Showing papers in "Acta Mechanica in 1978"
TL;DR: In this paper, the authors present a nonlinear approach to determine the safe temperature increase in the rails of a continuously welded track to prevent lateral buckling, based on the post-buckling equilibrium branches of the track.
Abstract: The determination of the safe temperature increase in the rails of a continuously welded track, to prevent lateral buckling is presented. The criterion used is based on the post-buckling equilibrium branches of the track. The range of safe temperature increases is defined asT
0
116 citations
TL;DR: In this article, a method for the formulation of elastostatical boundary value problems as integral equations is presented, the basic idea of which consists of superimposing in a suitable fashion singular solutions for the infinite medium.
Abstract: A method for the formulation of elastostatical boundary value problems as integral equations is presented, the basic idea of which consists of superimposing in a suitable fashion singular solutions for the infinite medium. Since mechanical aspects play an important role in the concept of the method, all quantities in the equations can be interpreted physically. The applicability of the method is illustrated by examples of the geometrical and statical boundary value problem ofplane elastostatics for which 32 different formulations as integral equations are established. The second aim of the paper consists of revealing an analogy between the most important notions of the singularity method, viz. between state variables and singularities. The analogy is manifested by certain symmetries of influence functions, and enables the systematical representation of the basic relations and their interpretation within a larger context.
54 citations
TL;DR: In this article, an analysis of the steady state laminar thermal boundary layer of liquid metals is carried out for the case of the simultaneous linear variation in thermal capacity and conductivity.
Abstract: An analysis of the steady state laminar thermal boundary layer of liquid metals is carried out for the case of the simultaneous linear variation in thermal capacity and conductivity. Explicit closed form analytical solutions are given for temperature distributions using perturbation technique, for a general class of potential flows specified by the power law distribution.
51 citations
TL;DR: In this paper, the authors examined some antiplane crack problems in an elastic material with variable shear modulus and derived an expression for the energy release rate for each of the cracks considered and a comparison made with the corresponding crack in a homogeneous material.
Abstract: This paper examines some antiplane crack problems in an elastic material with variable shear modulus. An expression for the energy release rate is obtained for each of the cracks considered and a comparison made with the energy release rate for the corresponding crack in a homogeneous material.
29 citations
TL;DR: In this article, the theory of mixtures of inert elastic materials is extended to allow for long-range elastic interactions between selected sets of particles, and the model presented generalizes one proposed by Bedford and Stern.
Abstract: The theory of mixtures of inert elastic materials is extended to allow for long-range elastic interactions between selected sets of particles. The model presented generalizes one proposed by Bedford and Stern [1]. An entropy inequality proposed by Bowen is used to obtain the thermodynamic restrictions for a class of elastic materials which includes heat conduction and diffusion in addition to the special long-range interaction. When heat conduction and diffusion are omitted, it is shown that the momentum supplies are determined by the free energies of the constituents.
23 citations
TL;DR: In this paper, a sudden increase of pressure at the entrance of a fluid-filled semi-infinite elastic tube is considered as a model to investigate mathematically the possibility of shock-wave formation.
Abstract: Theoretical and experimental evidence is available for the occurrence of shock waves in arterial blood flow. A sudden increase of pressure at the entrance of a fluid-filled semi-infinite elastic tube is considered as a model to investigate mathematically the possibility of shock-wave formation. By use of the method of wavefront expansions explicit results are obtained about the circumstances under which shocks may form and about the time and distance at which this may occur.
18 citations
18 citations
TL;DR: In this paper, a detailed study of cylindrical shear waves in inhomogeneous Maxwellian viscoelastic materials whose parameters depend continuously on a single radial coordinate is presented.
Abstract: A detailed study is presented of cylindrical shear waves in inhomogeneous Maxwellian viscoelastic materials whose parameters depend continuously on a single radial coordinate. A formal asymptotic technique is employed to investigate various impact problems. Rigorous arguments are then used to show that the formal technique gives results that are asymptotic to the exact solution even when boundaries or interfaces are present. Simple termination in the Karal-Keller series is shown to be associated with the Baecklund transformation method.
16 citations
TL;DR: In this article, a variational method based on Gyarmati's principle for the solution of boundary layer flow along a flat plate was proposed, and the results obtained with the help of the force representation of the principle are the same as obtained by the local potential method of Glansdorff and Prigogine.
Abstract: The paper deals with the development of a new variational method based on Gyarmati's principle for the solution of boundary layer flow along a flat plate. It is found that the variational solution differs by about 4% from exact result when a trial function of third degree is chosen for velocity profile. The results obtained with the help of the force representation of the principle are the same as obtained by the local potential method of Glansdorff and Prigogine. A polynomial of sixth degree with the help of universal form of the principle gives a result which differs by about 0.65% from the exact solution. The governing principle of dissipative processes, it seems, will prove itself quite satisfactory analytical method for the boundary layer flows.
15 citations
TL;DR: In this article, the authors investigated the case of static (buckling) instability of continuous elastic systems under non-conservative forces and analyzed the nonlinear equilibrium equations in the neighborhood of a critical point, in order to determine the post-buckling equilibrium paths.
Abstract: The post-buckling behavior and imperfection-sensitivity of conservative elastic systems has been studied extensively. The general theory, which was originated by Koiter, is not applicable if instability is caused by nonconservative forces. In that case, either static or dynamic instability may occur. This paper investigates the case of static (buckling) instability of continuous elastic systems under nonconservative forces. The nonlinear equilibrium equations are analyzed in the neighborhood of a critical point, in order to determine the post-buckling equilibrium paths. The analysis utilizes the adjoint system to the linearized problem. Conservative systems appear as a special case. Two examples are presented to illustrate the results, a cantilever with partial follower load at its tip and a compressed column attached to an elastic foundation.
14 citations
TL;DR: In this paper, the evaporation from a meniscus (an air-liquid interface) on the end of a small bore, vertically oriented capillary tube was studied.
Abstract: This work is concerned with evaporation from a meniscus (an air-liquid interface) on the end of a small bore, vertically oriented capillary tube. The equations governing the dynamics of the meniscus are derived by considering an evaporation-driven fluid flow. They lead to a nonlinear differential-integral equation which is linearized for small meniscus motions about steady state equilibrium. The linearized equation is shown to contain a single dimensionless parameterK. The motion resulting from a step increase in evaporation rate is shown to be monotone forKK
0a damped oscillatory motion results. A closed form approximate solution is presented, valid for smallK. This work was motivated by the study of transpiration in plants.
TL;DR: In this article, the problem of a cruciform crack with unequal arms in an infinite isotropic elastic medium under conditions of generalized plane stress or plane strain is reduced to a system of two real Cauchy type singular integral equations.
Abstract: The problem of a cruciform crack with unequal arms in an infinite isotropic elastic medium under conditions of generalized plane stress or plane strain is reduced, by using Muskhelishvili's [1] complex potentials technique, to a system of two real Cauchy type singular integral equations. The Gauss-Legendre or the Lobatto-Chebyshev numerical integration methods can be further used for the reduction of the system of these equations to a linear system of equations. Values of the stress intensity factors, obtained numerically for a special geometry and loading case, are also given.
TL;DR: In this paper, the boundary layer flow and heat transfer on a horizontal plate whose temperature differs from that of ambient fluid is investigated. And two separate solutions for high and low frequency ranges are developed.
Abstract: The paper deals with the boundary layer flow and heat transfer on a horizontal plate whose temperature differs from that of ambient fluid. The basic flow is purely induced by buoyancy which is caused by the difference of temperature in the plate and the fluid. The oscillation in the plate temperature causes a time dependent boundary layer flow and heat transfer. Two separate solutions for high and low frequency ranges are developed. The velocity and temperature fields are obtained with the help of Karman-Pohlhausen method in the low frequency range while for high frequencies we have employed a series expansion method in terms of frequency parameters. For very high frequencies, the oscillatory flow pattern is of ‘shear wave’ type unaffected by the mean flow and predicts a phase lead of π/4 in the local rate of heat transfer fluctuations while the skin friction has a phase lead of π/2.
TL;DR: In this article, the authors studied the higher order heat transfer from a sphere rotating in a fluid at low Reynolds number,R, about thez-axis when the free stream velocity is directed along thex-axis.
Abstract: Asymptotic expansions are used to study the higher order heat transfer from a sphere rotating in a fluid at low Reynolds number,R, about thez-axis when the free stream velocity is directed along thex-axis. Navier-Stokes equations involving the effect of the azimuthal velocity both in the Stokes (inner) and the Oseen (outer) regions give the velocity field equations which are used to determine the forced convection field for the above asymmetric case. It is found that the Nusselt number is affected by the rotation at terms of 0(σ2R2) where σ is the Prandtl number of the fluid.
TL;DR: In this paper, a phenomenological thermodynamic theory of viscoplasticity is presented, in which the internal variables are the plastic deformation tensor and a hardening variable.
Abstract: A phenomenological thermodynamic theory of viscoplasticity is presented in which the internal variables are the plastic deformation tensor and a hardening variable. The latter is defined in such a way that a yield criterion follows from the dissipation inequality if the free energy is an increasing function of the hardening variable. The limiting case of inviscid plasticity is explored, and the significance of the results is discussed in terms of dislocation kinematics.
TL;DR: In this paper, a model of crack propagation is proposed, where space and time dependent cohesive-type tractions act along the crack faces, and the tractions terminate away from the arbitrarily moving tips at some time-dependent interior points.
Abstract: A model of crack propagation is envisaged wherein space and time dependent cohesive-type tractions act along the crack faces. These tractions terminate away from the arbitrarily moving tips at some time-dependent interior points. Relative to just one crack tip, phenomena differ in three distinct reception regimes. Application of a Barenblatt's postulate yields, in these regimes, three nonlinear integral equations consistent, under relevant initial conditions, with continuities of the various boundary paths. Under certain analyticities, both integral equations in two leading adjacent regimes reduce to algebraic ones, while the integral equation in the rear regime becomes transcendental; the corresponding non-singular solutions can be expanded infinitely in terms of hypergeometric functions. Explicit results are deduced for a linear mean stress drop model with uniform tractions, and the recovery of path relations during regime transitions is examined. Finally, the consequence of contracting the traction zones is explored, particularly with reference to (i) a constant traction, (ii) is singularly growing traction.
TL;DR: In this paper, the effect of the temperature dependent heat sources (sinks) on the oscillatory flow and heat transfer has been analyzed with a view to estimate the effect on the temperature.
Abstract: The title problem has been analysed with a view to estimate the effect of the temperature dependent heat sources (sinks) on the oscillatory flow and heat transfer. The governing equations have been reduced to two non-linear ordinary differential equations which have been solved approximately subject to the relevant boundary conditions. The flow- and heat-transfer characteristics have been found to depend on the heat source parameter α besides the usual free convection parameterG, the wall temperature-ratio parameterm, the Prandtl numberP and the Eckert numberE. For convenience the work has been divided into two parts, Part I dealing with the mean flow and heat transfer and the Part II with the unsteady flow and heat transfer. Several qualitatively interesting results concerning the effect of heat sources (sinks) on the mean flow and heat transfer have been pointed out clearly in Section 3.
TL;DR: In this paper, some partial differntial equations are developed to describe the diffusion of a dilute solute in a linear elastic solid supporting a static deformation, based exclusively on the use of the conservation laws of mass and momentum, as well as on the introduction of an internal diffusive force to evaluate the diffusion effects.
Abstract: Some new partial differntial equations are developed to describe the diffusion of a dilute solute in a linear elastic solid supporting a static deformation. The analysis is based exclusively on the use of the conservation laws of mass and momentum, as well as, on the introduction of an internal diffusive force to evaluate the diffusion effects.
TL;DR: The effects of geometry and material properties on the linear constitutive equations for curved and twisted, initially stressed elastic rods are investigated in this article, where special materials in undistorted and natural states, special cross sectional symmetries and for slightly curved and thin rods are given.
Abstract: The effects of geometry and material properties on the linear constitutive equations for curved and twisted, initially stressed elastic rods are investigated. Forms of the constitutive equations are given for special materials in undistorted and natural states, special cross sectional symmetries and for slightly curved and thin rods.
TL;DR: In this article, it is shown that a crack may be viewed as an imperfectly torn elastically distorted space, which is characterized by the presence of a quantity termed an anholonomic object.
Abstract: The methods of differential geometry have been applied to the process of cracking. In particular, it is shown that a crack may be viewed as an imperfectly torn elastically distorted space. Such a space in turn is characterized by the presence of a quantity termed an anholonomic object. The anholonomic object is shown to play the same role in torn spaces as does the torsion tensor in dislocated spaces.
TL;DR: In this article, a model for peristaltische wellenbewegung is presented, which besteht aus einem elastischen Schlauch, verbunden with zwei starren Behaltern, die with Flussigkeit gefullt sind.
Abstract: In dieser Arbeit ist ein theoretisches Modell fur eine peristaltische Stromung durch elastische Leitungen kreisformigen Querschnitts entwickelt worden. Das Modell besteht aus einem elastischen Schlauch, verbunden mit zwei starren Behaltern, die mit Flussigkeit gefullt sind. Die peristaltische Wellenbewegung wird durch einen auseren peristaltischen Druck entlang der Achse des Schlauches hervorgerufen. Es wird vorausgesetzt, das die Wand der Leitung derartig dunn sei, so das die Tangentialspannung als konstant uber der Wandstarke angesehen werden kann. In dieser eindimensionalen instationaren Theorie wird laminare Stromung vorausgesetzt. Das nichtlineare partielle Differentialgleichungssystem hyperbolischen Typs ist durch ein Differenzenverfahren 2. Ordnung numerisch gelost worden. Die Ergebnisse zeigen, das der Einflus der elastischen Wand und der Nichtlinearitaten sehr gros werden kann.
TL;DR: In this article, the arrangements of inextensible fibers for which homogeneous deformations by surface loads alone are possible in every homogeneous, elastic material of a certain variety are determined.
Abstract: The arrangements of inextensible fibers for which homogeneous deformations by surface loads alone are possible in every homogeneous, elastic material of a certain variety are determined. It is proved that only three types of fiber structures can support homogeneous strains; all are structures whose fiber lines of inextensibility necessarily are straight lines. The fiber orientation for Type 1 is constant on each of a family of parallel planes, the fiber direction twisting continuously with the distance measured normal to these, like the radius following the threads of a helical screw; and the reaction stress is constant on each fiber line. The uniformly directed fiber structure is a special case. Otherwise, at each point the fiber line must be collinear with a rule line of a developable surface and have non-vanishing curl. Type 2 is an arrangement of fibers that form the radii of coaxial circular cylinders, and along each fiber line the reaction stress is inversely proportional to the radius. Type 3 is an arrangement that forms the radii of concentric spheres, and on each fiber line the reaction stress is inversely proportional to the squared radius. These results are independent of the body configuration used to characterize the fiber arrangement.
TL;DR: In this article, the effect of heat transfer process on the flow of a compressible viscous fluid, impulsively started to move from rest, in the vicinity of forward stagnation point of an infinite plane wall is investigated.
Abstract: The effect of heat transfer process on the flow of a compressible viscous fluid, impulsively started to move from rest, in the vicinity of forward stagnation point of an infinite plane wall is investigated. The study utilizes an alternative combination of an expansion method into power series of small time and a very efficient numerical method employing the differencedifferential method. Special attention is given to the transient phenomena from the initial flow to the final steady-state distribution. Numerical results are given for the velocity and temperature profiles as well as for the skin-friction and rate of heat transfer coefficients.
TL;DR: In this paper, an optical method for measuring time varying local film thickness is briefly described, where recordings of film thickness were made for Reynolds numbers (equal to 4Q/v) from 145 to 4030 at varying distances along the direction of the flow.
Abstract: An optical method for measuring time varying local film thickness is briefly described. Recordings of film thickness were made for Reynolds numbers (equal to 4Q/v) from 145 to 4030 at varying distances along the direction of the flow. These recordings were digitized and analyzed by digital computer for the following statistical parameters: a) frequency spectrum, b) probability density and c) wave velocity. Where possible these results are compared with those obtained by different thickness measurement methods and recorded at different locations relative to the entrance to the flow. For the length of flow used here, 134 cm, surface characteristics are strongly dependent on distance from the entrance. This dependence appears to lessen after a transition zone where the wave motion stabilizes. There are at least three Reynolds number regions within which the surface characteristics are quite distinct, wavy laminar, transitional and turbulent. These differences are shown by changes in probability density curves from one region to another.
TL;DR: In this article, a two-dimensional mixture theory for wave propagation in a laminated composite material is developed for the treatment of a semi-infinite crack propagating in the composite in mode-I and II types of motion.
Abstract: A two-dimensional mixture theory is developed for wave-propagation in a laminated composite material. The formulated theory is applied for the treatment of a semiinfinite crack propagating in the composite in mode-I and II types of motion. The maximum velocity of the crack tip is determined by the minimum value of the dispersion curves of the relevant generalized Rayleigh waves in the medium. A numerical procedure is applied for the determination of the dynamic stress fields induced by the propagating crack in a laminated composite made of glass-epoxy layers.
TL;DR: An approximate method for obtaining solutions of nonlinear problems, based on Jourdain's differential variational principle, is presented in this article, which is equally applicable to ordinary and partial differential equations.
Abstract: An approximate method for obtaining solutions of nonlinear problems, based on Jourdain's differential variational principle, is presented The method is equally applicable to ordinary and partial differential equations The utility of the method is illustrated by a few concrete examples Fur die Losung nichtlinearer Probleme wird eine Naherungsmethode, basierend auf dem Journdainschen Differential-Variationsprinzip, prasentiert Die Methode ist gleich anwendbar auf gewohnliche und partielle Differentialgleichungen Die Brauchbarkeit der Methode wird an ein paar konkreten Beispielen gezeigt
TL;DR: In this paper, conservation postulates for a chemically reacting mixture are introduced in which the mass, momentum and energy gained and lost by a given constituent due to chemical reaction are explicitly included.
Abstract: Conservation postulates for a chemically reacting mixture are introduced in which the mass, momentum and energy gained and lost by a given constituent due to chemical reaction are explicitly included. The resulting local forms of the balance equations are derived.