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David Yang Gao - One of the best experts on this subject based on the ideXlab platform.

  • post buckling solutions of hyper Elastic Beam by canonical dual finite element method
    Mathematics and Mechanics of Solids, 2014
    Co-Authors: Kun Cai, David Yang Gao, Qinghua Qin
    Abstract:

    The post-buckling problem of a large deformed Beam is analyzed using the canonical dual finite element method (CD-FEM). The feature of this method is to choose correctly the canonical dual stress so that the original non-convex potential energy functional is reformulated in a mixed complementary energy form with both displacement and stress fields, and a pure complementary energy is explicitly formulated in finite dimensional space. Based on the canonical duality theory and the associated triality theorem, a primal–dual algorithm is proposed, which can be used to find all possible solutions of this non-convex post-buckling problem. Numerical results show that the global maximum of the pure-complementary energy leads to a stable buckled configuration of the Beam, while the local extrema of the pure-complementary energy present unstable deformation states. We discovered that the unstable buckled state is very sensitive to the number of total elements and the external loads. Theoretical results are verified ...

  • post buckling solutions of hyper Elastic Beam by canonical dual finite element method
    arXiv: Computational Engineering Finance and Science, 2013
    Co-Authors: Kun Cai, David Yang Gao, Qinghua Qin
    Abstract:

    Post buckling problem of a large deformed Beam is analyzed using canonical dual finite element method (CD-FEM). The feature of this method is to choose correctly the canonical dual stress so that the original non-convex potential energy functional is reformulated in a mixed complementary energy form with both displacement and stress fields, and a pure complementary energy is explicitly formulated in finite dimensional space. Based on the canonical duality theory and the associated triality theorem, a primal-dual algorithm is proposed, which can be used to find all possible solutions of this nonconvex post-buckling problem. Numerical results show that the global maximum of the pure-complementary energy leads to a stable buckled configuration of the Beam. While the local extrema of the pure-complementary energy present unstable deformation states, especially. We discovered that the unstable buckled state is very sensitive to the number of total elements and the external loads. Theoretical results are verified through numerical examples and some interesting phenomena in post-bifurcation of this large deformed Beam are observed.

  • canonical dual finite element method for solving post buckling problems of a large deformation Elastic Beam
    International Journal of Non-linear Mechanics, 2012
    Co-Authors: H A F A Santos, David Yang Gao
    Abstract:

    Abstract This paper presents a canonical dual mixed finite element method for the post-buckling analysis of planar Beams with large Elastic deformations. The mathematical Beam model employed in the present work was introduced by Gao in 1996, and is governed by a fourth-order non-linear differential equation. The total potential energy associated with this model is a non-convex functional and can be used to study both the pre- and the post-buckling responses of the Beams. Using the so-called canonical duality theory, this non-convex primal variational problem is transformed into a dual problem. In a proper feasible space, the dual variational problem corresponds to a globally concave maximization problem. A mixed finite element method involving both the transverse displacement field and the stress field as approximate element functions is derived from the dual variational problem and used to compute global optimal solutions. Numerical applications are illustrated by several problems with different boundary conditions.

Jian Bo Liu - One of the best experts on this subject based on the ideXlab platform.

Xishao Xie - One of the best experts on this subject based on the ideXlab platform.

  • free transverse vibrations of double walled carbon nanotubes using a theory of nonlocal Elasticity
    Physical Review B, 2005
    Co-Authors: Yi Zhang, G R Liu, Xishao Xie
    Abstract:

    Based on theory of nonlocal Elasticity, a nonlocal double-Elastic Beam model is developed for the free transverse vibrations of double-walled carbon nanotubes. The effect of small length scale is incorporated in the formulation. With this nonlocal double-Elastic Beam model, explicit expressions are derived for natural frequencies and associated amplitude ratios of the inner to the outer tubes for the case of simply supported double-walled carbon nanotubes. The effect of small length scale on the properties of vibrations is discussed. It is demonstrated that the natural frequencies and the associated amplitude ratios of the inner to the outer tubes are dependent upon the small length scale. The effect of small length scale is related to the vibrational mode and the aspect ratio.

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

  • Sound wave propagation in multiwall carbon nanotubes
    Journal of Applied Physics, 2003
    Co-Authors: J. Yoon, A. Mioduchowski
    Abstract:

    This article studies transverse sound wave propagation in individual multiwall carbon nanotubes. The present model predicts that there exist (N-1) critical frequencies (within terahertz range) for an N-wall carbon nanotube. When the frequency is below all critical frequencies, vibrational mode is almost coaxial and the associated sound speed can be predicted satisfactorily by the existing single-Elastic Beam model. However, when the frequency is higher than at least one of the critical frequencies, non-coaxial vibrational modes emerge which propagate at various speeds significantly higher or lower than the speed predicted by the single-Elastic Beam model. Hence, terahertz sound waves in multiwall carbon nanotubes exhibit complex phenomena and are essentially noncoaxial. In particular, terahertz sound waves in multiwall carbon nanotubes propagate at various speeds, depending not only on the frequency but also on the noncoaxial vibrational modes.

H A F A Santos - One of the best experts on this subject based on the ideXlab platform.

  • canonical dual finite element method for solving post buckling problems of a large deformation Elastic Beam
    International Journal of Non-linear Mechanics, 2012
    Co-Authors: H A F A Santos, David Yang Gao
    Abstract:

    Abstract This paper presents a canonical dual mixed finite element method for the post-buckling analysis of planar Beams with large Elastic deformations. The mathematical Beam model employed in the present work was introduced by Gao in 1996, and is governed by a fourth-order non-linear differential equation. The total potential energy associated with this model is a non-convex functional and can be used to study both the pre- and the post-buckling responses of the Beams. Using the so-called canonical duality theory, this non-convex primal variational problem is transformed into a dual problem. In a proper feasible space, the dual variational problem corresponds to a globally concave maximization problem. A mixed finite element method involving both the transverse displacement field and the stress field as approximate element functions is derived from the dual variational problem and used to compute global optimal solutions. Numerical applications are illustrated by several problems with different boundary conditions.