zones. The central recirculation zone formed by the swirling jet is strongly affected by the cylindrical centre body which acts as a bluff body. The flow features coherent structures such as Precessing Vortex Cores (PVCs), which create regions with high velocity fluctuations. The simulations presented comprise a detailed investigation of the parameters controlling the inert flow and a thorough comparison with the experimental data.     

On moving heat sources

The two-dimensional thermal problem due to relative motion of a medium and a suddenly activated circular heat source is solved for several boundary conditions. The solutions can be interpreted as for a moving heat source in a stationary medium or a medium moving past a stationary heat source. Uniform and non-uniform temperature, and uniform and non-uniform heat flux boundary conditions are considered. The effect of velocity and radial direction on the temperature distribution is examined. Average, steady-state Nusselt numbers are derived. The transient response of a continuous line source is obtained as a limiting case of the prescribed heat flux solution. Received on 24 September 1996     

Numerical modeling of the self-oscillation onset near a three-dimensional backward-facing step in a transonic flow

The results of a numerical investigation of the nature of self-oscillation processes occurring in transonic flow past a backward-facing step and a cavity with a flow of the open type are presented. The turbulent flow past the above-mentioned bodies is modeled using the NOISEtte software package intended for solving problems of aerodynamics and aeroacoustics on unstructured grids. The modeling is performed using the eddy-resolving IDDES method that belongs to the class of hybrid RANS-LES approaches. The adequacy of the calculations is confirmed by means of comparing the results obtained with the available experimental data. The structure and the salient features of the self-oscillatory, hydrodynamic-in-nature process, which arises in flow past a cavity and a backward-facing step, are established.     

Finite element modeling of contact conditions in multibody system dynamics

In this paper a new method is developed for the dynamic analysis of contact conditions in flexible multibody systems undergoing a rolling type of motion. The relative motion between the two contacting bodies is treated as a constraint condition describing their kinematic and geometric relations. Equations of motion of the system are presented in a matrix form making use of Kane's equations and finite element method. The method developed has been implemented in a general purpose program called DARS and applied to the simulation and analysis of a rotating wheel on a track. Both the bodies are assumed flexible and discretized using a three dimensional 8-noded isoparametric elements. The time variant constraint conditions are imposed on the nodal points located at the peripheral surfaces of the bodies under consideration. The simulation is carried out under two different boundary conditions describing the support of the track. The subsequent constraint forces associated with the generalized coordinates of the system are computed and plotted. The effects of friction are also discussed.     

Momentum transport in a turbulent mixing layer

The turbulent momentum transport phenomena in a two-dimensional mixing layer are investigated numerically by a discrete vortex method. The numerical model and calculations are verified through a comparison with existing numerical simulations and experimental measurements. The main emphasis is placed on the exploration of the detailed time-dependent instantaneous local momentum fluctuations and on the comparison of numerical results with available experimental measurements. The current simulations confirm qualitatively the various trends in the turbulent momentum flux and fluctuating components of the velocity in the mixing layer found with several experimental results. The study shows that similarity exists in turbulent momentum quantities along the axial direction of the mixing layer. The calculations also show a definite correlation between the passage of a large-scale structure and a burst in the turbulent momentum flux. The probability density functions of the fluctuating quantities are shown to be mostly Gaussian-like, with only a few exceptions.