Showing papers in "Acta Mechanica in 1984"
TL;DR: In this article, the minimum requirements for the form closure of a rigid body are investigated and the requirements are reduced to a conceptually simple and powerful form: the contacts should be applied in the senses in which the equilibrating forces act along the contact normals in the absence of any applied forces.
Abstract: The minimum requirements for the form closure of a rigid body are investigated. This necessarily involves the use of point contacts. The requirements are reduced to a conceptually simple and powerful form: the contacts should be applied in the senses in which the equilibrating forces act along the contact normals in the absence of any applied forces. The number of contacts necessary, the number of unloaded contacts and their identification, the case where the problem is solved in stages and the condition for the determinacy of the reactions are effectively dealt with. Illustrative examples are included.
236 citations
TL;DR: In this paper, it was shown that in large deformation generalized plasticity, a local maximum-dissipation postulate is equivalent to the condition that the plastic strain rate cannot oppose the total strain rate, when strain space is regarded as a Riemannian manifold.
Abstract: It is shown that in large-deformation generalized plasticity a local maximum-dissipation postulate is equivalent to the condition that the plastic strain rate (in the sense of Rice) cannot oppose the total strain rate, when strain space is regarded as a Riemannian manifold with the instantaneous Lagrangian tangent elastic stiffness as the metric tensor. From this condition, normality conditions in strain space (in this sense) and in the space of the second Piola-Kirchhoff stress (in the usual sense) are derived. With the additive decomposition of strain, the loading surface has essentially the same properties as in infinitesimal-strain plasticity. For the multiplicative decomposition, approximate normality rules are derived.
148 citations
TL;DR: In this paper, the behavior of spiral vortices being generated in transition regime of a disk rotating in otherwise undisturbed fluid is experimentally studied in detail through visualizations of the transition regime by using close-up camera.
Abstract: Behaviour of spiral vortices being generated in transition regime of a disk rotating in otherwise undisturbed fluid is experimentally studied in detail. Through visualizations of the transition regime by using close-up camera, new striped flow patterns originating along the axis of spital vortices are found to be ring-like vortices which occur on the surfaces of each spiral vortices. Mechanism of the spiral vortex is clarified by cutting the vortices by strobo slit light. It is also found out experimentally that the phase velocity of the vortices is zero.
129 citations
TL;DR: In this paper, the governing equation for steady two-dimensional channel flow is deduced from the equations of inviscid fluid dynamics, and the integration procedure aims at the elimination of the spatially transverse coordinate; through it one arrives at a second order non-linear ordinary differential equation for the free surface profile having the form of an extended Bernoulli-equation and providing formulae for the pressure and velocity distributions.
Abstract: The governing equation for steady two-dimensional channel flow are deduced from the equations of inviscid fluid dynamics. Streamline inclination and curvature effects are approximately accounted for. The integration procedure aims at the elimination of the spatially transverse coordinate; through it one arrives at a second order non-linear ordinary differential equation for the free surface profile having the form of an (extended) Bernoulli-equation and providing formulae for the pressure and velocity distributions. A second derivation, applicable to channels with horizontal Thalweg and arbitrary prismatic cross section, leads to a similar equation for the free surface profile. Illustrations concern solitary waves in rectangular and trapezoidal cross sections. Comparison of theoretical predictions of wave geometry with experiments indicate advantages of our formulation over previous more extensive ones.
67 citations
TL;DR: In this article, the differential equation that governs the longitudinal variation of the surface profileh(x) in steady plane channel flow is qualitatively discussed for the case of pseudo-uniform flow states.
Abstract: The differential equation that governs the longitudinal variation of the surface profileh(x) in steady plane channel flow is qualitatively discussed for the case of pseudo-uniform flow states. The solutions are either of the cnoidal or solitary wave type. It is shown that, among all cnoidal waves, solitary waves have minimum energy head. Further, surface profiles mustbreak whenever the Froude-number exceeds the value\(\sqrt 2 \) (which is close to experimentally determined values). The model equations are applied to the undular hydraulic jump, and it is shown how the equations can be used in practical situations of open channel flow hydraulics.
55 citations
TL;DR: In this paper, the static and dynamic axisymmetric buckling of elastic orthotropic thin shallow spherical shells with elastically restrained edge for inplane and rotational displacements was investigated.
Abstract: This investigation deals with the static and dynamic axisymmetric buckling of elastic orthotropic thin shallow spherical shells with elastically restrained edge for inplane and rotational displacements. Governing equations in terms of normal displacementw and stress function ψ have been employed. Orthogonal point collocation method is used for spatial discretisation and Newmark-β scheme is used for time-marching. The uniformly distributed static and step function conservative loadings normal to the underformed surface are considered. The present results are in good agreement with the available results. The influence of orthotropicity parameter β and the support stiffness parameters on the static and dynamic buckling loads has been investigated.
41 citations
TL;DR: In this article, it was shown that the components of a sixth rank anisotropy tensor are physically significant in representing the distortion observed in both the initial and subsequent yield surface for a polycrystalline material.
Abstract: It is shown that the components of a sixth rank anisotropy tensor are physically significant in representing the distortion observed in both the initial and subsequent yield surface for a polycrystalline material. This feature of anisotropy does not appear in the ellipsoidal surface given by previous theories in which second and fourth rank anisotropy tensors are employed. The number of tensor components, for a series function embodying tensor terms in ascending rank, reduces to a manageable number by the imposition of symmetry and coincidence between the axes of stress and principal orthotropic directions. The identification is made between the yield limits, as found from biaxial stress experiments and tensor components in composite sum form. A one-to-one correspondence is found from a further simplification through the assumption of incompressibility. This is confirmed experimentally for an orthotropic rolled copper and copper alloy sheet.
35 citations
TL;DR: In this paper, the similarity equations for combined forced and free convection flow over a horizontal plate when the wall temperature is inversely proportional to the square root of the distance from the leading edge are solved by introducing a scaling similar to that for the Blasius equation.
Abstract: The similarity equations for combined forced and free convection flow over a horizontal plate when the wall temperature is inversely proportional to the square root of the distance from the leading edge are solved by introducing a scaling similar to that for the Blasius equation. The technique is also applied to the local similarity equations for the case of a constant wall temperature.
35 citations
TL;DR: The dynamical equations of motion of a multibody system with closed loops are reduced to state space equations within the framework of the computer-oriented Roberson/Wittenburg multibODY formalism.
Abstract: The dynamical equations of motion of a multibody system with closed loops are reduced to state space equations within the framework of the computer-oriented Roberson/Wittenburg multibody formalism First, that formalism is reviewed One obtains unreduced equations of motion for systems with tree configuration as well as systems with closed loops The constraint equations are discussed next, formulated in terms of variables representing the relative motion of contiguous interacting bodies For systems with tree configurations, such constraint equations can be used without further modification to reduce the dynamical equations to state space form, by applying methods of linear algebra Modes of motion are derived from the constraints and the interaction forces and torques between the bodies are separated into generalized applied and constraint forces The latter are eliminated, thus reducing the dynamical equations to state space form Finally, the relations for the determination of the generalized constraint forces are given, assuming that the motion of the system has been determined from its state space representation
31 citations
TL;DR: In this paper, the boundary layer transition process and the behavior of spiral vortices appearing in the transition range of the boundary layers on a 30°-cone, rotating in axial flow are investigated experimentally.
Abstract: The purpose of the present paper is to investigate experimentally in detail the boundary layer transition process and the behaviour of spiral vortices appearing in the transition range of the boundary layer on a 30°-cone, rotating in axial flow. Counterrotating spiral vortices in the transition range are visualized with a white smoke method, and observed the time dependent behaviour of them using a drum camera and a light sheet illumination method with a stroboscope flash light. The light passes a slit in order to illuminate only a thin sheet in the flow. With this method, the time dependent growing up and breaking down process of these spiral vortices is greatly clarified. A hot wire anemometer is also used for measuring in the flow field quantitatively. The results show that the spiral vortices are generated in the thin region of the steep shear velocity gradients near the wall. As the vortices grow up in z-direction, they are strongly distorted by the mean velocity field there, and finally they are teared off.
30 citations
TL;DR: In this article, the state space equations for systems with tree configurations are developed, and the consistency equations on the motions of bodies forming closed loops are introduced, and a state-space representation of the dynamical equations is obtained.
Abstract: In Part I the state space equations for systems with tree configurations are developed. Part II turns to systems with closed loops, for which one also must consider the consistency equations on the motions of bodies forming closed loops. Introducing all the constraint equations on the relative motion of contiguous bodies in the loops into the consistency equations and generalizing the procedure used in Part I, a state-space representation of the dynamical equations is obtained.
TL;DR: In this paper, it was shown that concrete pavement blowups are caused by axial compression forces induced into the pavement by a rise in temperature and moisture, and that the blowup mechanism has not yet been fully understood.
Abstract: Concrete pavement blowups are caused by axial compression forces induced into the pavement by a rise in temperature and moisture. Although many papers and reports were published on this subject, research in this area has not resulted in an understanding of the blowup mechanism and the derivation of a generally accepted analysis.
TL;DR: In this article, the effects of rotation of the body on the phase velocity, energy loss and decay coefficient are discussed in some detail for waves of small and large frequencies, and for small coupling between the thermal and mechanical fields.
Abstract: Plane waves in a homogeneous and isotropic unbounded thermoelastic solid rotating with a uniform angular velocity are discussed in the context of the generalised thermoelasticity theory of Green and Lindsay. The effects of rotation of the body on the phase velocity, energy loss and decay coefficient are discussed in some detail for waves of small and large frequencies, and for small coupling between the thermal and mechanical fields. Results of earlier works are deduced as particular cases of the more general results obtained here.
TL;DR: In this article, an attempt is made to study the non-isothermal flow of a power law lubricant through the gap of a conical journal bearing, where the authors assumed the width of the bearing to be infinite in order to reduce a three-dimensional problem to the two-dimensional one.
Abstract: The hydrodynamic theory of lubrication for non-Newtonian power law lubricants has been recently developed by I. Teipel et al. [1], [2], and K. Wierzcholski [3]. They restricted, however, their investigations to the cylindrical journal bearings only. Moreover, the authors assumed the width of the bearing to be infinite in order to reduce a three-dimensional problem to the two-dimensional one. In this paper an attempt is made to study the non-isothermal flow of a power law lubricant through the gap of a conical journal bearing. At first, the more general equations in curvilinear coordinates are derived which describe the flow of a power law lubricant in the bearing gap of a quite arbitrary geometry. Afterwards, as a special case, a conical bearing gap is considered. It seems to the authors that they succeeded in omitting the necessity of using numerical procedures and obtained a relatively simple, analytical solution to the problem discussed.
TL;DR: In this article, the magnetoelastic buckling of a soft ferromagnetic elastic cantilever of elliptic crosssection due to a transverse magnetic field is discussed and the magnetic fields referring to the deflected beam are determined analytically by means of Mathieu functions.
Abstract: The magnetoelastic buckling of a soft ferromagnetic elastic cantilever of elliptic crosssection due to a transverse magnetic field is discussed. The magnetic fields referring to the deflected beam are determined analytically by means of Mathieu functions. These fields are used in the derivation of the buckling value for a slender cantilever. It turns out that this value not only depends upon the thickness-to-length ratio of the beam, but also upon the shape of the cross-section. A comparison with results known from the literature is given for two limiting cases, viz. the circular cross-section and the very wide (and thin) one. In the first case complete agreement is observed; for the second case an essential improvement of the usual approach (based upon the assumption of an infinitely wide cross-section) is attained.
TL;DR: In this paper, generalized ray integrals for multi-reflected rays in the top layer are formulated by using two rotated coordinate systems, one for each interface, and are expressed in terms of local wave slowness along each interface.
Abstract: The theory of generalized ray is applied to analyzing transient elastic waves in a layered half-space with non-parallel interface. The propagation, reflection and refraction of longitudinal (P-) and transverse (SV-) waves which are generated by a line source in the surface layer of a two layer model are considered, each of the two homogeneous and isotropic layers having different density and inverse of wave speeds. Generalized ray integrals for multi-reflected rays in the top layer are formulated by using two rotated coordinate systems, one for each interface, and are expressed in terms of local wave slowness along each interface. Through a series of transformations of the local slowness, all ray integrals are expressible in a common slowness variable. Special attention is given to wave mode changes during reflection. The arrival time of each ray is then determined from the stationary value of the phase function with common slowness of the ray integral. Arrivals of head waves corresponding to rays refracted at a fast bottom are calculated from proper branch points of the Cagniard-mapping.
TL;DR: In this paper, a new exact solution was obtained for the axially symmetric flow in the kinematically determined regime of a rigid-perfectly plastic solid which obeys Tresca's yield condition and associated flow rule.
Abstract: A new exact solution is obtained of the equations which govern the axially symmetric flow, in the kinematically determined regime, of a rigid-perfectly plastic solid which obeys Tresca's yield condition and associated flow rule. The solution is also valid for an ideal granular material which obeys the Coulomb-Mohr condition and the double-shearing flow equations. This solution is applied to the problem of flow of an infinite medium past a smooth rigid infinite cone. By the superposition of an axial velocity, the solution also describes the penetration of an infinite body by a cone.
TL;DR: In this paper, a constitutive equation of rate type is derived from Onsager's theory of non-equilibrium processes, and simple solutions of the equation are discussed, and it is found that the material at hand exhibits different kinds of relaxation phenomena, normal stress effects, non-Newtonian behaviour, plastic properties as well as the creep and elasticity at small loads.
Abstract: In the present paper a constitutive equation of rate type is derived from Onsager's theory of non-equilibrium processes. Some simple solutions of the equation are discussed, and it is found that the material at hand exhibits different kinds of relaxation phenomena, normal stress effects, non-Newtonian behaviour, plastic properties as well as the creep and elasticity at small loads.
TL;DR: In this paper, it was shown that shakiness is preserved under affine and projective transformations, which leads to the construction of new shaky frameworks in space from plane ones, and there is no theoretical reason to restrict the investigations to low-dimensional ambient spaces.
Abstract: Let there be given a spatial or plane system of rigid rods having freely movable connections at their endpoints, the knots of the system. Such a framework is called shaky if there exists a nonisometric infinitesimal deformation of its knots which preserves the lengths of the rods. In this paper it is shown that shakiness is preserved under affine and projective transformations The method of proof gives an easy interpretation of this invariance property and leads to the construction of new shaky frameworks in space from plane ones. Furthermore it shows that there is no theoretical reason to restrict the investigations to low-dimensional ambient spaces.
TL;DR: In this article, Fourier transforms of the equations of axially symmetric longitudinal waves in an infinite circularly cylindrical rod are established and decoupled according to the Pochhammer procedure.
Abstract: After determining the values of the nonlocal moduli for longitudinal waves in an infinite space, Fourier transforms of the equations of axially symmetric longitudinal waves in an infinite circularly cylindrical rod are established and decoupled according to the Pochhammer procedure. Dispersion equation is obtained from the conditions of traction free surface of the rod, and compared with its classical counterpart. While the velocity of long waves coincides, as required, with that derived in the classical case, the velocity of short waves turns out to be about 36% less.
TL;DR: In this article, the authors discuss the Kelvin-Helmholtz instability for the interface between a visous and an inviscid fluid and modelled the incipient boundary layer as a two dimensional viscous interface.
Abstract: This paper discusses the Kelvin-Helmholtz instability for the interface between a visous and an inviscid fluid. The incipient boundary layer is modelled as a two dimensional viscous interface.
TL;DR: In this paper, an approximate treatment based on the Biots theory of incremental deformation is proposed to study the wave propagation in two thin layered laminated medium under initial stresses, where the cross-sectional distortion which plays an important role in the coupling of adherent layers is taken into account.
Abstract: The present paper is an attempt to provide an approximate treatment based on Biots theory of incremental deformation to study the wave propagation in two thinly layered laminated medium under initial stresses. The cross-sectional distortion which plays an important role in the coupling of adherent layers is taken into account. The theory is derived in the context of plane strain deformation and the frequency equation for phase velocity of waves propagated has been obtained. It has been shown that under certain conditions when wave length becomes small compared to thickness of each layer, the wave approaches to Rayleigh waves at the two outer surfaces with the possibility of Stoneley waves at the interface.
TL;DR: Generalized Ilyushin's deviatoric stress and strain spaces are introduced in this paper, which make it possible to apply directly the postulate of isotropy to initially isotropic materials with plastic properties influenced by the third deviating stress invariant and to a certain class of initially anisotropic materials.
Abstract: Generalized Ilyushin's deviatoric stress and strain spaces are introduced, which make it possible to apply directly the postulate of isotropy to initially isotropic materials with plastic properties influenced by the third deviatoric stress invariant and to a certain class of initially anisotropic materials. The generalizations proposed are connected with a new concept of description of plastic hardening, the main idea of which is also briefly presented.
TL;DR: In this article, it was shown that when the equations for the wave-hierarchy problems discussed by Whitham (1974) are augmented by a term expressing dissipation, the linearised stability condition remains unaltered.
Abstract: We show that, when the equations for the wave-hierarchy problems discussed by Whitham (1974) are augmented by a term expressing dissipation, the linearised stability condition remains unaltered. Further, we show that when the basic uniform state is unstable, it can restabilise into a quasi-steady periodic state, parametrized by the propagation speed.
TL;DR: Theoretical and experimental analyses have been carried out for determining the injection condition below which the formation of air core does not take place in the course of flow of a time-independent power-law fluid through a swirl nozzle as discussed by the authors.
Abstract: Theoretical and experimental analyses have been carried out for determining the injection condition below which the formation of air core does not take place in the course of flow of a time-independent power-law fluid through a swirl nozzle. Analytical solution lends one distinct value of generalized Reynolds number at the inlet to a nozzle below which the air core is not formed. Experiments reveal that there exist two limiting values of such generalized Reynolds number regarding the formation of air core in a nozzle. One value being the upper limit below which steady flow occurs without air core, the other one is the lower limit above which steady flow with fully developed air core persists. In between these two limiting values, there prevails a transition zone through which fully developed air core is set up within the nozzle. For all the nozzles, theoretical results are in fair agreement with the experimental values of upper limit of generalized Reynolds numbers with respect to steady flow without air core. Amongst all the pertinent independent geometrical parameters of a nozzle, the orifice-to-swirl chamber-diameter ratio has the remarkable influence on generalized Reynolds number describing the initiation of air core.
TL;DR: In this article, a viscoelastic shell theory model for transient pressure perturbations in fluid filled tubes is presented and tested against experiments involving water filled latex tubes, and the agreement between theory and experiment is good.
Abstract: A viscoelastic shell theory model for transient pressure perturbations in fluid filled tubes is presented and tested against experiments involving water filled latex tubes. The agreement between theory and experiment is good.
TL;DR: In this paper, all rigid motions of a wire forming a closed loop are determined under the hypothesis that the wire is inextensible, perfectly flexible and free of external forces, and it is found that all rigid motion of the wire are uniform rotations and that there exist countably many non trivial configurations of the wires that are consistent with a rigid motion.
Abstract: All rigid motions of a wire forming a closed loop are determined under the hypothesis that the wire is inextensible, perfectly flexible and free of external forces. It is found that all rigid motions of the wire are uniform rotations and that there exist countably many non trivial configurations of the wire that are consistent with a rigid motion. All these configurations have multiple points.
TL;DR: In this article, an internal variable theory of rate-independent plasticity is presented incorporating a combination of classical models of kinematic hardening as well as isotropic hardening.
Abstract: An internal variable theory of rate-independent plasticity is presented incorporating a combination of classical models of kinematic hardening as well as isotropic hardening. In addition to the yield surface a second “bounding surface” has been introduced to accommodate to problems with non-radial loading paths. The behaviour of this model unter uniaxial and complex loading has been tested and compared with experimental results and other theoretical predictions.
TL;DR: In this paper, a complete nonlinear analysis is presented for establishing critical loads and the general response of a simple frame with a column of varying moment of inertia, and the individual and coupling effects of the foregoing parameter in connection with other parameters are also assessed.
Abstract: A complete nonlinear analysis is presented for establishing critical loads and the general response of a simple frame with a column of varying moment of inertia. Considerable discrepancies between nonlinear and linear buckling analyses render necessary the application of the former analysis for the evaluation of the actual response of a nonuniform frame. It is found that the variation of the column moment of inertia may have a very beneficial or detrimental effect. The individual and coupling effects of the foregoing parameter in connection with other parameters are also assessed.
TL;DR: In this article, the mutual relations in coupled problems of 1 heat and mass flow in a viscoelastic medium have been derived and the results obtained within the paper can made a base to construct the solutions of initial and boundary problems of visco-elastic thermal diffusion.
Abstract: In the paper, the mutual relations in coupled problems of 1 heat and mass flow in a viscoelastic medium have been derived. The results obtained within the paper can made a base to construct the solutions of initial and boundary problems of viscoelastic thermal diffusion.