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

  • Nonlinear inElastic uniform torsion of composite bars by BEM
    Computers & Structures, 2009
    Co-Authors: Evangelos J. Sapountzakis, V.j. Tsipiras
    Abstract:

    In this paper the Elastic-plastic uniform torsion analysis of composite cylindrical bars of arbitrary cross-section consisting of materials in contact, each of which can surround a finite number of inclusions, taking into account the effect of geometric nonlinearity is presented employing the boundary element method. The stress-strain relationships for the materials are assumed to be Elastic-plastic-strain hardening. The incremental torque-rotation relationship is computed based on the finite displacement (finite rotation) theory, that is the transverse displacement components are expressed so as to be valid for large rotations and the longitudinal normal strain includes the second-order geometric nonlinear term often described as the "Wagner strain". The proposed formulation does not stand on the assumption of a thin-walled structure and therefore the cross-section's torsional rigidity is evaluated exactly without using the so-called Saint Venant's torsional constant. The torsional rigidity of the cross-section is evaluated directly employing the primary warping function of the cross-section depending on both its shape and the progress of the plastic region. A boundary value problem with respect to the aforementioned function is formulated and solved employing a BEM approach. The influence of the second Piola-Kirch-hoff normal stress component to the plastic/Elastic Moment ratio in uniform inElastic torsion is demonstrated. (C) 2008 Elsevier Ltd. All rights reserved

  • Nonlinear inElastic uniform torsion of composite bars by BEM
    Computers & Structures, 2008
    Co-Authors: Evangelos J. Sapountzakis, V.j. Tsipiras
    Abstract:

    In this paper the Elastic-plastic uniform torsion analysis of composite cylindrical bars of arbitrary cross-section consisting of materials in contact, each of which can surround a finite number of inclusions, taking into account the effect of geometric nonlinearity is presented employing the boundary element method. The stress-strain relationships for the materials are assumed to be Elastic-plastic-strain hardening. The incremental torque-rotation relationship is computed based on the finite displacement (finite rotation) theory, that is the transverse displacement components are expressed so as to be valid for large rotations and the longitudinal normal strain includes the second-order geometric nonlinear term often described as the ''Wagner strain''. The proposed formulation does not stand on the assumption of a thin-walled structure and therefore the cross-section's torsional rigidity is evaluated exactly without using the so-called Saint Venant's torsional constant. The torsional rigidity of the cross-section is evaluated directly employing the primary warping function of the cross-section depending on both its shape and the progress of the plastic region. A boundary value problem with respect to the aforementioned function is formulated and solved employing a BEM approach. The influence of the second Piola-Kirchhoff normal stress component to the plastic/Elastic Moment ratio in uniform inElastic torsion is demonstrated.

  • Nonlinear inElastic uniform torsion of bars by BEM
    Computational Mechanics, 2008
    Co-Authors: Evangelos J. Sapountzakis, V.j. Tsipiras
    Abstract:

    In this paper the Elastic–plastic uniform torsion analysis of simply or multiply connected cylindrical bars of arbitrary cross-section taking into account the effect of geometric nonlinearity is presented employing the boundary element method. The stress–strain relationship for the material is assumed to be Elastic–plastic–strain hardening. The incremental torque–rotation relationship is computed based on the finite displacement (finite rotation) theory, that is the transverse displacement components are expressed so as to be valid for large rotations and the longitudinal normal strain includes the second-order geometric nonlinear term often described as the “Wagner strain”. The proposed formulation does not stand on the assumption of a thin-walled structure and therefore the cross-section’s torsional rigidity is evaluated exactly without using the so-called Saint-Venant’s torsional constant. The torsional rigidity of the cross-section is evaluated directly employing the primary warping function of the cross-section depending on both its shape and the progress of the plastic region. A boundary value problem with respect to the aforementioned function is formulated and solved employing a BEM approach. The influence of the second Piola–Kirchhoff normal stress component to the plastic/Elastic Moment ratio in uniform inElastic torsion is demonstrated. The developed procedure retains most of the advantages of a BEM solution over a pure domain discretization method, although it requires domain discretization, which is used only to evaluate integrals.

Hyeonbae Kang - One of the best experts on this subject based on the ideXlab platform.

  • Small-Volume Expansions of the Displacement Fields
    Mathematical Methods in Elasticity Imaging, 2015
    Co-Authors: Habib Ammari, Hyeonbae Kang, Hyundae Lee, Elie Bretin, Josselin Garnier, Abdul Wahab
    Abstract:

    This chapter deals with small-volume expansions of the displacement fields. It first introduces the notion of Elastic Moment tensor, a geometric quantity associated with a small-volume inclusion, before discussing some of its important properties such as symmetry and positive-definiteness. The asymptotic expansion of the displacement in the presence of a small-volume inclusion is expressed in terms of the Elastic Moment tensor. The chapter proceeds by deriving formulas for the Elastic Moment tensors under linear transformations and computes those associated with ellipses and balls. It also considers both the static and time-harmonic regimes and extends the small-volume asymptotic framework to anisotropic Elasticity. Finally, it provides the leading-order terms in the asymptotic expansions of the solutions to the static and time-harmonic Elasticity equations with respect to the size of a small inclusion.

  • polarization and Moment tensors with applications to inverse problems and effective medium theory
    2010
    Co-Authors: Habib Ammari, Hyeonbae Kang
    Abstract:

    Introduction.- Layer Potentials and Transmission Problems.- Uniqueness for Inverse Conductivity Problems.- Generalized Isotropic and Anisotropic Polarization Tensors.- Full Asymptotic Formula for the Potentials.- Near-Boundary Conductivity Inclusions.- Impedance Imaging of Conductivity Inclusions.- Effective Properties of Electrical Composites.- Transmission Problem for Elastostatics.- Elastic Moment Tensor.- Full Asymptotic Expansion of the Displacement Field.- Imaging of Elastic Inclusions.- Effective Properties of Elastic Composites.- Appendices.- References.- Index.

  • progress on the strong eshelby s conjecture and extremal structures for the Elastic Moment tensor
    arXiv: Analysis of PDEs, 2009
    Co-Authors: Habib Ammari, Hyeonbae Kang, Yves Capdeboscq, Hyundae Lee, Graeme W Milton, Habib Zribi
    Abstract:

    We make progress towards proving the strong Eshelby's conjecture in three dimensions. We prove that if for a single nonzero uniform loading the strain inside inclusion is constant and further the eigenvalues of this strain are either all the same or all distinct, then the inclusion must be of ellipsoidal shape. As a consequence, we show that for two linearly independent loadings the strains inside the inclusions are uniform, then the inclusion must be of ellipsoidal shape. We then use this result to address a problem of determining the shape of an inclusion when the Elastic Moment tensor (Elastic polarizability tensor) is extremal. We show that the shape of inclusions, for which the lower Hashin-Shtrikman bound either on the bulk part or on the shear part of the Elastic Moment tensor is attained, is an ellipse in two dimensions and an ellipsoid in three dimensions.

  • Improved Hashin-Shtrikman Bounds for Elastic Moment Tensors and an Application
    Applied Mathematics and Optimization, 2008
    Co-Authors: Yves Capdeboscq, Hyeonbae Kang
    Abstract:

    This paper is devoted to the derivation of trace bounds for Elastic Moment tensors. Starting from the integral equation formulation of the Elastic Moment tensor, we establish that its trace can be obtained as a sum of minimal energies. We then recover the so-called Hashin-Shtrikman bounds, and show that these bounds can be tightened for inclusions which have some local thickness. As an application, we show that the volume of the inclusion can be estimated by the Elastic Moment tensor.

  • Improved Hashin–Shtrikman Bounds for Elastic Moment Tensors and an Application
    Applied Mathematics and Optimization, 2007
    Co-Authors: Yves Capdeboscq, Hyeonbae Kang
    Abstract:

    This paper is devoted to the derivation of trace bounds for Elastic Moment tensors. Starting from the integral equation formulation of the Elastic Moment tensor, we establish that its trace can be obtained as a sum of minimal energies. We then recover the so-called Hashin-Shtrikman bounds, and show that these bounds can be tightened for inclusions which have some local thicknes. As an application, we show that the volume of the inclusion can be estimated by the Elastic Moment tensor

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

  • Nonlinear inElastic uniform torsion of composite bars by BEM
    Computers & Structures, 2009
    Co-Authors: Evangelos J. Sapountzakis, V.j. Tsipiras
    Abstract:

    In this paper the Elastic-plastic uniform torsion analysis of composite cylindrical bars of arbitrary cross-section consisting of materials in contact, each of which can surround a finite number of inclusions, taking into account the effect of geometric nonlinearity is presented employing the boundary element method. The stress-strain relationships for the materials are assumed to be Elastic-plastic-strain hardening. The incremental torque-rotation relationship is computed based on the finite displacement (finite rotation) theory, that is the transverse displacement components are expressed so as to be valid for large rotations and the longitudinal normal strain includes the second-order geometric nonlinear term often described as the "Wagner strain". The proposed formulation does not stand on the assumption of a thin-walled structure and therefore the cross-section's torsional rigidity is evaluated exactly without using the so-called Saint Venant's torsional constant. The torsional rigidity of the cross-section is evaluated directly employing the primary warping function of the cross-section depending on both its shape and the progress of the plastic region. A boundary value problem with respect to the aforementioned function is formulated and solved employing a BEM approach. The influence of the second Piola-Kirch-hoff normal stress component to the plastic/Elastic Moment ratio in uniform inElastic torsion is demonstrated. (C) 2008 Elsevier Ltd. All rights reserved

  • Nonlinear inElastic uniform torsion of composite bars by BEM
    Computers & Structures, 2008
    Co-Authors: Evangelos J. Sapountzakis, V.j. Tsipiras
    Abstract:

    In this paper the Elastic-plastic uniform torsion analysis of composite cylindrical bars of arbitrary cross-section consisting of materials in contact, each of which can surround a finite number of inclusions, taking into account the effect of geometric nonlinearity is presented employing the boundary element method. The stress-strain relationships for the materials are assumed to be Elastic-plastic-strain hardening. The incremental torque-rotation relationship is computed based on the finite displacement (finite rotation) theory, that is the transverse displacement components are expressed so as to be valid for large rotations and the longitudinal normal strain includes the second-order geometric nonlinear term often described as the ''Wagner strain''. The proposed formulation does not stand on the assumption of a thin-walled structure and therefore the cross-section's torsional rigidity is evaluated exactly without using the so-called Saint Venant's torsional constant. The torsional rigidity of the cross-section is evaluated directly employing the primary warping function of the cross-section depending on both its shape and the progress of the plastic region. A boundary value problem with respect to the aforementioned function is formulated and solved employing a BEM approach. The influence of the second Piola-Kirchhoff normal stress component to the plastic/Elastic Moment ratio in uniform inElastic torsion is demonstrated.

  • Nonlinear inElastic uniform torsion of bars by BEM
    Computational Mechanics, 2008
    Co-Authors: Evangelos J. Sapountzakis, V.j. Tsipiras
    Abstract:

    In this paper the Elastic–plastic uniform torsion analysis of simply or multiply connected cylindrical bars of arbitrary cross-section taking into account the effect of geometric nonlinearity is presented employing the boundary element method. The stress–strain relationship for the material is assumed to be Elastic–plastic–strain hardening. The incremental torque–rotation relationship is computed based on the finite displacement (finite rotation) theory, that is the transverse displacement components are expressed so as to be valid for large rotations and the longitudinal normal strain includes the second-order geometric nonlinear term often described as the “Wagner strain”. The proposed formulation does not stand on the assumption of a thin-walled structure and therefore the cross-section’s torsional rigidity is evaluated exactly without using the so-called Saint-Venant’s torsional constant. The torsional rigidity of the cross-section is evaluated directly employing the primary warping function of the cross-section depending on both its shape and the progress of the plastic region. A boundary value problem with respect to the aforementioned function is formulated and solved employing a BEM approach. The influence of the second Piola–Kirchhoff normal stress component to the plastic/Elastic Moment ratio in uniform inElastic torsion is demonstrated. The developed procedure retains most of the advantages of a BEM solution over a pure domain discretization method, although it requires domain discretization, which is used only to evaluate integrals.

Franco Mastroddi - One of the best experts on this subject based on the ideXlab platform.

  • Limit-cycle stability reversal via singular perturbation and wing-flap flutter
    Journal of Fluids and Structures, 2004
    Co-Authors: Daniele Dessi, Franco Mastroddi
    Abstract:

    Abstract A three-degree-of-freedom aeroElastic typical section with a trailing-edge control surface is theoretically modelled, including nonlinear springs for both the nonlinear description of the torsional stiffness and of the hinge Elastic Moment. Furthermore, augmented states for linear unsteady aerodynamic of 2-D incompressible potential flow, have been considered in the model. First, the system response is determined by numerically integrating the governing equations using a standard Runge–Kutta algorithm in conjunction with a ‘shooting method’. The numerical analysis has revealed the presence of stable and unstable limit cycles, along with stability reversal in the neighborhood of a Hopf bifurcation. Consequently, the equations of motion are analysed by a singular perturbation technique based on the normal-form method. This method, originally introduced by strictly applying a resonance condition, is herein extended by applying a near-resonance condition in order to improve the semi-analytical description of the stability reversal behavior. Therefore, amplitudes and frequencies of limit cycles depending on the flow speed V are obtained from the normal-form equations, and the terms which are essentially responsible for the nonlinear system behavior are identified.

Habib Ammari - One of the best experts on this subject based on the ideXlab platform.

  • Small-Volume Expansions of the Displacement Fields
    Mathematical Methods in Elasticity Imaging, 2015
    Co-Authors: Habib Ammari, Hyeonbae Kang, Hyundae Lee, Elie Bretin, Josselin Garnier, Abdul Wahab
    Abstract:

    This chapter deals with small-volume expansions of the displacement fields. It first introduces the notion of Elastic Moment tensor, a geometric quantity associated with a small-volume inclusion, before discussing some of its important properties such as symmetry and positive-definiteness. The asymptotic expansion of the displacement in the presence of a small-volume inclusion is expressed in terms of the Elastic Moment tensor. The chapter proceeds by deriving formulas for the Elastic Moment tensors under linear transformations and computes those associated with ellipses and balls. It also considers both the static and time-harmonic regimes and extends the small-volume asymptotic framework to anisotropic Elasticity. Finally, it provides the leading-order terms in the asymptotic expansions of the solutions to the static and time-harmonic Elasticity equations with respect to the size of a small inclusion.

  • polarization and Moment tensors with applications to inverse problems and effective medium theory
    2010
    Co-Authors: Habib Ammari, Hyeonbae Kang
    Abstract:

    Introduction.- Layer Potentials and Transmission Problems.- Uniqueness for Inverse Conductivity Problems.- Generalized Isotropic and Anisotropic Polarization Tensors.- Full Asymptotic Formula for the Potentials.- Near-Boundary Conductivity Inclusions.- Impedance Imaging of Conductivity Inclusions.- Effective Properties of Electrical Composites.- Transmission Problem for Elastostatics.- Elastic Moment Tensor.- Full Asymptotic Expansion of the Displacement Field.- Imaging of Elastic Inclusions.- Effective Properties of Elastic Composites.- Appendices.- References.- Index.

  • progress on the strong eshelby s conjecture and extremal structures for the Elastic Moment tensor
    arXiv: Analysis of PDEs, 2009
    Co-Authors: Habib Ammari, Hyeonbae Kang, Yves Capdeboscq, Hyundae Lee, Graeme W Milton, Habib Zribi
    Abstract:

    We make progress towards proving the strong Eshelby's conjecture in three dimensions. We prove that if for a single nonzero uniform loading the strain inside inclusion is constant and further the eigenvalues of this strain are either all the same or all distinct, then the inclusion must be of ellipsoidal shape. As a consequence, we show that for two linearly independent loadings the strains inside the inclusions are uniform, then the inclusion must be of ellipsoidal shape. We then use this result to address a problem of determining the shape of an inclusion when the Elastic Moment tensor (Elastic polarizability tensor) is extremal. We show that the shape of inclusions, for which the lower Hashin-Shtrikman bound either on the bulk part or on the shear part of the Elastic Moment tensor is attained, is an ellipse in two dimensions and an ellipsoid in three dimensions.

  • A Boundary Integral Method for Computing Elastic Moment Tensors for Ellipses and Ellipsoids
    2007
    Co-Authors: Habib Ammari, Hyeonbae Kang, Hyundae Lee
    Abstract:

    The concept of Elastic Moment tensor occurs in several interesting contexts, in particular in imaging small Elastic inclusions and in asymptotic models of dilute Elastic composites. In this paper, we compute the Elastic Moment tensors for ellipses and ellipsoids by using a systematic method based on layer potentials. Our computations reveal an underlying elegant relation between the Elastic Moment tensors and the single layer potential.

  • 7. Elastic Moment Tensor
    2004
    Co-Authors: Habib Ammari, Hyeonbae Kang
    Abstract:

    7.1. Asymptotic Expansion in Free Space 7.2. Properties of EMT’s 7.3. EMT’s Under Linear Transforms 7.4. EMT’s for Ellipses 7.5. EMT’s for Elliptic Holes and Hard Ellipses