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X L Gao - One of the best experts on this subject based on the ideXlab platform.

  • A new Timoshenko Beam Model incorporating microstructure and surface energy effects
    Acta Mechanica, 2014
    Co-Authors: X L Gao
    Abstract:

    A new Timoshenko Beam Model is developed using a modified couple stress theory and a surface elasticity theory. A variational formulation based on Hamilton’s principle is employed, which leads to the simultaneous determination of the equations of motion and complete boundary conditions for a Timoshenko Beam. The new Model contains a material length scale parameter accounting for the microstructure effect in the bulk of the Beam and three surface elasticity constants describing the mechanical behavior of the Beam surface layer. The inclusion of these additional material constants enables the new Model to capture the microstructure-and surface energy-dependent size effect. In addition, both bending and axial deformations are considered, and the Poisson effect is incorporated in the current Model, unlike existing Timoshenko Beam Models. The new Beam Model includes the Models considering only the microstructure dependence or the surface energy effect as limiting cases and recovers the Bernoulli–Euler Beam Model incorporating the two effects as a special case. Also, the current Model reduces to the classical Timoshenko Beam Model when the microstructure dependence, surface energy and Poisson’s effect are all suppressed. To demonstrate the new Model, the static bending and free vibration problems of a simply supported Beam are analytically solved by directly applying the general formulas derived. The numerical results for the static bending problem reveal that both the deflection and rotation of the simply supported Beam predicted by the new Model are smaller than those predicted by the classical Timoshenko Beam Model. In addition, the differences in both the deflection and rotation predicted by the two Models are very large when the Beam thickness is small, but they are diminishing with the increase of the Beam thickness. Similar trends are observed for the free vibration problem, where it is shown that the natural frequency predicted by the new Model is higher than that given by the classical Model, with the difference between them being significantly large for very thin Beams. These predicted trends of the size effect in Beam bending at the micron scale agree with those observed experimentally.

  • A new Bernoulli–Euler Beam Model incorporating microstructure and surface energy effects
    Zeitschrift für angewandte Mathematik und Physik, 2013
    Co-Authors: X L Gao, F. F. Mahmoud
    Abstract:

    A new Bernoulli–Euler Beam Model is developed using a modified couple stress theory and a surface elasticity theory. A variational formulation based on the principle of minimum total potential energy is employed, which leads to the simultaneous determination of the equilibrium equation and complete boundary conditions for a Bernoulli–Euler Beam. The new Model contains a material length scale parameter accounting for the microstructure effect in the bulk of the Beam and three surface elasticity constants describing the mechanical behavior of the Beam surface layer. The inclusion of these additional material constants enables the new Model to capture the microstructure- and surface energy-dependent size effect. In addition, Poisson’s effect is incorporated in the current Model, unlike existing Beam Models. The new Beam Model includes the Models considering only the microstructure dependence or the surface energy effect as special cases. The current Model reduces to the classical Bernoulli–Euler Beam Model when the microstructure dependence, surface energy, and Poisson’s effect are all suppressed. To demonstrate the new Model, a cantilever Beam problem is solved by directly applying the general formulas derived. Numerical results reveal that the Beam deflection predicted by the new Model is smaller than that by the classical Beam Model. Also, it is found that the difference between the deflections predicted by the two Models is very significant when the Beam thickness is small but is diminishing with the increase of the Beam thickness.

  • a microstructure dependent timoshenko Beam Model based on a modified couple stress theory
    Journal of The Mechanics and Physics of Solids, 2008
    Co-Authors: H M, X L Gao, J N Reddy
    Abstract:

    Abstract A microstructure-dependent Timoshenko Beam Model is developed using a variational formulation. It is based on a modified couple stress theory and Hamilton's principle. The new Model contains a material length scale parameter and can capture the size effect, unlike the classical Timoshenko Beam theory. Moreover, both bending and axial deformations are considered, and the Poisson effect is incorporated in the current Model, which differ from existing Timoshenko Beam Models. The newly developed non-classical Beam Model recovers the classical Timoshenko Beam Model when the material length scale parameter and Poisson's ratio are both set to be zero. In addition, the current Timoshenko Beam Model reduces to a microstructure-dependent Bernoulli–Euler Beam Model when the normality assumption is reinstated, which also incorporates the Poisson effect and can be further reduced to the classical Bernoulli–Euler Beam Model. To illustrate the new Timoshenko Beam Model, the static bending and free vibration problems of a simply supported Beam are solved by directly applying the formulas derived. The numerical results for the static bending problem reveal that both the deflection and rotation of the simply supported Beam predicted by the new Model are smaller than those predicted by the classical Timoshenko Beam Model. Also, the differences in both the deflection and rotation predicted by the two Models are very large when the Beam thickness is small, but they are diminishing with the increase of the Beam thickness. Similar trends are observed for the free vibration problem, where it is shown that the natural frequency predicted by the new Model is higher than that by the classical Model, with the difference between them being significantly large only for very thin Beams. These predicted trends of the size effect in Beam bending at the micron scale agree with those observed experimentally. Finally, the Poisson effect on the Beam deflection, rotation and natural frequency is found to be significant, which is especially true when the classical Timoshenko Beam Model is used. This indicates that the assumption of Poisson's effect being negligible, which is commonly used in existing Beam theories, is inadequate and should be individually verified or simply abandoned in order to obtain more accurate and reliable results.

  • bernoulli euler Beam Model based on a modified couple stress theory
    Journal of Micromechanics and Microengineering, 2006
    Co-Authors: S K Park, X L Gao
    Abstract:

    A new Model for the bending of a Bernoulli–Euler Beam is developed using a modified couple stress theory. A variational formulation based on the principle of minimum total potential energy is employed. The new Model contains an internal material length scale parameter and can capture the size effect, unlike the classical Bernoulli–Euler Beam Model. The former reduces to the latter in the absence of the material length scale parameter. As a direct application of the new Model, a cantilever Beam problem is solved. It is found that the bending rigidity of the cantilever Beam predicted by the newly developed Model is larger than that predicted by the classical Beam Model. The difference between the deflections predicted by the two Models is very significant when the Beam thickness is small, but is diminishing with the increase of the Beam thickness. A comparison shows that the predicted size effect agrees fairly well with that observed experimentally.

Omer Civalek - One of the best experts on this subject based on the ideXlab platform.

  • a novel microstructure dependent shear deformable Beam Model
    International Journal of Mechanical Sciences, 2015
    Co-Authors: Bekir Akgoz, Omer Civalek
    Abstract:

    Abstract A new size-dependent Beam Model is introduced on the basis of hyperbolic shear deformation Beam and modified strain gradient theory. The governing differential equations and corresponding boundary conditions are obtained with the aid of minimum total potential energy principle. The static bending and buckling behaviors of simply supported microBeams embedded in an elastic medium are investigated. The interactions between the microBeam and elastic medium are simulated by Winkler foundation Model. Navier solution procedure is employed to obtain analytical solutions for deflections under sinusoidal load and critical buckling loads. The effects of material length scale parameter, length-to-thickness ratio, shear correction factors and Winkler modulus on the bending and buckling responses of microBeams are discussed in detail. The results are comparatively presented with the results of other Beam theories. It is observed that the new results predicted by the present Model and the results evaluated by sinusoidal shear deformation Beam Model are in good agreement.

  • a new trigonometric Beam Model for buckling of strain gradient microBeams
    International Journal of Mechanical Sciences, 2014
    Co-Authors: Bekir Akgoz, Omer Civalek
    Abstract:

    Abstract In this paper, a new microstructure-dependent sinusoidal Beam Model for buckling of microBeams is presented using modified strain gradient theory. This microBeam Model can take into consideration microstructural and shear deformation effects. The equilibrium equations and corresponding boundary conditions in buckling are derived with the minimum total potential energy principle. Buckling problem of a simply supported microBeam subjected to an axial compressive force is analytically solved by Navier solution procedure. Influences of thickness-to-length scale parameter and slenderness ratios on buckling behavior are discussed in detail. It is observed that the size dependency becomes more important when the thickness of the microBeam is closer to material length scale parameter. Also, it can be said that the effects of shear deformation are more considerable for short and thick Beams with lower slenderness ratios.

J N Reddy - One of the best experts on this subject based on the ideXlab platform.

  • A NONLOCAL CURVED Beam Model BASED ON A MODIFIED COUPLE STRESS THEORY
    International Journal of Structural Stability and Dynamics, 2011
    Co-Authors: Yiping Liu, J N Reddy
    Abstract:

    A nonlocal Timoshenko curved Beam Model is developed using a modified couple stress theory and Hamilton's principle. The Model contains a material length scale parameter that can capture the size effect, unlike the classical Timoshenko Beam theory. Both bending and axial deformations are considered, and the Poisson effect is incorporated in the Model. The newly developed nonlocal Model recovers the classical Model when the material length scale parameter and Poisson's ratio are both taken to be zero and the straight Beam Model when the radius of curvature is set to infinity. In addition, the nonlocal Bernoulli–Euler curved Beam Model can be realized when the normal cross-section assumption is restated. To illustrate the new Model, the static bending and free vibration problems of a simply supported curved Beam are solved by directly applying the formulas derived. The numerical results for the static bending problem reveal that both the deflection and rotation of the simply supported Beam predicted by the new Model are smaller than those predicted by the classical Timoshenko curved Beam Model. Also, the differences in both the deflection and rotation predicted by the current and classical Timoshenko Model are very large when the Beam thickness is small, but they diminish with the increase of the Beam height. Similar trends are observed for the free vibration problem, where it is shown that the natural frequency predicted by the nonlocal Model is higher than that by the classical Model, and the difference between them is significantly large only for very thin Beams. These predicted trends of the size effect at the micron scale agree with those observed experimentally.

  • a microstructure dependent timoshenko Beam Model based on a modified couple stress theory
    Journal of The Mechanics and Physics of Solids, 2008
    Co-Authors: H M, X L Gao, J N Reddy
    Abstract:

    Abstract A microstructure-dependent Timoshenko Beam Model is developed using a variational formulation. It is based on a modified couple stress theory and Hamilton's principle. The new Model contains a material length scale parameter and can capture the size effect, unlike the classical Timoshenko Beam theory. Moreover, both bending and axial deformations are considered, and the Poisson effect is incorporated in the current Model, which differ from existing Timoshenko Beam Models. The newly developed non-classical Beam Model recovers the classical Timoshenko Beam Model when the material length scale parameter and Poisson's ratio are both set to be zero. In addition, the current Timoshenko Beam Model reduces to a microstructure-dependent Bernoulli–Euler Beam Model when the normality assumption is reinstated, which also incorporates the Poisson effect and can be further reduced to the classical Bernoulli–Euler Beam Model. To illustrate the new Timoshenko Beam Model, the static bending and free vibration problems of a simply supported Beam are solved by directly applying the formulas derived. The numerical results for the static bending problem reveal that both the deflection and rotation of the simply supported Beam predicted by the new Model are smaller than those predicted by the classical Timoshenko Beam Model. Also, the differences in both the deflection and rotation predicted by the two Models are very large when the Beam thickness is small, but they are diminishing with the increase of the Beam thickness. Similar trends are observed for the free vibration problem, where it is shown that the natural frequency predicted by the new Model is higher than that by the classical Model, with the difference between them being significantly large only for very thin Beams. These predicted trends of the size effect in Beam bending at the micron scale agree with those observed experimentally. Finally, the Poisson effect on the Beam deflection, rotation and natural frequency is found to be significant, which is especially true when the classical Timoshenko Beam Model is used. This indicates that the assumption of Poisson's effect being negligible, which is commonly used in existing Beam theories, is inadequate and should be individually verified or simply abandoned in order to obtain more accurate and reliable results.

Xavier Cespedes - One of the best experts on this subject based on the ideXlab platform.

  • A new higher-order elastoplastic Beam Model for reinforced concrete
    Meccanica, 2020
    Co-Authors: Grégoire Corre, Arthur Lebée, Karam Sab, Mohammed Khalil Ferradi, Xavier Cespedes
    Abstract:

    The present paper introduces a new elastoplastic Beam Model for reinforced concrete based on a higher-order Beam Model previously developed [1]. Steel and concrete are both defined as elastoplastic materials. The Beam Model represents the concrete body whereas rebars are given a specific discretization. A Rankine criterion is used for concrete in both tension and compression, and a closed-form solution for the local projection of the trial stress on the yield surface is formulated. Steel rebars are Modelled with 1D bar elements and added to the global stiffness of the concrete Beam Model. The kinematics of the higher-order Beam Model is enriched by a systematic method with displacement modes. This extension of the kinematics leads to local accuracy and yields results comparable to 3D computations. The present reinforced concrete Model is validated through a set of case studies. Implemented within the software programs of the company Strains Engineering, the objective is to develop a fast computing and efficient Model that can be directly used by engineers.

  • The Asymptotic Expansion Load Decomposition elastoplastic Beam Model
    International Journal for Numerical Methods in Engineering, 2018
    Co-Authors: Grégoire Corre, Arthur Lebée, Karam Sab, Mohammed Ferradi, Xavier Cespedes
    Abstract:

    A new higher-order elasto-plastic Beam Model is derived and implemented in this paper. The reduced kinematic approximation is based on a higher-order elastic Beam Model using the asymptotic expansion method. This Model introduces new degrees of freedom associated to arbitrary loads as well as eigenstrains applied to the Beam. In order to capture the effect of plasticity on the structure, the present elasto-plastic Model considers the plastic strain as an eigenstrain imposed on the structure and new degrees of freedom are added on the fly into the kinematics during the incremental-iterative process. The radial return algorithm of 2 plastic flow is used. Because of the constant evolution of the Beam kinematics, the Newton-Raphson algorithm for satisfying the global equilibrium is modified. An application to a cantilever Beam loaded at its free extremity is presented and compared to a 3D reference solution. The Beam Model shows satisfying results even at a local scale and for a computation time significantly reduced.

  • The Asymptotic Expansion Load Decomposition elasto-plastic Beam Model
    International Journal for Numerical Methods in Engineering, 2018
    Co-Authors: Grégoire Corre, Arthur Lebée, Karam Sab, Mohammed Ferradi, Xavier Cespedes
    Abstract:

    A new higher-order elasto-plastic Beam Model is derived and implemented in this paper. The reduced kinematic approximation is based on a higher-order elastic Beam Model using the asymptotic expansion method. This Model introduces new degrees of freedom associated to arbitrary loads as well as eigenstrains applied to the Beam. In order to capture the effect of plasticity on the structure, the present elasto-plastic Model considers the plastic strain as an eigenstrain imposed on the structure and new degrees of freedom are added on the fly into the kinematics during the incremental-iterative process. The radial return algorithm of 2 plastic flow is used. Because of the constant evolution of the Beam kinematics, the Newton-Raphson algorithm for satisfying the global equilibrium is modified. An application to a cantilever Beam loaded at its free extremity is presented and compared to a 3D reference solution. The Beam Model shows satisfying results even at a local scale and for a computation time significantly reduced.

  • Higher‐order Beam Model with eigenstrains: theory and illustrations
    ZAMM - Journal of Applied Mathematics and Mechanics Zeitschrift für Angewandte Mathematik und Mechanik, 2018
    Co-Authors: Grégoire Corre, Arthur Lebée, Karam Sab, Mohammed Ferradi, Xavier Cespedes
    Abstract:

    A higher-order Beam Model based on the asymptotic expansion method was suggested by Ferradi et al.[11] Introducing new degrees of freedom specific to the applied loads into the kinematics of the Beam, this Model yields fast and accurate results. The present paper focuses on the extension of this Model to the case of arbitrary eigenstrains expressed in a separate form between the longitudinal coordinate and the in-section coordinates. The asymptotic expansion procedure is recalled and the derivation of a higher-order Beam Model performed. The Beam Model is interpolated with NURBS. The case of a bridge deck heated on a localized area is studied. A second case study of a prestressed cantilever Beam is then investigated. The results of the higher-order Beam Model are compared to a 3D solution in each example. The performances of the Beam Model appears to be accurate and very time-efficient.

  • Higher-order Beam Model with eigenstrains: theory and illustrations
    Journal of Applied Mathematics and Mechanics Zeitschrift für Angewandte Mathematik und Mechanik, 2018
    Co-Authors: Grégoire Corre, Arthur Lebée, Karam Sab, Mohammed Ferradi, Xavier Cespedes
    Abstract:

    A higher-order Beam Model based on the asymptotic expansion method was suggested by Ferradi et al.. Introducing new degrees of freedom specific to the applied loads into the kinematics of the Beam, this Model yields fast and accurate results. The present paper focuses on the extension of this Model to the case of arbitrary eigenstrains expressed in a separate form between the longitudinal coordinate and the in-section coordinates. The asymptotic expansion procedure is recalled and the derivation of a higher-order Beam Model performed. The Beam Model is interpolated with NURBS. The case of a bridge deck heated on a localized area is studied. A second case study of a prestressed cantilever Beam is then investigated. The results of the higher-order Beam Model are compared to a 3D solution in each example. The performances of the Beam Model appears to be accurate and very time-efficient.

Lin Wang - One of the best experts on this subject based on the ideXlab platform.

  • Strain gradient Beam Model for dynamics of microscale pipes conveying fluid
    Applied Mathematical Modelling, 2011
    Co-Authors: Li Yin, Q. Qian, Lin Wang
    Abstract:

    Abstract Based on the strain gradient theory, we present a microstructure-dependent Bernoulli–Euler Model to analyze the vibration and stability of microscale pipes conveying fluid. The equation of motion and boundary conditions are derived using Hamilton’s principle. The proposed strain gradient Beam Model contains three material length scale parameters to capture the size effect. This new Model may be reduced to the modified couple stress Beam Model when two of these three material length scale parameters vanish and may be reduced to the classical Beam Model in the absence of all the material length scale parameters. From the numerical calculations for micropipes with both ends positively supported, it is found that the natural frequency and the critical flow velocity are size-dependent. The results show that the microscale pipe displays remarkable size effect when its outside diameter becomes comparable to the material length scale parameter, while the size effect is almost diminishing as the diameter is far greater than the material length scale parameter. Moreover, the size effect predicted by the current strain gradient Beam Model is stronger than that predicted by the modified couple stress Beam Model, since two other material length scale parameters have been accounted for in the former.

  • A MODIFIED NONLOCAL Beam Model FOR VIBRATION AND STABILITY OF NANOTUBES CONVEYING FLUID
    Physica E: Low-dimensional Systems and Nanostructures, 2011
    Co-Authors: Lin Wang
    Abstract:

    Abstract In this paper, a new, modified nonlocal Beam Model is developed for analyzing the vibration and stability of nanotubes conveying fluid, in which one single nonlocal nanoscale parameter is included. Using Hamilton’s principle, a new higher-order differential equation of motion and the corresponding higher-order, non-classical boundary conditions are obtained for nanotubes conveying fluid. Based on this modified nonlocal Model, effect of nonlocal nanoscale parameter on natural frequencies and critical flow velocities is presented and discussed through numerical calculations. It is found that this factor has great influence on the vibration and stability of nanotubes conveying fluid. In particular, the nonlocal effect tends to induce higher natural frequencies and higher critical flow velocities as compared to the results obtained from the classical and partial nonlocal Beam Models.