DSpace-CRIS at TU Wienhttps://repositum.tuwien.atThe reposiTUm digital repository system captures, stores, indexes, preserves, and distributes digital research material.Tue, 04 Oct 2022 03:30:48 GMT2022-10-04T03:30:48Z50201Modeling the Dynamics of a Flexible Belt Drive Using the Equations of a Deformable String with Discontinuitieshttp://hdl.handle.net/20.500.12708/67418Title: Modeling the Dynamics of a Flexible Belt Drive Using the Equations of a Deformable String with Discontinuities
Authors: Vetyukov, Yu.; Eliseev, V.; Krommer, M.
Abstract: The transient analysis of a belt drive is based on a nonlinear dynamic model of an extensible string at contour motion, in which the trajectories of particles of the belt are predetermined. The equations of string dynamics at the free spans are considered in a fixed domain by transforming into a spatial frame. Assuming the absence of slip of the belt on the surface of the pulleys, we arrive at a new model with a discontinuous velocity field and concentrated contact forces. Finite difference discretization allows numerical analysis of the resulting system of partial differential equations with delays. Example solution for the case of start up and accelerated motion of a friction belt drive is presented and discussed.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/20.500.12708/674182015-01-01T00:00:00ZModeling finite deformations of an axially moving elastic plate with a mixed Eulerian-Lagrangian kinematic descriptionhttp://hdl.handle.net/20.500.12708/67359Title: Modeling finite deformations of an axially moving elastic plate with a mixed Eulerian-Lagrangian kinematic description
Authors: Vetyukov, Yury; Gruber, Peter; Krommer, Michael
Editors: Kleiber, M.
Abstract: We consider the motion of a flexible plate across a domain, bounded by two parallel lines. Kinematically prescribed velocities of the plate, entering the domain and leaving it, may vary in space and time. The corresponding deformation of the plate is quasistatically analyzed using the geometrically nonlinear model of a Kirchhoff shell with a mixed Eulerian-Lagrangian kinematic description. In contrast to the formulations, available in the literature, both the in-plane and the out-of-plane deformations are unknown a priori and may be arbitrarily large. The particles of the plate travel across a finite element mesh, which remains fixed in the axial direction. The evident advantage of the approach is that the boundary conditions need to be applied at fixed edges of the finite elements. In the paper, we present the mathematical formulation and demonstrate its consistency by comparing the solution of a benchmark problem against results, obtained with conventional Lagrangian finite elements.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/20.500.12708/673592015-01-01T00:00:00ZBuckling and supercritical behavior of axially moving plateshttp://hdl.handle.net/20.500.12708/67360Title: Buckling and supercritical behavior of axially moving plates
Authors: Vetyukov, Yury
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/20.500.12708/673602015-01-01T00:00:00ZNonlinear Mechanics of Thin-Walled Structures. Asymptotics, Direct Approach and Numerical Analysishttp://hdl.handle.net/20.500.12708/24851Title: Nonlinear Mechanics of Thin-Walled Structures. Asymptotics, Direct Approach and Numerical Analysis
Authors: Vetyukov, Yury
Abstract: This book presents a hybrid approach to the mechanics of thin bodies. Classical theories of rods, plates and shells with constrained shear are based on asymptotic splitting of the equations and boundary conditions of three-dimensional elasticity. The asymptotic solutions become accurate as the thickness decreases, and the three-dimensional fields of stresses and displacements can be determined. The analysis includes practically important effects of electromechanical coupling and material inhomogeneity. The extension to the geometrically nonlinear range uses the direct approach based on the principle of virtual work. Vibrations and buckling of pre-stressed structures are studied with the help of linearized incremental formulations, and direct tensor calculus rounds out the list of analytical techniques used throughout the book.
A novel theory of thin-walled rods of open profile is subsequently developed from the models of rods and shells, and traditionally applied equations are proven to be asymptotically exact. The influence of pre-stresses on the torsional stiffness is shown to be crucial for buckling analysis. Novel finite element schemes for classical rod and shell structures are presented with a comprehensive discussion regarding the theoretical basis, computational aspects and implementation details. Analytical conclusions and closed-form solutions of particular problems are validated against numerical results. The majority of the simulations were performed in the Wolfram Mathematica environment, and the compact source code is provided as a substantial and integral part of the book.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/20.500.12708/248512014-01-01T00:00:00ZPlastic Deformation of Axially Moving Continuum in Mixed Eulerian-Lagrangian Formulationhttp://hdl.handle.net/20.500.12708/67358Title: Plastic Deformation of Axially Moving Continuum in Mixed Eulerian-Lagrangian Formulation
Authors: Gruber, Peter; Vetyukov, Yury; Krommer, Michael
Editors: Kleiber, M.
Abstract: We present a new approach to model the motion of a metal sheet during a rolling mill process. In particular, we focus on the planar motion of the sheet as seen from the bird´s eye view in the area between two consecutive roll stands. The outflow of the sheet from the preceding roll stand, as well as the infeed of the sheet into the subsequent roll stand are subject to given entry and exit velocity profiles, which are inhomogeneous and varying in time. The method takes advantage of a mixed Eulerian-Lagrangian formulation, meaning that the governing equations are based on spatial coordinates and material points at the same time. The resulting Finite Element mesh is spatially fixed with respect to the direction of the rolling process, whereas material is transported across the geometry of the mesh. The overall deformation is described by a multiplicative scheme, allowing for an exact geometrical representation and the study of specifically non-linear effects. Particular emphasis is placed on modeling plastic material behavior, and the transport of the inelastic strain field required thereby.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/20.500.12708/673582015-01-01T00:00:00ZNonlinear Modelling Of Dielectric Elastomer Single Layer Plates Using A Multiplicative Decomposition Of The Deformation Gradient To Account For Electrostrictionhttp://hdl.handle.net/20.500.12708/67730Title: Nonlinear Modelling Of Dielectric Elastomer Single Layer Plates Using A Multiplicative Decomposition Of The Deformation Gradient To Account For Electrostriction
Authors: Hansy-Staudigl, Elisabeth; Krommer, Michael; Vetyukov, Yury
Editors: Güemes, Alfredo; Benjeddou, Ayech; Rodellar, Jose; Leng, J.
Abstract: In this paper we study dielectric elastomers accounting for constitutive cou- pling by means of electrostriction using a multiplicative decomposition of the deformation gradient tensor. The resulting constitutive relations are reduced to the special case of thin single layer plates made of incompressible dielectric elastomers. As an example problem we study the electro-mechanically coupled behavior of such a single layer plate in the ab- sence of mechanical forces with special emphasis on the effect of electrostriction on the breakdown instability.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/20.500.12708/677302017-01-01T00:00:00ZHybrid asymptotic–direct approach to finite deformations of electromechanically coupled piezoelectric shellshttp://hdl.handle.net/20.500.12708/89Title: Hybrid asymptotic–direct approach to finite deformations of electromechanically coupled piezoelectric shells
Authors: Vetyukov, Yury; Hansy-Staudigl, Elisabeth; Krommer, Michael
Abstract: We present a novel multistage hybrid asymptotic–direct approach to the modeling of the nonlinear behavior of thin shells with piezoelectric patches or layers, which is formulated in a holistic form for the first time in this paper. The key points of the approach are as follows: (1) the asymptotic reduction in the three-dimensional linear theory of piezoelasticity for a thin plate; (2) a direct approach to geometrically nonlinear piezoelectric shells as material surfaces, which is justified and completed by demanding the mathematical equivalence of its linearized form with the asymptotic solution for a plate; and (3) the numerical analysis by means of an FE scheme based on the developed model of the reduced electromechanically coupled continuum. Our approach is illustrated by examples of static and steady-state analysis and verified with three-dimensional solutions computed with the commercially available FE code ABAQUS as well as by comparison with results reported in the literature.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/20.500.12708/892018-01-01T00:00:00ZNon-material finite element modelling of large vibrations of axially moving strings and beamshttp://hdl.handle.net/20.500.12708/844Title: Non-material finite element modelling of large vibrations of axially moving strings and beams
Authors: Vetyukov, Yury
Abstract: We present a new mathematical model for the dynamics of a beam or a string, which moves in a given axial direction across a particular domain. Large in-plane vibrations are coupled with the gross axial motion, and a Lagrangian (material) form of the equations of structural mechanics becomes inefficient. The proposed mixed Eulerian-Lagrangian description features mechanical fields as functions of a spatial coordinate in the axial direction. The material travels across a finite element mesh, and the boundary conditions are applied in fixed nodes. Beginning with the variational equation of virtual work in its material form, we analytically derive the Lagrange's equations of motion of the second kind for the considered case of a discretized non-material control domain and for geometrically exact kinematics. The dynamic analysis is straightforward as soon as the strain and the kinetic energies of the control domain are available. In numerical simulations we demonstrate the rapid mesh convergence of the model, the effect of the bending stiffness and the dynamic instability when the axial velocity gets high. We also show correspondence to the results of fully Lagrangian benchmark solutions.
Description: The final publication is available via <a href="https://doi.org/10.1016/j.jsv.2017.11.010" target="_blank">https://doi.org/10.1016/j.jsv.2017.11.010</a>.
Sat, 03 Feb 2018 00:00:00 GMThttp://hdl.handle.net/20.500.12708/8442018-02-03T00:00:00ZMixed Eulerian–Lagrangian shell model for lateral run-off in a steel belt drive and its experimental validationhttp://hdl.handle.net/20.500.12708/20412Title: Mixed Eulerian–Lagrangian shell model for lateral run-off in a steel belt drive and its experimental validation
Authors: Scheidl, Jakob; Vetyukov, Yury; Schmidrathner, Christian; Schulmeister, Klemens; Proschek, Michael
Abstract: A non-material shell finite element model is developed and applied to the example problem of a slack steel belt moving on two rotating drums. For the first time in the open literature we demonstrate an approach for predicting the time evolution of the lateral run-off velocity of the belt in response to its geometric imperfection and angular drum misalignment. We adopt a novel Eulerian–Lagrangian kinematic description featuring a mixed parametrisation of the configurational space with a Eulerian circumferential coordinate and two Lagrangian coordinates for the transverse and lateral deflections. A nonlinear finite element approximation provides the necessary C1 inter-element continuity in this compound coordinate system. Using the model of elastic tangential contact, we account for the convective term in the local increments of the relative displacement between the contacting surfaces during the time integration. A thorough convergence study with respect to the mesh and time step sizes justifies the approach. Together with the successful validation against the results of a series of physical experiments, this makes the present contribution an important step towards a model-based controller design.
Sun, 15 Aug 2021 00:00:00 GMThttp://hdl.handle.net/20.500.12708/204122021-08-15T00:00:00ZThin Shells With Piezoelctric Transducers: Theory, Numerical Modelling And Verificationhttp://hdl.handle.net/20.500.12708/67218Title: Thin Shells With Piezoelctric Transducers: Theory, Numerical Modelling And Verification
Authors: Krommer, Michael; Pieber, Michael; Vetyukov, Yury
Editors: Arauo, A.L.; Mota Soares, C.A.
Abstract: For the modelling of thin elastic shells with attached piezoelectric transducers, we consider a material surface with certain mechanical degrees of freedom in each point. Addi- tionally, electrical unknowns are present within the domain, where the piezoelectric transducers are attached, such that the sensing and actuating behavior can be properly accounted for. The modelling is done in the geometrically nonlinear regime, but the electromechanically coupled constitutive relations are treated within the framework of Voigt´s linear theory of piezoelec- tricity. Owing to the assumed thinness of the shell the influence of shear is neglected in the modeling. A Finite Element scheme for the solution of the resulting model is implemented and the solutions computed with the present theory are compared to results computed with the commercially available FE code Abaqus. Different examples are presented ranging from large deformations, to snap through instability and to a linear analysis. A very good agreement be- tween the results is obtained, from which the accuracy of the thin shell formulation as a material surface is concluded. Next, an existing physical shell is modeled within the linearized version of the present theory and the computational results are compared to measurement results from the physical experiment. The agreement is reasonably good; natural frequencies as well as eigenmodes are considered for the comparison. Concerning the eigenmodes the MAC crite- rion is used. Finally, the resulting linear time invariant dynamical system for the simulation of the physical shell is imported into Mathematica and different strategies for passive and active control are tested and compared to each other. Concerning passive control methods classical single mode shunt-damping using an optimized RL-network is studied.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/20.500.12708/672182015-01-01T00:00:00ZNon-material Finite Elements for Spatial Deformations of Beltshttp://hdl.handle.net/20.500.12708/30558Title: Non-material Finite Elements for Spatial Deformations of Belts
Authors: Schmidrathner, Christian; Vetyukov, Yury
Editors: Altenbach, Holm; Irschik, H; Matveenko, Valery P.
Abstract: We present a novel mixed Eulerian-Lagrangian beam finite element formulation. Large spatial deformations of shear-rigid, but extensible rods with natural curvature are considered. The three-dimensional deformation of a thin strip clamped at both ends is computed with this novel method and compared with semi-analytic solutions of the boundary value problem of the incremental rod theory as well as with the finite element solution for an equivalent shell model. Stability of the straight clamped beam in the absence of gravity is considered analytically for the sake of comparison and the critical value of the natural curvature is found. Finally, the contact problem of a belt spanned between two pulleys is discussed.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/20.500.12708/305582019-01-01T00:00:00ZA Non-linear Theory of Thin-Walled Rods of Open Profile Deduced with Incremental Shell Equationshttp://hdl.handle.net/20.500.12708/30559Title: A Non-linear Theory of Thin-Walled Rods of Open Profile Deduced with Incremental Shell Equations
Authors: Scheidl, Jakob; Vetyukov, Yury
Editors: Altenbach, Holm; Chróścielewski, Jacek; Eremeyev, Victor A.; Wiśniewski, Krzysztof
Abstract: We study the structural behaviour of rods with thin-walled open cross-sections. Such members are best known for their low torsional rigidity and extensive warping deformation when subjected to twisting. Proceeding to large deformations one needs to account for the geometrically non-linear effects in the cross-section, that affect the structural response and prevent a simple generalisation of the linear theory. We here further elaborate a novel approach that utilizes the equations of incremental shell theory to quantify these non-linear effects and incorporate them into an augmented beam theory, which is then put to test on an example of a circularly curved rod. The linear deformation analysis reveals, that arbitrarily curved and straight rods do not share the same asymptotic behaviour. The torsional-flexural buckling loads obtained with the incremental beam theory correspond well to reference computations with shell finite elements, given that subcritical pre-deformations are negligible. The narration concludes with the post-buckling analysis using shell finite elements.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/20.500.12708/305592019-01-01T00:00:00ZCoulomb dry friction contact in a non-material shell finite element model for axially moving endless steel beltshttp://hdl.handle.net/20.500.12708/68222Title: Coulomb dry friction contact in a non-material shell finite element model for axially moving endless steel belts
Authors: Scheidl, Jakob; Vetyukov, Yury
Abstract: Having developed a mixed, quasistatic Eulerian-Lagrangian shell finite element model for the simulation of axially moving, endless steel belts, we focus on how to efficiently treat the Coulomb contact between belt and drums. The proposed method relies on the penalty regularization for normal contact and on an augmented Lagrangian strategy for tangential contact. The presented results demonstrate the robustness of the applied scheme.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/20.500.12708/682222019-01-01T00:00:00ZNon-material finite element rod model for out-of-plane bending of an elastic strip with natural curvaturehttp://hdl.handle.net/20.500.12708/68223Title: Non-material finite element rod model for out-of-plane bending of an elastic strip with natural curvature
Authors: Schmidrathner, Christian; Vetyukov, Yury
Abstract: A novel finite element formulation for elastic unshearable rods in three-dimensional space is presented. Looking forward to future implementations of axially moving belts, we use a mixed Eulerian-Lagrangian kinematic formulation, which has the advantage that the element nodes are fixed in one spatial coordinate and the material points are flowing through the mesh, hence it is possible to discretize the elements in the free spans coarser than the ones in contact with the pulleys. Here, we present the solution of hanging rods with a flat cross-section including a natural curvature, which causes an out-of-plane bending as well as torsion of the rod. For validation purposes we limit ourselves to equilibrium solutions (for which purely Lagrangian elements would be also applicable) with clamped boundary conditions. The results are compared with a shell model of the hanging strip. Preliminary results concerning the frictionless contact problem for a steel belt hanging on two pulleys are discussed.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/20.500.12708/682232019-01-01T00:00:00ZModeling electro-elastic coupling phenomena in electrostrictive polymers in the context of structural mechanicshttp://hdl.handle.net/20.500.12708/68224Title: Modeling electro-elastic coupling phenomena in electrostrictive polymers in the context of structural mechanics
Authors: Hansy-Staudigl, Elisabeth; Krommer, Michael; Vetyukov, Yury; Humer, Alexander
Abstract: Bringing into focus the design aspect of thin film electro-active polymer actuators justifies the deployment of a structural mechanics framework. We propose a physically consistent constitutive model for such actuators, which is valid for plates and shells as material surfaces within a complete direct formulation. To this end, we use the principle of virtual work to deduce the general form of the constitutive law from an augmented Helmholtz free energy, as a function of the structural Green-Lagrange type strain measures and of the material electric field, without the need of a-priori assumptions concerning the state of strain and stress.
Mechanical deformations of thin film devices - e.g. made of polyurethane - under the action of an external electric field, are caused by two different sources. On the one hand, the applied electric field causes a dielectric polarization of the polymer matrix, yielding to corresponding attractive electrostatic forces between the electroded surfaces resulting into a squeezing of the film. On the other hand, crystalline graft units with a certain natural, but arbitrarily directed polarization, embedded in between the polymer chains, have to align in the direction of the applied electric field such that a rotation of the whole crystal unit takes place. This rotation results in an additional macroscopic thickness squeeze- known as the electrostrictive effect.
We treat both electromechanical coupling phenomena separately, where it turns out, that the electrostatic forces can be accounted for by an electrical contribution to the augmented free energy, whereas, the electrostrictive effect is taken into account in the elastic part of the augmented free energy by virtue of a hybrid multiplicative and additive decomposition of the plate/shell deformation measures.
Benefiting from the structural mechanics formulation, we gain a lower - two-dimensional - formulation, which provides a clear physical insight into the nature of the deformation process initiated by the external electric field. E.g. for the linearised problem, a comparison to the literature on thermoelastic plates and shells uncovers the action of the electric field as a combined source of self-stresses. In order to solve particular problems, the constitutive relation of the geometrically and physically nonlinear formulation is implemented into our in-house finite element code. The computed results, which were tested against results from the literature as well as against test problems of our previous work (where numerical integration of the three dimensional plate/shell augmented free energy through the thickness was employed), show a very good agreement.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/20.500.12708/682242019-01-01T00:00:00ZMixed Eulerian-Lagrangian description in the statics of a flexible belt with tension and bending hanging on two pulleyshttp://hdl.handle.net/20.500.12708/67914Title: Mixed Eulerian-Lagrangian description in the statics of a flexible belt with tension and bending hanging on two pulleys
Authors: Scheidl, Jakob; Vetyukov, Yury; Oborin, Evgenii; Krommer, Michael; Schmidrathner, Christian
Abstract: Studying the mechanics of thin, axially moving strings, beams or plates (e.g.: belt drives, cable cars, ...) at mixed Eulerian-Lagrangian description, which features the transformation of material coordinates to spatial ones, is more appropriate than the classical material (Lagrangian) one. Aiming at testing a newly proposed non‐material finite element formulation we study the statics of a looped belt as a rod hanging in contact with two pulleys. Numerical experiments demonstrate rapid mesh convergence as well as correspondence to semi‐analytical results and conventional Lagrangian finite element solutions.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/20.500.12708/679142018-01-01T00:00:00ZNonlinear electro-elastic modeling of thin dielectric elastomer plate actuatorshttp://hdl.handle.net/20.500.12708/67918Title: Nonlinear electro-elastic modeling of thin dielectric elastomer plate actuators
Authors: Hansy-Staudigl, Elisabeth; Krommer, Michael; Vetyukov, Yury; Humer, Alexander
Abstract: Electro-active polymers undergo large deformations while being typically very thin; this encourages us to study the geometric nonlinear set up within the structural mechanics framework of thin plates and shells as a material surface. In this paper, the full set of three dimensional, geometric nonlinear field equations are incorporated to develop constitutive relations by introducing a generalized free energy function, which takes parts from a pure mechanical strain energy (e.g. neo-Hookean) and a mixed electro-mechanical free energy. The key feature is the multiplicative decomposition of the deformation gradient tensor, which allows for separate constitutive models for any electro-mechanic coupling phenomenon. We apply this model exemplary to the case of electrostriction and use the Gauss law of electrostatics in order to incorporate charge controlled actuation, which has been reported to omit pull-in instability. In order to translate the resulting equations to their two-dimensional geometrically nonlinear counterparts for thin plates, a plane stress condition is imposed on the total stress tensor and the effect of the electrostrictive coupling is investigated on voltage controlled as well as on charge controlled actuation, employing non-linear Finite Elements. Finally, results are compared to numerical as well as experimental results on electrostrictive coupling and charge controlled actuation.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/20.500.12708/679182018-01-01T00:00:00ZModeling Electro-Active Dielectric And Electrostrictive Elastomer Plates In The Framework Of Nonlinear Structural Electro-Mechanicshttp://hdl.handle.net/20.500.12708/67919Title: Modeling Electro-Active Dielectric And Electrostrictive Elastomer Plates In The Framework Of Nonlinear Structural Electro-Mechanics
Authors: Hansy-Staudigl, Elisabeth; Krommer, Michael; Vetyukov, Yury
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/20.500.12708/679192018-01-01T00:00:00ZStability and Supercritical Deformation of a Circular Ring with Intrinsic Curvaturehttp://hdl.handle.net/20.500.12708/29387Title: Stability and Supercritical Deformation of a Circular Ring with Intrinsic Curvature
Authors: Vetyukov, Yury
Editors: Irschik, H; Belyaev, Alexander K.; Krommer, Michael
Abstract: Stability of a circular ring, pre-stressed by a temperature-like intrinsic deformation, is studied using the equations of the nonlinear theory of rods. The temperature gradient in the radial direction results in a bending moment. The critical state depends on the ratio of the bending stiffness coefficients. In the supercritical range, the ring begins to turn inside out as its cross-sections rotate about the axis. The analytical solutions are successfully compared against results of finite element simulations for a shell model of the ring.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/20.500.12708/293872017-01-01T00:00:00ZBeams, Plates, and Shellshttp://hdl.handle.net/20.500.12708/29967Title: Beams, Plates, and Shells
Authors: Krommer, Michael; Vetyukov, Yury
Editors: Altenbach, H; Öchsner, Andreas
Abstract: In this article we shortly present the fundamental relations of the classical theories for straight and slender beams as well as for thin plates and shells. In particular, Bernoulli-Euler beams, Kirchhoff plates, and Kirchhoff-Love shells are discussed in a geometrically and physically linear regime. Further, we restrict the content to homogenous beams, plates, and shells, for which the material behavior is assumed isotropic. Our presentation rests on the use of a direct tensor notation, which avoids unnecessarily lengthy equations using specific coordinates but rather enables a compact and concise formulation.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/20.500.12708/299672018-01-01T00:00:00Z