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Showing papers in "Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik in 2000"


Journal ArticleDOI
TL;DR: The exposition of the ideas behind the devising of these methods as well as on the mechanisms that allow them to perform so well in such a variety of problems are concentrated on.
Abstract: This paper is a short essay on discontinuous Galerkin methods intended for a very wide audience. We present the discontinuous Galerkin methods and describe and discuss their main features. Since the methods use completely discontinuous approximations, they produce mass matrices that are block-diagonal. This renders the methods highly parallelizable when applied to hyperbolic problems. Another consequence of the use of discontinuous approximations is that these methods can easily handle irregular meshes with hanging nodes and approximations that have polynomials of different degrees in different elements. They are thus ideal for use with adaptive algorithms. Moreover, the methods are locally conservative (a property highly valued by the computational fluid dynamics community) and, in spite of providing discontinuous approximations, stable, and high-order accurate. Even more, when applied to non-linear hyperbolic problems, the discontinuous Galerkin methods are able to capture highly complex solutions presenting discontinuities with high resolution. In this paper, we concentrate on the exposition of the ideas behind the devising of these methods as well as on the mechanisms that allow them to perform so well in such a variety of problems.

768 citations


Journal ArticleDOI
TL;DR: In this article, a phenomenological theory of sedimentation-consolidation processes of flocculated suspensions is developed, which are considered as mixtures of two superimposed continuous media.
Abstract: We develop a general phenomenological theory of sedimentation-consolidation processes of flocculated suspensions, which are considered as mixtures of two superimposed continuous media. Following the standard approach of continuum mechanics, we derive a mathematical model for these processes by applying constitutive assumptions and a subsequent dimensional analysis to the mass and linear momentum balance equations of the solid and liquid component. The resulting mathematical model can be viewed as a system of Navier-Stokes type coupled to a degenerating convection-diffusion equation by singular perturbation terms. In two or three space dimensions, solvability of these equations depends on the choice of phase and mixture viscosities. In one space dimension, however, this model reduces to a quasilinear strongly degenerate parabolic equation, for which analytical and numerical solutions are available. The theory is applied to a batch sedimentation-consolidation process. Wir formulieren eine allgemeine phanomenologische Theorie fur Sedimentations-Konsolidations-Prozesse ausgeflockter Suspensionen, die als Mischungen zweier kontinuierlicher Medien betrachtet werden konnen. Entsprechend dem ublichen Ansatz der Kontinuumsmechanik wird ein mathematisches Modell fur diese Prozesse hergeleitet, indem konstitutive Annahmen und eine anschliesende Dimensionsanalyse auf die Massen- und Impulsbilanzen der Feststoff- und der Flussigkomponente angewendet werden. Das resultierende mathematische Modell kann als ein durch singulare Storterme an eine entartende Konvektions-Diffusions-Gleichung gekoppeltes System vom Navier-Stokes-Typ aufgefast werden. In zwei oder drei Raumdimensionen hangt die Losbarkeit dieser Gleichungen stark von der Wahl der Phasen- und Mischungsviskositaten ab. In einer Raumdimension reduziert sich das Modell auf eine quasilineare stark entartende parabolische Gleichung, fur welche analytische und numerische Ergebnisse bekannt sind. Die Theorie wird durch das Beispiel eines schubweisen Sedimentations-Konsolidationsprozesses veranschaulicht.

113 citations


Journal ArticleDOI
TL;DR: In this article, an approximate numerical solution for the steady MHD flow over an infinite horizontal plate in the presence of species concentration and chemical reaction has been obtained by solving the nonlinear governing equations using R. K. Gill's method.
Abstract: An approximate numerical solution for the steady MHD flow over an infinite horizontal plate in the presence of species concentration and chemical reaction has been obtained by solving the non-linear governing equations using R. K. Gill's method. The fluid is assumed to be viscous, incompressible, and electrically conducting. A uniform transverse magnetic field is applied. It has been observed that in the presence of chemical reaction (1) the velocity and the concentration decrease with increase of the chemical reaction parameter and vice versa, (2) the velocity decreases and the concentration is uniform with increase of the magnetic parameter and vice versa.

82 citations


Journal ArticleDOI
TL;DR: In this paper, the authors make a case for a somewhat unconventional use of the results of scale analyses and multiple scales asymptotics, and demonstrate how,thr ough the judicious implementation of the Asymptotic results,numeric al discretizations of the full governing equations can be designed so that they operate with uniform accuracy and /or efficiency even when a singular limit regime is approached.
Abstract: Prandtl’s boundary layer theory may be considered one of the origins of systematic scale analysis and asymptotics in fluid mechanics. Due to the vast scale differences in atmospheric flows such analyses have a particularly strong tradition in theoretical meteorology. Simplified asymptotic limit equations,derive d through scale analysis,yield a deep insight into the dynamics of the atmosphere. Due to limited capacities of even the fastest computers, the use of such simplified equations has traditionally been a necessary precondition for successful approaches to numerical weather forecasting and climate modelling. In the face of the continuing increase of available compute power there is now a strong tendency to relax as many simplifying scaling assumptions as possible and to go back to more complete and more complex balance equations in atmosphere flow computations. However,the simplified equations obtained through scaling analyses are generally associated with singular asymptotic limits of the full governing equations,and this has important consequences for the numerical integration of the latter. In these singular limit regimes dominant balances of a few terms in the governing equations lead to degeneracies and singular changes of the mathematical structure of the equations. Numerical models based on comprehensive equation systems must simultaneously represent these dominant balances and the subtle,but important,deviations from them. These requirements are partly in contradiction,and this can lead to severe restrictions of the accuracy and/or efficiency of numerical models. The present paper makes a case for a somewhat unconventional use of the results of scale analyses and multiple scales asymptotics. It demonstrates how,thr ough the judicious implementation of asymptotic results,numeric al discretizations of the full governing equations can be designed so that they operate with uniform accuracy and efficiency even when a singular limit regime is approached.

79 citations


Journal ArticleDOI
TL;DR: An exact solution of hydromagnetic oscillatory Ekman boundary layer flow of an electrically conducting fluid between two parallel flat plates, one of which is at rest and the other oscillating in its own plane, is obtained when the entire system rotates about an axis normal to the plates.
Abstract: An exact solution of hydromagnetic oscillatory Ekman boundary layer flow of an electrically conducting fluid between two parallel flat plates, one of which is at rest and the other oscillating in its own plane, is obtained when the entire system rotates about an axis normal to the plates. Neglecting the induced magnetic field, the effects of the transversely applied magnetic field on the flow are studied. For M = 0, the problem reduces to the one discussed by Ganapathy [8]. During the mathematical analysis it is found that even the claim of Ganapathy [8] that the solution of Mazumder [7] explains the important phenomenon of resonance in rotating systems is incorrect.

74 citations


Journal ArticleDOI
TL;DR: A review of mathematical results, both analytic and computational, on the unsteady boundary layer equations is given in this article, including a review of the derivation and basic properties of the equations, singularity formation, well-posedness results, and infinite Reynolds number limits.
Abstract: Prandtl's boundary layer equations, first formulated in 1904, resolve the differences between the viscous and inviscid description of fluid flows. This paper presents a review of mathematical results, both analytic and computational, on the unsteady boundary layer equations. This includes a review of the derivation and basic properties of the equations, singularity formation, well-posedness results, and infinite Reynolds number limits.

72 citations


Journal ArticleDOI
TL;DR: In this article, the authors formally introduce several stability characterizations of systems of rigid bodies initially at rest and in unilateral contact with dry friction, which arise naturally from the dynamic model of the system, formulated as a complementary problem.
Abstract: This paper formally introduces several stability characterizations of systems of rigid bodies initially at rest and in unilateral contact with dry friction. These characterizations, weak stability and strong stability (and their complements), arise naturally from the dynamic model of the system, formulated as a complementary problem. Using the tools of complementarity theory, these characterizations are studied in detail to understand their properties and to develop techniques to identify the stability classifications of general systems subjected to known external loads.

51 citations


Journal ArticleDOI
TL;DR: In this article, a hierarchy of wave equations for axially symmetric elastic rods is derived by series expansions in the radial coordinate, and the dispersion relation and the displacements for these approximations and for Love's equation are compared with the lowest branch of the exact Pochhammer-Chree equation.
Abstract: The derivation of one-dimensional wave equtions for axially symmetric waves in elastic rods is discussed. By series expansions in the radial coordinate a hierarchy of wave equations are derived. As the lowest reasonable approximation the usual simple wave equation for the rod is recovered. At the next level a fourth order wave equation is obtained. The dispersion relation and the displacements for these approximations and for Love's equation are compared with the lowest branch of the exact Pochhammer-Chree equation. An excitation with a shear force is also solved and compared among the theories.

43 citations


Journal ArticleDOI
TL;DR: In this paper, the boundary layer for a flow in a channel with permeable walls is studied and the convergence of the Navier-Stokes equations to the Euler equations is shown.
Abstract: The goal of this article is to study the boundary layer for a flow in a channel with permeable walls. Observing that the Prandtl equation can be solved almost exactly in this case, we are able to derive rigorously a number of results concerning the boundary layer and the convergence of the Navier-Stokes equations to the Euler equations. We indicate also how to derive higher order terms in the inner and outer expansions with respect to the kinematic viscosity v.

35 citations


Journal ArticleDOI
TL;DR: In this paper, the exact strain-displacement expressions of an imperfect laminated composite circular cylindrical shell undergoing large deflections are developed based on the general form of Green's strain tensor in curvilinear coordinates.
Abstract: Based on the general form of Green's strain tensor in curvilinear coordinates, the exact strain-displacement expressions of an imperfect laminated composite circular cylindrical shell undergoing large deflections are developed. The resulted relations may also be used for postbuckling analysis. Employing Hamilton's variational principle, the most general three dimensional and exact integral equations of motion are introduced in a hybrid form. No assumption or simplification is made in deriving the formulations. The resulting equations are solved using a Kantorovich type power series. Dynamic buckling loads treated in this paper, include mechanical loads (axial compression, external pressure, external fluid pressure, and torsion), thermal loads, or a combination of them. The resulted equations are then solved by means of an efficient solution procedure. In contrast to the well-known higher-order and layer-wise theories which are displacement-based, due to the hybrid form of the final equations, various edge conditions (displacement, stress, force, and moment boundary conditions) can be accurately incorporated. Furthermore, in contrast to the existing 3–D elasticity approaches, the solution procedure of the present method is self-started. Finally, few examples of the well-known references done in the mechanical and thermal buckling of the composite circular cylindrical shells, which are based on other theories, are reexamined for comparison purposes. The results are extended to check the capability of the present theory and to enable a sensitivity analysis.

31 citations


Journal ArticleDOI
TL;DR: It is shown that the a posteriori error bound of the proposed error estimator will not depend on jumps in the coefficient of the main part of the equation when the lines of discontinuity are resolved by the mesh.
Abstract: We study the adaptive finite element method to solve linear elliptic boundary value problems on bounded domains in R 2 . For this we first prove a posteriori error estimates that carefully take data error into account and show convergence of an adaptive algorithm. Then we propose an adaptive method that may start from very coarse meshes. A numerical example underlines the necessity of monitoring the data error in applications. Moreover, we can show that the a posteriori error bound of our proposed error estimator will (in a simple model situation) not depend on jumps in the coefficient of the main part of the equation when the lines of discontinuity are resolved by the mesh.

Journal ArticleDOI
TL;DR: In this paper, a coherent representation of the distribution of times, frequencies, and amplitudes is proposed for periodic, quasiperiodic, and chaotic motion in mechanical systems with a complex interplay of regular and chaotic behavior.
Abstract: For the engineering of mechanical systems with a complex interplay of regular and chaotic behavior it is important to know the forces involved. It is shown how they can be computed and their time developntent evaluated. Characteristic features of periodic, quasiperiodic, and chaotic motion are identified. Classical methods such as Fourier transform and various statistics are used and compared to a redundant version of wavelet analysis. The latter is proposed as the most informative coherent representation of the distribution of times, frequencies, and amplitudes.

Journal ArticleDOI
TL;DR: In this article, an iterative approach to reconstruct both the activity f (x) and the attenuation μ(x) directly frorn the emission sinogram data is presented. But the approach is limited to the case where f is a linear operator and μ is a bilinear operator.
Abstract: We report on an iterative approach to reconstruct both the activity f(x) and the attenuation μ(x) directly frorn the emission sinogram data. The proposed algorithm is based on the iterative methods for solving linear operator equations. Whenever an operator F is the sum of a linear and a bilinear operator, a modified iteration sequence can be defined. Using a Taylor series about a fixed approximate distribution μ 0 , the attenuated Radon transform can be well approximated as the sum of a linear operator in f and a bilinear operator in f and μ. The algorithm alternates between updates of f and updates of μ. In our test computations, the proposed algorithms achieve good reconstruction results both for generated and real data.

Journal ArticleDOI
TL;DR: This paper considers partitioned methods for unsteady fluid‐structure interaction, where different codes are used for the different physical domains, and investigates the numerical efficiency of these methods.
Abstract: The numerical simulation of coupled problems is one of the great challenges in scientific computing. In this paper, we consider partitioned methods for unsteady fluid-structure interaction, where different codes are used for the different physical domains. There are various procedures how to couple the fluid and structure part: the coupling conditions and the moving domain can be treated in a fully explicit or implicit or in a mixed explicit/implicit manner. Depending on the different coupling procedures, the numerical efficiency of the staggered partitioned methods is investigated.

Journal ArticleDOI
TL;DR: In this paper, a model describing vibration of nonlinear von Karman thin plates excited by actuators made of piezoelectric ceramics is considered, and the unique solvability of the resulting system is proved.
Abstract: A model describing vibration of nonlinear von Karman thin plates excited by actuators made of piezoelectric ceramics is considered. The model contains strong oscillating coefficients due to the piezoelectric actuators. A procedure of homogenization based on the so-called two-scale convergence is applied to the model. This yields a nonlinear system of equations with constant coefficients. The unique solvability of the resulting system is proved. The convergence of all solutions of the original system to the solution of the resulting system as the number of piezoelectric actuators goes to infinity is proved.

Journal ArticleDOI
TL;DR: In this article, an analytical model for the rise of pulsating bubbles in a Bingham medium, commonly used to model fluids with a yield stress, is derived and experimental results for an aqueous gel show that the effect discussed does exist and is in good qualitative agreement with the model.
Abstract: Liquids important to the process industries sometimes have a yield stress, i.e., they only start flowing if a certain level of shear stress is reached. This can limit processes which require mass transfer to or from bubbles dispersed in the liquid, because bubbles below a certain size can get stuck in the liquid. One possibility of making such bubbles rise is investigated in this work. It consists of subjecting the liquid containing the bubbles to an oscillating external pressure. The deformation outside the bubbles causes the yield stress to be overcome and bubbles to rise which would otherwise have remained stationary. This effect has been investigated both theoretically and experimentally. An analytical model for the rise of pulsating bubbles in a Bingham medium, commonly used to model fluids with a yield stress, is derived. Experimental results for an aqueous gel show that the effect discussed does exist and is in good qualitative agreement with the model.

Journal ArticleDOI
TL;DR: In this article, it is shown that symmetry groups and particularly scaling groups are essential for the derivation of wall-bounded flows and the logarithmic law of the wall for turbulent flows.
Abstract: Investigating analytic solutions of wall-bounded flows such as the Blasius or the Falkner-Skan solution for laminar flows and the logarithmic law of the wall for turbulent flows it is demonstrated that symmetry groups and particularly scaling groups are essential for their derivation. Both sub-models for laminar and turbulent wall-bounded flows, i.e. Prandtl's boundary layer equations and the multi-point correlation equations, are derived from the Navier-Stokes equations. The latter have significantly different symmetry properties compared to the former sub-models. Essential to both laminar and turbulent sub-models is that they admit two scaling groups while the Navier-Stokes equations only admit one scaling group. It is important for the understanding of both sub-models that their admitted two scaling groups have essentially different physical and mathematical properties. The scaling groups of boundary layer theory admit independent scaling in strcamwise and wall-normal direction. Reynolds number is a fundamental parameter in the equations. In contrast the multi-point correlation equations for turbulent flows admit essentially the same groups as the inviscid equotions of fluid motion. Hence to leader order no Reynolds number dependence is contained in the solutions for turbulent flows.

Journal ArticleDOI
TL;DR: In this paper, the authors present a general model of oriented continuum within the frame of Newtonian-Eshelbian continuum mechanics to describe macro-and microdeformations of solids taking into account the evolution of defects as voids and cracks.
Abstract: The aim of this paper is to present a general model of oriented continuum within the frame of Newtonian-Eshelbian continuum mechanics to describe macro- and microdeformations of solids taking into account the evolution of defects as voids and cracks. Within a manifold-theoretical setting, position- and direction-dependent metric, deformation and strain measures are derived to describe macro- and micromotion of the body. A variational formulation is introduced leading to balance laws, boundary and transversality conditions for macro- and microstresses of deformational as well as configurational type, where the latter have to be satisfied by the driving forces on macro- and microdefects. A dissipation inequality for macro- and micromotion is derived via a sufficiency condition for the action integral. The Helmholtz free energy treated as the relevant thermodynamic potential is used to define thermo-inelastic stress-strain relations of incremental type. For the macro-micro constitutive equations associated phenomenological macro constitutive equations are derived by introducing a second potential with corresponding evolution laws. Finally, the presented microtheory is applied to analyze the evolution of shear bands in a rod under tension and the decrease of the load-deflection behaviour. Numerical results are given. It is shown that contrary to phenomenological theories, where shear bands are determined as bifurcation from a homogeneous state via the admittance of weak discontinuities on singular sufaces, conditions of this type are not needed within the presented micromodel of oriented continuum.

Journal ArticleDOI
TL;DR: In this paper, the historical context in which Reissner's famous shear deformation plate theory was derived is discussed and the importance of variational principle for the development of hybrid finite element models is pointed out, as well as how these formulations can be easily extended to a completely threedimensional model allowing to apply unmodified 3D constitutive equations and to include large strain effects but keeping the essential features of a thin-walled structure.
Abstract: The paper first focuses on the historical context in which Reissner's famous shear deformation plate theory was derived. Here essentially Eric Reissner's own view on this matter, in particular the relation to Mindlin's contribution, is followed [15]. The significance of shear deformable plate and shell theories for the derivation of finite elements is briefly described. As a major aspect it is shown how these formulations can be easily extended to a completely three-dimensional model allowing to apply unmodified 3D constitutive equations and to include large strain effects but keeping the essential features of a thin-walled structure. Finally, the importance of Reissner's variational principle for the development of hybrid finite element models is pointed out.

Journal ArticleDOI
TL;DR: In this article, the authors review the main results in the vast field of stability of structures, including columns, frames, arches, thin-wall beams, plates, and shells, as well as massive but soft bodies buckling three-dimensionalally.
Abstract: The article attempts to review the main results in the vast field of stability of structures. The classical field of elastic stability is covered succinctly. The coverage emphasizes the modern problems of anelastic structures exhibiting plasticity and creep, and especially structures disintegrating due to localized fracture and distributed damage. The treatment encompasses thin or slender structures, i.e. the columns, frames, arches, thin-wall beams, plates, and shells, as well as massive but soft bodies buckling three-dimensionally, and includes the static as well as dynamic concepts of stability, dynamic instability of nonconservative systems, energy methods for discrete and continuous structures, thermodynamics of structures, postcritical behavior, and imperfection sensitivity. The legacy of Ludwig Prandtl, who is commemorated by the present Special Issue, is briefly highlighted. The mathematics is kept to the bare minimum, and the derivations as well as the differential equations are omitted. Main attention is paid to the physical causes, mechanisms, and results. Only the main literature sources to this vast field are cited.


Journal ArticleDOI
TL;DR: In this paper, the authors investigated the effect of permeability variation on the heat transfer and the flow through a highly porous medium bounded by an infinite flat porous plate with constant suction, and found that the amplitudes |L, |M|, |H|, respectively, of the skin friction components in the main and transverse directions and the rate of heat transfer, all decrease with the increase of the permeability of the porous medium.
Abstract: This communication investigates the effect of permeability variation on the heat transfer and the flow through a highly porous medium bounded by an infinite flat porous plate with constant suction. The permeability of the porous medium varies in space and tune both. The problem becomes three dimensional due to the periodic variation of permeability in the transverse direction. The governing equations are solved by adopting complex variable notations and the expressions for the velocity and temperature fields are obtained. The wall shear stress and rate of heat transfer are finally discussed. It is found that the amplitudes |L|, |M|, |H|, respectively, of the skin friction components in the main and transverse directions and the rate of heat transfer, all decrease with the increase of the permeability of the porous medium, K 0 , or the frequency of the permeability fluctuations, ω.

Journal ArticleDOI
TL;DR: In this article, the effects of foundation parameters, material parameters, cdge conditions, and aspect ratio of the plate are examined, and the influence of in-plane boundary conditions (movable and immovable edges) on nonlinear frequency is significant.
Abstract: Studies are made on the elastic behaviour of laminated rectangular thin plates with non-linear vibration. The effects of foundation parameters, the material parameters, cdge conditions, and the aspect ratio of the plate are examined. In all the cases considered, the nonlinear frequency increases with the amplitude and a hardening type of non-linearity is noted. The influence of in-plane boundary conditions (movable and immovable edges) on non-lincar frequency is significant. The non-linear frequency for any specified amplitude increases with the elastic foundation parameters.

Journal ArticleDOI
TL;DR: In this paper, the authors consider the Taylor-Couette problem in an infinitely extended cylindrical domain and present modulated front solutions which describe the spreading of the stable Taylor vortices into the region of the unstable Couette flow.
Abstract: We consider the Taylor-Couette problem in an infinitely extended cylindrical domain. There exist modulated front solutions which describe the spreading of the stable Taylor vortices into the region of the unstable Couette flow. These transient solutions have the form of a front-like envelope advancing in the laboratory frame and leaving behind the stationary, spatially periodic Taylor vortices. We prove the nonlinear stability of these solutions with respect to small spatially localized perturbations.

Journal ArticleDOI
TL;DR: In this paper, a nonlinear constitutive equation for complex axisymmetric flow generated by a double annular burner is proposed to overcome the limitations of linear eddy-viscosity models to describe complex turbulent flows.
Abstract: Nonlinear constitutive equations have been proposed to overcome the limitations of linear eddy-viscosity models to describe complex turbulent flows. These new equations have been mainly indirectly compared to experimental data, through the outputs of numerical models. It is proposed in this paper to directly check the constitutive equation, using a projection of the stress tensor onto a tensor basis. The test case chosen is a complex axisymmetric flow generated by a double annular burner. Measurements have been taken on a fine grid, enabling the local estimate of the stress and strain tensors. A map of the Prandtl mixing-length is then given, together with the experimental evaluation of several invariants of the flow. The nonlinear constitutive equation is then tested using a 4 terms development. The angles of the stress tensor with the terms of the tensor basis are plotted, indicating which direction is predominant for each region of the flow. The different invariants are finally used to experimentally estimate the dissipation rate.

Journal ArticleDOI
TL;DR: In this article, a new material formulation to describe nonlinear hyperelastic orthotropic behavior of composite membranes at finite strains is presented, and a reduced integration scheme avoiding locking and hourglass instabilities is used.
Abstract: A new material formulation to describe nonlinear hyperelastic orthotropic behaviour of composite membranes at finite strains is presented in this article. To provide numerically efficient calculations, a reduced integration scheme avoiding locking and hourglass instabilities is used. Restrictions concerning material parameters are discussed, and material parameters are adapted to experimental data. Numerical calculations are used to demonstrate the potential of the approach to inflated rubber matrix membranes applications.

Journal ArticleDOI
TL;DR: In this paper, a low Prandtl number fluid driven by the combined mechanism of buoyancy and surface tension is investigated in the presence of a uniform vertical magnetic field, where the fluid is contained in a square cavity with the upper surface open and isothermal vertical walls.
Abstract: Convection in a low Prandtl number fluid driven by the combined mechanism of buoyancy and surface tension is investigated in the presence of a uniform vertical magnetic field. The fluid is contained in a square cavity with the upper surface open and isothermal vertical walls. The thermal conductivity k of the fluid is assumed to vary linearly with temperature The governing equations are solved using ADI and SOR numerical techniques. The heat transfer is found to decrease appreciably across the cavity with a decrease in k. The accumulation of streamlines by Lorentz force is seen for linearly varying k.

Journal ArticleDOI
TL;DR: A complete mechanical model of the part feeding dynamics, based on unilateral constraints with Coulomb friction is presented, enabling a theoretical investigation of the multiple part transportation dynamics and consequently an improvement of the transportation process.
Abstract: Vibratory feeders are used in automated assembly to feed small parts. They are capable to store, transport, orientate, and isolate the parts. An oscillating track with a frequency up to 100 Hz excites the transportation process, which is mainly based on impact and friction phenomena between the parts and the track. The design of the feeders is usually performed by trial and error, with various requirements concerning the robustness of the transportation process. This paper presents a complete mechanical model of the part feeding dynamics, based on unilateral constraints with Coulomb friction. This model enables a theoretical investigation of the multiple part transportation dynamics and consequently an improvement of the transportation process. The developed spatial impact model was verified by measurements, that were carried out using a special experimental setup. For this purpose the motion of the transported part was measured by laser distance sensors. Based on the resulting coefficients of friction and restitution average transportation rates were calculated and also verified by measurements. The benefit of the developed simulation tool is pointed out by some exemplary simulation results.

Journal ArticleDOI
TL;DR: In this paper, the authors investigate the limit of vanishing hardening and vanishing material inhomogenuity and show that the limit depends on their relative size within the limit procedure, and the analytical and numerical results show that under small hardening the phase transformation process is very sensitive to any inhomogeneities which may be present (e.g. geometric ones) or are developed in the two-phase system in the course of the loading/unloading sequences.
Abstract: The paper is concerned with the mathematical modelling and computational simulation of hysteretic behaviour typically exhibited by shape memory alloys in the pseudoelas-tic temperature range, as observed by I. M uller and his co-workers in experimental tests for CuZnAl monocrystals. The point of departure is the one-dimensional ther-momechanical model due to I. M uller and due to V.I. Levitas. The internal hysteresis loops are described by means of a discrete memory variable which can be handled by a monotone path rule. Existence and uniqueness of solutions is shown in the presence of hardening. We investigate the limit of vanishing hardening and vanishing material inhomogenuity and show that the limit depends on their relative size within the limit procedure. The analytical and numerical results show that under small hardening the phase transformation process is very sensitive to any inhomogenuities which may be present (e.g. geometric ones) or are developed in the two-phase system in the course of the loading/unloading sequences. Great diierences in the local response at a material point and the system behaviour are observed, in particular the system displays internal loops only if the hardening is signiicantly larger than the material inhomogenuities.

Journal ArticleDOI
TL;DR: In this article, a theory of geometrically-exact multilayer beams and one-dimensional plates that account for the through-the-thickness deformation in each layer, in addition to shear deformation, is presented.
Abstract: We formulate a theory of geometrically-exact multilayer beams and one-dimensional plates that account for the through-the-thickness deformation in each layer, in addition to shear deformation. The complete set of nonlinear equations of motion together with the appropriate boundary conditions are derived, and a linear constitutive law is postulated for the model. The number of layers is arbitrary and unlimited, with a reference layer arbitrarily chosen among the layers. The length and the thickness of each layer are also variable, making the modeling of multilayer structures with ply drop-offs possible. The present theory reduces exactly to the case of multilayer structures without through-the-thickness deformation, and to the case of single-layer structures. The formulation allows the description of large deformation and large overall motion in multilayer structures.