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S Kitipornchai - One of the best experts on this subject based on the ideXlab platform.

  • nonlinear free vibration of single walled carbon nanotubes using nonlocal timoshenko Beam Theory
    Physica E-low-dimensional Systems & Nanostructures, 2010
    Co-Authors: Jie Yang, Liaoliang Ke, S Kitipornchai
    Abstract:

    Nonlinear free vibration of single-walled carbon nanotubes (SWCNTs) is studied in this paper based on von Karman geometric nonlinearity and Eringen's nonlocal elasticity Theory. The SWCNTs are modeled as nanoBeams where the effects of transverse shear deformation and rotary inertia are considered within the framework of Timoshenko Beam Theory. The governing equations and boundary conditions are derived by using the Hamilton's principle. The differential quadrature (DQ) method is employed to discretize the nonlinear governing equations which are then solved by a direct iterative method to obtain the nonlinear vibration frequencies of SWCNTs with different boundary conditions. Zigzag (5, 0), (8, 0), (9, 0) and (11, 0) SWCNTs are considered in numerical calculations and the elastic modulus is obtained through molecular mechanics (MM) simulation. A detailed parametric study is conducted to study the influences of nonlocal parameter, length and radius of the SWCNTs and end supports on the nonlinear free vibration characteristics of SWCNTs.

  • nonlinear free vibration of embedded double walled carbon nanotubes based on nonlocal timoshenko Beam Theory
    Computational Materials Science, 2009
    Co-Authors: Liaoliang Ke, Jie Yang, Yang Xiang, S Kitipornchai
    Abstract:

    Nonlinear free vibration of embedded double-walled carbon nanotubes (DWNTs) is studied in this paper based on Eringen's nonlocal elasticity Theory and von Karman geometric nonlinearity. The effects of the transverse shear deformation and rotary inertia are considered within the framework of Timoshenko Beam Theory. The surrounding elastic medium is described as the Winkler model characterized by the spring. The governing equations and boundary conditions are derived by using the Hamilton's principle. The differential quadrature (DQ) method is employed to discretize the nonlinear governing equations, which are then solved by a direct iterative method to obtain the nonlinear vibration frequencies of nonlocal DWNTs with different boundary conditions. A detailed parametric study is conducted to investigate the influences of nonlocal parameter, length of the tubes, spring constant and end supports on the nonlinear free vibration characteristics of DWNTs.

  • Beam bending solutions based on nonlocal timoshenko Beam Theory
    Journal of Engineering Mechanics-asce, 2008
    Co-Authors: C.w. Lim, C M Wang, S Kitipornchai, Moshe Eisenberger
    Abstract:

    This paper is concerned with the bending problem of micro- and nanoBeams based on the Eringen nonlocal elasticity Theory and Timoshenko Beam Theory. In the former Theory, the small-scale effect is taken into consideration while the effect of transverse shear deformation is accounted for in the latter Theory. The governing equations and the boundary conditions are derived using the principle of virtual work. General solutions for the deflection, rotation, and stress resultants are presented for transversely loaded Beams. In addition, specialized bending solutions are given for Beams with various end conditions. These solutions account for a better representation of the bending behavior of short, stubby, micro- and nanoBeams where the small-scale effect and transverse shear deformation are significant. Considering particular loading and boundary conditions, the effects of small-scale and shear deformation on the bending results may be observed because of the analytical forms of the solutions.

  • buckling analysis of micro and nano rods tubes based on nonlocal timoshenko Beam Theory
    Journal of Physics D, 2006
    Co-Authors: C M Wang, Yingyan Zhang, Sai Sudha Ramesh, S Kitipornchai
    Abstract:

    This paper is concerned with the elastic buckling analysis of micro- and nano-rods/tubes based on Eringen's nonlocal elasticity Theory and the Timoshenko Beam Theory. In the former Theory, the small scale effect is taken into consideration while the effect of transverse shear deformation is accounted for in the latter Theory. The governing equations and the boundary conditions are derived using the principle of virtual work. Explicit expressions for the critical buckling loads are derived for axially loaded rods/tubes with various end conditions. These expressions account for a better representation of the buckling behaviour of micro- and nano-rods/tubes where small scale effect and transverse shear deformation effect are significant. By comparing it with the classical Beam theories, the sensitivity of the small scale effect on the buckling loads may be observed.

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

  • experimental validation of the modified couple stress timoshenko Beam Theory for web core sandwich panels
    Composite Structures, 2014
    Co-Authors: Jani Romanoff, Jn Reddy
    Abstract:

    Abstract The paper presents experimental validation of the modified couple stress Timoshenko Beam Theory for web-core sandwich panels. The face and web-plates are assumed to be isotropic and to behave according to the kinematics of the Euler–Bernoulli Beam Theory. First, a modified couple stress Theory for Timoshenko Beams is reviewed. Then shear, bending and couple stress responses of homogenized web-core sandwich Beams are examined. The developed Theory is validated with experiments from open literature for Beams in 3- and 4-point bending. The Beams have 4, 9 and 15 unit cells along their length. It is seen that the developed Theory is in excellent agreement with experiments. It is also seen that the Theory converges to physically correct solutions in the cases of infinite and zero shear stiffness; while the first corresponds the case of Euler–Bernoulli sandwich Beam, the second corresponds the case where the sandwich effect is lost and the bending is carried out purely by the bending of the faces. The paper also gives explicit expression for the couple stress stiffness in terms of unit cell dimensions and materials.

  • a unified higher order Beam Theory for buckling of a functionally graded microBeam embedded in elastic medium using modified couple stress Theory
    Composite Structures, 2013
    Co-Authors: Mesut şimsek, Jn Reddy
    Abstract:

    Abstract Based on the modified couple stress Theory (MCST), a unified higher order Beam Theory which contains various Beam theories as special cases is proposed for buckling of a functionally graded (FG) microBeam embedded in elastic Pasternak medium. This non-classical microBeam model incorporates the material length scale parameter which can capture the size effect. The non-classical Beam model reduces to the classical Beam model when the material length scale parameter is set to zero. The material properties of the FG microBeam are assumed to vary in the thickness direction and are estimated through the Mori–Tanaka homogenization technique and the classical rule of mixture. The governing equations and the related boundary conditions are derived using the principal of the minimum total potential energy. The Navier-type solution is developed for simply-supported boundary conditions, and explicit expressions related to each type of Beam Theory are proposed for the critical buckling load. Numerical results are presented to investigate the influences the material length scale parameter, aspect ratio, different estimation method of material properties, various material compositions, and the parameters of the elastic medium on the critical buckling load. Comparison study is also performed to verify the present formulation.

  • a nonlinear finite element framework for viscoelastic Beams based on the high order reddy Beam Theory
    Journal of Engineering Materials and Technology-transactions of The Asme, 2013
    Co-Authors: G S Payette, Jn Reddy
    Abstract:

    A weak form Galerkin finite element model for the nonlinear quasi-static and fully transient analysis of initially straight viscoelastic Beams is developed using the kinematic assumptions of the third-order Reddy Beam Theory. The formulation assumes linear viscoelastic material properties and is applicable to problems involving small strains and moderate rotations. The viscoelastic constitutive equations are efficiently discretized using the trapezoidal rule in conjunction with a two-point recurrence formula. Locking is avoided through the use of standard low-order reduced integration elements as well through the employment of a family of elements constructed using high-polynomial order Lagrange and Hermite interpolation functions.

  • a spectral hp nonlinear finite element analysis of higher order Beam Theory with viscoelasticity
    International Journal of Applied Mechanics, 2012
    Co-Authors: V P Vallala, G S Payette, Jn Reddy
    Abstract:

    In this paper, a finite element model for efficient nonlinear analysis of the mechanical response of viscoelastic Beams is presented. The principle of virtual work is utilized in conjunction with the third-order Beam Theory to develop displacement-based, weak-form Galerkin finite element model for both quasi-static and fully-transient analysis. The displacement field is assumed such that the third-order Beam Theory admits C0 Lagrange interpolation of all dependent variables and the constitutive equation can be that of an isotropic material. Also, higher-order interpolation functions of spectral/hp type are employed to efficiently eliminate numerical locking. The mechanical properties are considered to be linear viscoelastic while the Beam may undergo von Karman nonlinear geometric deformations. The constitutive equations are modeled using Prony exponential series with general n-parameter Kelvin chain as its mechanical analogy for quasi-static cases and a simple two-element Maxwell model for dynamic cases. The fully discretized finite element equations are obtained by approximating the convolution integrals from the viscous part of the constitutive relations using a trapezoidal rule. A two-point recurrence scheme is developed that uses the approximation of relaxation moduli with Prony series. This necessitates the data storage for only the last time step and not for the entire deformation history.

Liaoliang Ke - One of the best experts on this subject based on the ideXlab platform.

  • nonlinear free vibration of single walled carbon nanotubes using nonlocal timoshenko Beam Theory
    Physica E-low-dimensional Systems & Nanostructures, 2010
    Co-Authors: Jie Yang, Liaoliang Ke, S Kitipornchai
    Abstract:

    Nonlinear free vibration of single-walled carbon nanotubes (SWCNTs) is studied in this paper based on von Karman geometric nonlinearity and Eringen's nonlocal elasticity Theory. The SWCNTs are modeled as nanoBeams where the effects of transverse shear deformation and rotary inertia are considered within the framework of Timoshenko Beam Theory. The governing equations and boundary conditions are derived by using the Hamilton's principle. The differential quadrature (DQ) method is employed to discretize the nonlinear governing equations which are then solved by a direct iterative method to obtain the nonlinear vibration frequencies of SWCNTs with different boundary conditions. Zigzag (5, 0), (8, 0), (9, 0) and (11, 0) SWCNTs are considered in numerical calculations and the elastic modulus is obtained through molecular mechanics (MM) simulation. A detailed parametric study is conducted to study the influences of nonlocal parameter, length and radius of the SWCNTs and end supports on the nonlinear free vibration characteristics of SWCNTs.

  • nonlinear free vibration of embedded double walled carbon nanotubes based on nonlocal timoshenko Beam Theory
    Computational Materials Science, 2009
    Co-Authors: Liaoliang Ke, Jie Yang, Yang Xiang, S Kitipornchai
    Abstract:

    Nonlinear free vibration of embedded double-walled carbon nanotubes (DWNTs) is studied in this paper based on Eringen's nonlocal elasticity Theory and von Karman geometric nonlinearity. The effects of the transverse shear deformation and rotary inertia are considered within the framework of Timoshenko Beam Theory. The surrounding elastic medium is described as the Winkler model characterized by the spring. The governing equations and boundary conditions are derived by using the Hamilton's principle. The differential quadrature (DQ) method is employed to discretize the nonlinear governing equations, which are then solved by a direct iterative method to obtain the nonlinear vibration frequencies of nonlocal DWNTs with different boundary conditions. A detailed parametric study is conducted to investigate the influences of nonlocal parameter, length of the tubes, spring constant and end supports on the nonlinear free vibration characteristics of DWNTs.

D J Oehlers - One of the best experts on this subject based on the ideXlab platform.

  • dynamic response of composite Beams with partial shear interaction using a higher order Beam Theory
    Journal of Structural Engineering-asce, 2013
    Co-Authors: Anupam Chakrabarti, A H Sheikh, Michael C Griffith, D J Oehlers
    Abstract:

    Dynamic response of composite Beams with partial interaction is presented using a one-dimensional finite-element model based on a higher-order Beam Theory. The proposed model takes into account the effect of partial shear interaction between the adjacent layers, as well as the transverse shear deformation of the Beam. A third order variation of the axial displacement of the fibers over the Beam depth is taken to have a parabolic variation of shear stress, which vanishes at both the top and bottom fibers of the transverse composite surface, as clearly derived on the free and tangentially unloaded surface of the continua. In the proposed finite-element model, there is no need to incorporate any shear correction factor, and the model is free from the shear locking problem. The proposed numerical model is validated by comparing the results with those available in the literature. Many new results are presented, because there are no published results on vibration and buckling of composite Beams based on higher-order Beam Theory.

  • analysis of composite Beams with longitudinal and transverse partial interactions using higher order Beam Theory
    International Journal of Mechanical Sciences, 2012
    Co-Authors: Anupam Chakrabarti, A H Sheikh, Michael C Griffith, D J Oehlers
    Abstract:

    Abstract A new one dimensional finite element model based on a higher order Beam Theory is presented for the analysis of composite Beams taking into account the effect of longitudinal as well as vertical partial interaction between the adjacent layers. The proposed method models the transverse shear deformation of the Beam components in a refined manner. A third order variation of the axial displacement of the fibres over the Beam depth is taken to have a parabolic variation of shear stress which is also made zero at the Beam top and bottom surfaces. In the proposed FE model, there is no need of incorporating any shear correction factor and the model is free from shear locking problem. In addition to correctly predicting the global responses of the Beam, the model can predict better distribution of stresses than the existing models based on Euler–Bernoulli or Timoshenko Beam Theory. Many new results are presented as there is no published result on the present problem based on higher order Beam Theory.

  • analysis of composite Beams with partial shear interactions using a higher order Beam Theory
    Engineering Structures, 2012
    Co-Authors: Anupam Chakrabarti, A H Sheikh, Michael C Griffith, D J Oehlers
    Abstract:

    A new finite element model based on a higher order Beam Theory is presented for the analysis of composite Beams. The proposed model takes into account the effect of partial shear interaction between the adjacent layers as well as transverse shear deformation of the Beam. A third order variation of the axial displacement of the fibres over the Beam depth is taken to have a parabolic variation of shear stress which is also made zero at the Beam top and bottom surfaces. In the proposed FE model, there is no need of incorporating any shear correction factor and the model is free from shear locking problem. In addition to correctly predicting the global responses of the Beam, the model can predict better distribution of stresses than the existing models based on Euler–Bernoulli or Timoshenko Beam Theory. The proposed finite element model is validated by comparing the results with those available in literature. Many new results are presented for future references as there is no published result on composite Beams based on higher order Beam Theory.

Huu-tai Thai - One of the best experts on this subject based on the ideXlab platform.

  • a nonlocal sinusoidal shear deformation Beam Theory with application to bending buckling and vibration of nanoBeams
    International Journal of Engineering Science, 2012
    Co-Authors: Huu-tai Thai
    Abstract:

    This paper presents a nonlocal sinusoidal shear deformation Beam Theory for the bending, buckling, and vibration of nanoBeams. The present model is capable of capturing both small scale effect and transverse shear deformation effects of nanoBeams, and does not require shear correction factors. Based on the nonlocal differential constitutive relations of Eringen, the equations of motion as well as the boundary conditions of the Beam are derived using Hamilton’s principle. Analytical solutions for the deflection, buckling load, and natural frequency are presented for a simply supported Beam, and the obtained results are compared with those predicted by the nonlocal Timoshenko Beam Theory. The comparison firmly establishes that the present Beam Theory can accurately predict the bending, buckling, and vibration responses of short nanoBeams where the small scale and transverse shear deformation effects are significant.

  • a nonlocal Beam Theory for bending buckling and vibration of nanoBeams
    International Journal of Engineering Science, 2012
    Co-Authors: Huu-tai Thai
    Abstract:

    Abstract A nonlocal shear deformation Beam Theory is proposed for bending, buckling, and vibration of nanoBeams using the nonlocal differential constitutive relations of Eringen. The Theory, which does not require shear correction factor, accounts for both small scale effects and quadratic variation of shear strains and consequently shear stresses through the thickness of the Beam. In addition, it has strong similarities with nonlocal Euler–Bernoulli Beam Theory in some aspects such as equations of motion, boundary conditions, and stress resultant expressions. The equations of motion are derived from Hamilton’s principle. Analytical solutions of deflection, buckling load, and natural frequency are presented for a simply supported Beam, and the obtained results compare well with those predicted by the nonlocal Timoshenko and Reddy Beam theories.