The Experts below are selected from a list of 249 Experts worldwide ranked by ideXlab platform

V. J. Tsipiras - One of the best experts on this subject based on the ideXlab platform.

  • Shear deformable bars of doubly symmetrical cross section under nonlinear nonuniform torsional vibrations—application to torsional postbuckling configurations and primary resonance excitations
    Nonlinear Dynamics, 2010
    Co-Authors: Evangelos J. Sapountzakis, V. J. Tsipiras
    Abstract:

    In this paper a boundary element method is developed for the nonuniform torsional vibration problem of bars of arbitrary doubly symmetric constant cross section, taking into account the effects of geometrical nonlinearity (finite displacement—Small Strain Theory) and secondary twisting moment deformation. The bar is subjected to arbitrarily distributed or concentrated conservative dynamic twisting and warping moments along its length, while its edges are subjected to the most general axial and torsional (twisting and warping) boundary conditions. The resulting coupling effect between twisting and axial displacement components is also considered and a constant along the bar compressive axial load is induced so as to investigate the dynamic response at the (torsional) postbuckled state. The bar is assumed to be adequately laterally supported so that it does not exhibit any flexural or flexural–torsional behavior. A coupled nonlinear initial boundary value problem with respect to the variable along the bar angle of twist and to an independent warping parameter is formulated. The resulting equations are further combined to yield a single partial differential equation with respect to the angle of twist. The problem is numerically solved employing the Analog Equation Method (AEM), a BEM based method, leading to a system of nonlinear Differential–Algebraic Equations (DAE). The main purpose of the present contribution is twofold: (i) comparison of both the governing differential equations and the numerical results of linear or nonlinear free or forced vibrations of bars ignoring or taking into account the secondary twisting moment deformation effect (STMDE) and (ii) numerical investigation of linear or nonlinear free vibrations of bars at torsional postbuckling configurations. Numerical results are worked out to illustrate the method, demonstrate its efficiency and wherever possible its accuracy.

  • Nonlinear nonuniform torsional vibrations of bars by the boundary element method
    Journal of Sound and Vibration, 2010
    Co-Authors: Evangelos J. Sapountzakis, V. J. Tsipiras
    Abstract:

    Abstract In this paper a boundary element method is developed for the nonuniform torsional vibration problem of bars of arbitrary doubly symmetric constant cross-section taking into account the effect of geometrical nonlinearity. The bar is subjected to arbitrarily distributed or concentrated conservative dynamic twisting and warping moments along its length, while its edges are supported by the most general torsional boundary conditions. The transverse displacement components are expressed so as to be valid for large twisting rotations (finite displacement–Small Strain Theory), thus the arising governing differential equations and boundary conditions are in general nonlinear. The resulting coupling effect between twisting and axial displacement components is considered and torsional vibration analysis is performed in both the torsional pre- or post-buckled state. A distributed mass model system is employed, taking into account the warping, rotatory and axial inertia, leading to the formulation of a coupled nonlinear initial boundary value problem with respect to the variable along the bar angle of twist and to an “average” axial displacement of the cross-section of the bar. The numerical solution of the aforementioned initial boundary value problem is performed using the analog equation method, a BEM based method, leading to a system of nonlinear differential-algebraic equations (DAE), which is solved using an efficient time discretization scheme. Additionally, for the free vibrations case, a nonlinear generalized eigenvalue problem is formulated with respect to the fundamental mode shape at the points of reversal of motion after ignoring the axial inertia to verify the accuracy of the proposed method. The problem is solved using the direct iteration technique (DIT), with a geometrically linear fundamental mode shape as a starting vector. The validity of negligible axial inertia assumption is examined for the problem at hand.

  • Warping shear stresses in nonlinear nonuniform torsional vibrations of bars by BEM
    Engineering Structures, 2010
    Co-Authors: Evangelos J. Sapountzakis, V. J. Tsipiras
    Abstract:

    Abstract In this paper a boundary element method is developed for the evaluation of warping shear stresses of bars of an arbitrary doubly symmetric constant cross section undergoing nonuniform torsional vibrations taking into account the effect of geometrical nonlinearity. The bar is subjected to arbitrarily distributed or concentrated conservative dynamic twisting and warping moments along its length, while its edges are supported by the most general torsional and axial boundary conditions. The transverse displacement components are expressed so as to be valid for large twisting rotations (finite displacement — Small Strain Theory), thus the arising governing differential equations and boundary conditions are in general nonlinear. Employing a variational approach, a coupled nonlinear initial boundary value problem with respect to the main unknown kinematical components and two boundary value problems with respect to the primary and secondary warping functions are formulated. The solution of the last two problems is performed by a pure BEM approach requiring exclusively boundary discretization of the bar’s cross section and leading to the evaluation of the warping shear stresses. The arising linear system of equations related to the secondary warping function is singular and a special technique is used to perform its regularization. The validity of the negligible axial inertia assumption is examined for the problem at hand.

Aleksandar Borković - One of the best experts on this subject based on the ideXlab platform.

  • Rotation-free isogeometric dynamic analysis of an arbitrarily curved plane Bernoulli-Euler beam
    Engineering Structures, 2019
    Co-Authors: Aleksandar Borković, Gligor Radenković, S. Kovacevic, S. Milovanović, D. Majstorović
    Abstract:

    Abstract A novel rotation-free isogeometric formulation of in-plane dynamic analysis of an arbitrarily curved Bernoulli-Euler beam in the convective frame of reference is presented. The driving force behind the present study has been the development of the NURBS-based element which enables an elegant framework of in-plane vibrations of arbitrarily curved Bernoulli-Euler beams, being a function only of the global Cartesian coordinates. Due to the fact that no additional simplifications are made, besides those related to the classic Bernoulli-Euler hypothesis and Small Strain Theory, the formulation is particularly applicable for problems regarding the behavior of strongly curved beams. An excellent agreement of the results is accomplished and efficiency for academic and practical use are shown. The influence of the product of the maximum curvature and the thickness of the beam on the accuracy of the solution is specially treated and debated. The effects of the hpk -refinements are thoroughly checked and a highly nonlinear convergence behavior under the h -refinement is noticed. The well-known fact that models with the highest interelement continuities return superior accuracy per degree of freedom is substantiated by an in-depth numerical analysis of order of convergence. Furthermore, the accuracy of the developed model is analyzed utilizing normalized numerical discrete spectrums. It is remarked that the accuracy per degree of freedom degrades with the complexity of reference geometry of the beam.

  • Linear static isogeometric analysis of an arbitrarily curved spatial Bernoulli–Euler beam
    Computer Methods in Applied Mechanics and Engineering, 2018
    Co-Authors: Gligor Radenković, Aleksandar Borković
    Abstract:

    Abstract The present research is focused on the linear analysis of a spatial Bernoulli–Euler beam. Metrics of the reference and deformed configurations are rigorously defined with respect to the convective coordinate frame of reference. No higher order terms are neglected which makes the formulation ideally suited for analysis of arbitrarily curved spatial beams in the frame of finite (but Small) Strain Theory. The well-known issue of nonorthogonality of local coordinate system at an arbitrary point of a spatial beam is solved by the introduction of a new coordinate line that is orthogonal to the normal plane of the beam axis at each point. Generalized coordinates of the present model are translations of the beam axis and the angle of twist of a cross section. Two different parameterizations of this angle are discussed and implemented. Both geometry and kinematics are described with the same set of NURBS functions, in line with the isogeometric approach. Numerical analysis proved that the theoretical considerations are correct and some limits of applicability are defined. An in-depth analysis of convergence properties has confirmed the fact that models with the highest interelement continuity have an improved accuracy per DOF, for problems that result in a smooth structural response.

  • Linear static isogeometric analysis of an arbitrarily curved spatial Bernoulli-Euler beam
    2018
    Co-Authors: Gligor Radenković, Aleksandar Borković
    Abstract:

    The present research is focused on the linear analysis of a spatial Bernoulli-Euler beam. Metrics of the reference and deformed configurations are rigorously defined with respect to the convective coordinate frame of reference. No higher order terms are neglected which makes the formulation ideally suited for analysis of arbitrarily curved spatial beams in the frame of finite (but Small) Strain Theory. The well-known issue of nonorthogonality of local coordinate system at an arbitrary point of a spatial beam is solved by the introduction of a new coordinate line that is orthogonal to the normal plane of the beam axis at each point. Generalized coordinates of the present model are translations of the beam axis and the angle of twist of a cross section. Two different parameterizations of this angle are discussed and implemented. Both geometry and kinematics are described with the same set of NURBS functions, in line with the isogeometric approach. Numerical analysis proved that the theoretical considerations are correct. An in-depth analysis of convergence properties has confirmed the fact that models with the highest interelement continuity have an improved accuracy per DOF, for problems that result in a smooth structural response.

M. A. Hicks - One of the best experts on this subject based on the ideXlab platform.

  • Large deformation elastic electro-osmosis consolidation of clays
    Computers and Geotechnics, 2013
    Co-Authors: Jiao Yuan, M. A. Hicks
    Abstract:

    Abstract This paper presents the theoretical background of an elastic electro-osmosis consolidation model for saturated soils experiencing large Strains, which considers volumetric Strains induced by changes in both the hydraulic and electric driven pore water flows. Three fully coupled governing equations, considering the soil mechanical behaviour, pore water transport and electrical field, and their numerical implementation within an updated Lagrangian finite element formulation, are presented. The proposed model is first verified against a classical one-dimensional analytical solution for electro-osmosis consolidation to demonstrate its accuracy and efficiency. Then, various numerical examples are investigated to study the deformation characteristics and time dependent evolution of excess pore pressure. Finally, the importance of considering large Strains in a consistent and proper way is demonstrated, and differences compared to models based on Small Strain Theory are highlighted.

  • Large deformation elastic electro-osmosis consolidation of clays
    Computers and Geotechnics, 2013
    Co-Authors: Jie Yuan, M. A. Hicks
    Abstract:

    This paper presents the theoretical background of an elastic electro-osmosis consolidation model for saturated soils experiencing large Strains, which considers volumetric Strains induced by changes in both the hydraulic and electric driven pore water flows. Three fully coupled governing equations, considering the soil mechanical behaviour, pore water transport and electrical field, and their numerical implementation within an updated Lagrangian finite element formulation, are presented. The proposed model is first verified against a classical one-dimensional analytical solution for electro-osmosis consolidation to demonstrate its accuracy and efficiency. Then, various numerical examples are investigated to study the deformation characteristics and time dependent evolution of excess pore pressure. Finally, the importance of considering large Strains in a consistent and proper way is demonstrated, and differences compared to models based on Small Strain Theory are highlighted. © 2013 Elsevier Ltd.

Gligor Radenković - One of the best experts on this subject based on the ideXlab platform.

  • Rotation-free isogeometric dynamic analysis of an arbitrarily curved plane Bernoulli-Euler beam
    Engineering Structures, 2019
    Co-Authors: Aleksandar Borković, Gligor Radenković, S. Kovacevic, S. Milovanović, D. Majstorović
    Abstract:

    Abstract A novel rotation-free isogeometric formulation of in-plane dynamic analysis of an arbitrarily curved Bernoulli-Euler beam in the convective frame of reference is presented. The driving force behind the present study has been the development of the NURBS-based element which enables an elegant framework of in-plane vibrations of arbitrarily curved Bernoulli-Euler beams, being a function only of the global Cartesian coordinates. Due to the fact that no additional simplifications are made, besides those related to the classic Bernoulli-Euler hypothesis and Small Strain Theory, the formulation is particularly applicable for problems regarding the behavior of strongly curved beams. An excellent agreement of the results is accomplished and efficiency for academic and practical use are shown. The influence of the product of the maximum curvature and the thickness of the beam on the accuracy of the solution is specially treated and debated. The effects of the hpk -refinements are thoroughly checked and a highly nonlinear convergence behavior under the h -refinement is noticed. The well-known fact that models with the highest interelement continuities return superior accuracy per degree of freedom is substantiated by an in-depth numerical analysis of order of convergence. Furthermore, the accuracy of the developed model is analyzed utilizing normalized numerical discrete spectrums. It is remarked that the accuracy per degree of freedom degrades with the complexity of reference geometry of the beam.

  • Linear static isogeometric analysis of an arbitrarily curved spatial Bernoulli–Euler beam
    Computer Methods in Applied Mechanics and Engineering, 2018
    Co-Authors: Gligor Radenković, Aleksandar Borković
    Abstract:

    Abstract The present research is focused on the linear analysis of a spatial Bernoulli–Euler beam. Metrics of the reference and deformed configurations are rigorously defined with respect to the convective coordinate frame of reference. No higher order terms are neglected which makes the formulation ideally suited for analysis of arbitrarily curved spatial beams in the frame of finite (but Small) Strain Theory. The well-known issue of nonorthogonality of local coordinate system at an arbitrary point of a spatial beam is solved by the introduction of a new coordinate line that is orthogonal to the normal plane of the beam axis at each point. Generalized coordinates of the present model are translations of the beam axis and the angle of twist of a cross section. Two different parameterizations of this angle are discussed and implemented. Both geometry and kinematics are described with the same set of NURBS functions, in line with the isogeometric approach. Numerical analysis proved that the theoretical considerations are correct and some limits of applicability are defined. An in-depth analysis of convergence properties has confirmed the fact that models with the highest interelement continuity have an improved accuracy per DOF, for problems that result in a smooth structural response.

  • Linear static isogeometric analysis of an arbitrarily curved spatial Bernoulli-Euler beam
    2018
    Co-Authors: Gligor Radenković, Aleksandar Borković
    Abstract:

    The present research is focused on the linear analysis of a spatial Bernoulli-Euler beam. Metrics of the reference and deformed configurations are rigorously defined with respect to the convective coordinate frame of reference. No higher order terms are neglected which makes the formulation ideally suited for analysis of arbitrarily curved spatial beams in the frame of finite (but Small) Strain Theory. The well-known issue of nonorthogonality of local coordinate system at an arbitrary point of a spatial beam is solved by the introduction of a new coordinate line that is orthogonal to the normal plane of the beam axis at each point. Generalized coordinates of the present model are translations of the beam axis and the angle of twist of a cross section. Two different parameterizations of this angle are discussed and implemented. Both geometry and kinematics are described with the same set of NURBS functions, in line with the isogeometric approach. Numerical analysis proved that the theoretical considerations are correct. An in-depth analysis of convergence properties has confirmed the fact that models with the highest interelement continuity have an improved accuracy per DOF, for problems that result in a smooth structural response.

Evangelos J. Sapountzakis - One of the best experts on this subject based on the ideXlab platform.

  • Shear deformable bars of doubly symmetrical cross section under nonlinear nonuniform torsional vibrations—application to torsional postbuckling configurations and primary resonance excitations
    Nonlinear Dynamics, 2010
    Co-Authors: Evangelos J. Sapountzakis, V. J. Tsipiras
    Abstract:

    In this paper a boundary element method is developed for the nonuniform torsional vibration problem of bars of arbitrary doubly symmetric constant cross section, taking into account the effects of geometrical nonlinearity (finite displacement—Small Strain Theory) and secondary twisting moment deformation. The bar is subjected to arbitrarily distributed or concentrated conservative dynamic twisting and warping moments along its length, while its edges are subjected to the most general axial and torsional (twisting and warping) boundary conditions. The resulting coupling effect between twisting and axial displacement components is also considered and a constant along the bar compressive axial load is induced so as to investigate the dynamic response at the (torsional) postbuckled state. The bar is assumed to be adequately laterally supported so that it does not exhibit any flexural or flexural–torsional behavior. A coupled nonlinear initial boundary value problem with respect to the variable along the bar angle of twist and to an independent warping parameter is formulated. The resulting equations are further combined to yield a single partial differential equation with respect to the angle of twist. The problem is numerically solved employing the Analog Equation Method (AEM), a BEM based method, leading to a system of nonlinear Differential–Algebraic Equations (DAE). The main purpose of the present contribution is twofold: (i) comparison of both the governing differential equations and the numerical results of linear or nonlinear free or forced vibrations of bars ignoring or taking into account the secondary twisting moment deformation effect (STMDE) and (ii) numerical investigation of linear or nonlinear free vibrations of bars at torsional postbuckling configurations. Numerical results are worked out to illustrate the method, demonstrate its efficiency and wherever possible its accuracy.

  • Nonlinear nonuniform torsional vibrations of bars by the boundary element method
    Journal of Sound and Vibration, 2010
    Co-Authors: Evangelos J. Sapountzakis, V. J. Tsipiras
    Abstract:

    Abstract In this paper a boundary element method is developed for the nonuniform torsional vibration problem of bars of arbitrary doubly symmetric constant cross-section taking into account the effect of geometrical nonlinearity. The bar is subjected to arbitrarily distributed or concentrated conservative dynamic twisting and warping moments along its length, while its edges are supported by the most general torsional boundary conditions. The transverse displacement components are expressed so as to be valid for large twisting rotations (finite displacement–Small Strain Theory), thus the arising governing differential equations and boundary conditions are in general nonlinear. The resulting coupling effect between twisting and axial displacement components is considered and torsional vibration analysis is performed in both the torsional pre- or post-buckled state. A distributed mass model system is employed, taking into account the warping, rotatory and axial inertia, leading to the formulation of a coupled nonlinear initial boundary value problem with respect to the variable along the bar angle of twist and to an “average” axial displacement of the cross-section of the bar. The numerical solution of the aforementioned initial boundary value problem is performed using the analog equation method, a BEM based method, leading to a system of nonlinear differential-algebraic equations (DAE), which is solved using an efficient time discretization scheme. Additionally, for the free vibrations case, a nonlinear generalized eigenvalue problem is formulated with respect to the fundamental mode shape at the points of reversal of motion after ignoring the axial inertia to verify the accuracy of the proposed method. The problem is solved using the direct iteration technique (DIT), with a geometrically linear fundamental mode shape as a starting vector. The validity of negligible axial inertia assumption is examined for the problem at hand.

  • Warping shear stresses in nonlinear nonuniform torsional vibrations of bars by BEM
    Engineering Structures, 2010
    Co-Authors: Evangelos J. Sapountzakis, V. J. Tsipiras
    Abstract:

    Abstract In this paper a boundary element method is developed for the evaluation of warping shear stresses of bars of an arbitrary doubly symmetric constant cross section undergoing nonuniform torsional vibrations taking into account the effect of geometrical nonlinearity. The bar is subjected to arbitrarily distributed or concentrated conservative dynamic twisting and warping moments along its length, while its edges are supported by the most general torsional and axial boundary conditions. The transverse displacement components are expressed so as to be valid for large twisting rotations (finite displacement — Small Strain Theory), thus the arising governing differential equations and boundary conditions are in general nonlinear. Employing a variational approach, a coupled nonlinear initial boundary value problem with respect to the main unknown kinematical components and two boundary value problems with respect to the primary and secondary warping functions are formulated. The solution of the last two problems is performed by a pure BEM approach requiring exclusively boundary discretization of the bar’s cross section and leading to the evaluation of the warping shear stresses. The arising linear system of equations related to the secondary warping function is singular and a special technique is used to perform its regularization. The validity of the negligible axial inertia assumption is examined for the problem at hand.