The Experts below are selected from a list of 252 Experts worldwide ranked by ideXlab platform
Yonggang Huang - One of the best experts on this subject based on the ideXlab platform.
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Buckling Analyses of Double-Wall Carbon Nanotubes: A Shell Theory Based on the Interatomic Potential
Journal of Applied Mechanics, 2010Co-Authors: Weibang Lu, Kuo Chu Hwang, Xi-qiao Feng, Jianping Wu, Yonggang HuangAbstract:Based on the finite-deformation Shell Theory for carbon nanotubes established from the interatomic potential and the continuum model for van der Waals (vdW) interactions, we have studied the buckling of double-walled carbon nanotubes subjected to compression or torsion. Prior to buckling, the vdW interactions have essentially no effect on the deformation of the double-walled carbon nanotube. The critical buckling strain of the double-wall carbon nanotubes is always between those for the inner wall and for the outer wall, which means that the vdW interaction decelerates buckling of one wall at the expenses of accelerating the buckle of the other wall.
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Numerical analyses for the atomistic-based Shell Theory of carbon nanotubes
International Journal of Plasticity, 2009Co-Authors: Zuoqi Zhang, Bo Liu, K. C. Hwang, Yonggang HuangAbstract:A Shell Theory established from the interatomic potential for carbon nanotubes is compared with the atomistic simulations. This Shell Theory is implemented in the finite element program ABAQUS via its user-material subroutine UGENS for Shells. The numerical results for the representative loadings of tension, torsion and bending agree well with the atomistic simulations, which provide direct validation of this atomistic-based Shell Theory for carbon nanotubes.
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an atomistic based finite deformation Shell Theory for single wall carbon nanotubes
Journal of The Mechanics and Physics of Solids, 2008Co-Authors: Jian Wu, Kehchih Hwang, Yonggang HuangAbstract:A finite-deformation Shell Theory is developed for single-wall carbon nanotubes (CNTs) based on the interatomic potential. The modified Born rule for Bravais multi-lattice is used to link the continuum strain energy density to the interatomic potential. The Theory incorporates the effect of bending moment and curvature for a curved surface, and accurately accounts for the nonlinear, multi-body atomistic interactions as well as the CNT chirality. It avoids the amibiguous definition of nanotube thickness, and provides the constitutive relations among stress, moment, strain and curvature in terms of the interatomic potential.
Adnan Ibrahimbegovic - One of the best experts on this subject based on the ideXlab platform.
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Stress Resultant Geometrically Exact Shell Theory for Finite Rotations and Its Finite Element Implementation
Applied Mechanics Reviews, 1997Co-Authors: Adnan IbrahimbegovicAbstract:This article reviews the significant progress on Shell problem theoretical foundation and numerical implementation attained over a period of the last several years. First, a careful consideration of the three-dimensional finite rotations is given including the choice of optimal parameters, their admissible variations and the much revealing relationship between different parameters. A non-conventional derivation of the stress resultant Shell Theory is presented, which makes use of the virtual work principle and local Cartesian frames. The presented derivation introduces no simplifying hypotheses regarding the Shell balance equations, hence the resulting Shell Theory is referred to as being geometrically exact. The strain measures energy-conjugate to the chosen stress resultants are identified and the nature of the stress resultants with respect to the three-dimensional stress tensor is explained along with the resulting constitutive restrictions. Comments are made regarding a rather useful extension of the Shell Theory which accounts for the rotational degree of freedom about the director, the so-called drilling rotation. A linear Shell Theory is obtained as a very useful by-product of the present work, by linearizing the present nonlinear Shell Theory about the reference configuration. It is shown that this non-conventional approach not only clarifies an often confusing derivation of the linear Shell Theory, but also leads to a novel linear Shell Theory capable of delivering significantly improved results and essentially exact solutions to the standard linear benchmark problems. Another important aspect of the nonlinear Shell problem solution, the finite element approximation of the Shell Theory, is also discussed. The model problem of assumed shear strain interpolation is used to illustrate that numerical implementation which preserves the salient features of the theoretical formulation often brings an improved final result. For the selected rotation parameterization and the finite element interpolation, the issues of the consistent linearization of the nonlinear Shell problem are addressed. In a number of numerical simulations, the latter is proved to play a crucial role not only in ensuring the robust performance of the Newton solution procedure, but also in linear and nonlinear buckling problems of Shells. Several directions for future research are pointed out and some contemporary works of special interest are listed. There are 127 references at the end of the article.
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Stress resultant geometrically non‐linear Shell Theory with drilling rotations. Part III: Linearized kinematics
International Journal for Numerical Methods in Engineering, 1994Co-Authors: Adnan Ibrahimbegovic, François FreyAbstract:A consistent formulation of the geometrically linear Shell Theory with drilling rotations is obtained by the consistent linearization of the geometrically non-linear Shell Theory considered in Parts I and II of this work. It was also shown that the same formulation can be recovered by linearizing the governing variational principle for the three-dimensional geometrically non-linear continuum with independent rotation field. In the finite element implementation of the presented Shell Theory, relying on the modified method of incompatible modes, we were able to construct a four-node Shell element which delivers a very high-level performance. In order to simplify finite element implementation, a shallow reference configuration is assumed over each Shell finite element. This approach does not impair the element performance for the present four-node element. The results obtained herein match those obtained with the state-of-the-art implementations based on the classical Shell Theory, over the complete set of standard benchmark problems.
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stress resultant geometrically nonlinear Shell Theory with drilling rotations part i a consistent formulation
Computer Methods in Applied Mechanics and Engineering, 1994Co-Authors: Adnan IbrahimbegovicAbstract:Abstract In this work we present a consistent theoretical framework for a novel stress resultant geometrically nonlinear Shell Theory. The main feature of the present Shell Theory development, which stands in contrast with the classical developments in the Shell Theory, is the presence of a rotation component around the Shell normal (so called drilling rotation) in the description of Shell finite rotations. The relationship of the proposed Theory with a finite deformation Theory of a three-dimensional continuum with independent rotation field is clearly identified. The latter is shown to be an important link which facilitates the proper choice of the Shell constitutive model, and a proper construction of the regularized form of the Theory capable of supporting the drilling rotations. The corresponding linearized form of the present Shell Theory is discussed in the closure.
Kiyoshi Yogo - One of the best experts on this subject based on the ideXlab platform.
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Beam equations for multi-walled carbon nanotubes derived from Flügge Shell Theory
Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences, 2009Co-Authors: Tsuneo Usuki, Kiyoshi YogoAbstract:The Flugge Shell Theory is frequently used for the analysis of carbon nanotubes (CNTs) due to the relatively accurate results it provides in spite of its theoretical simplicity. Based on the Flugge Shell Theory, a tubular beam Theory was established by considering non-locality. In order to convert a cylindrical Shell Theory for a curved plate per unit width into a tubular beam Theory by contour integration, the longitudinal coordinate that passes through the centre of the circular contour was defined, and, based on this, the radial coordinate was defined. In this way, a generalized beam Theory (GBT) was obtained as a further refined form of the Flugge Theory. This GBT coincides with the Flugge Theory, if the refined form and the non-locality are ignored. After obtaining the phase-velocity curve and the group-velocity curve with respect to single- to triple-walled CNTs, the influences of multiplicity, reduction of the plate-bending stiffness and the stiffness of the surrounding matrix were investigated.
D. Schöllhammer - One of the best experts on this subject based on the ideXlab platform.
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Kirchhoff–Love Shell Theory based on tangential differential calculus
Computational Mechanics, 2019Co-Authors: D. Schöllhammer, T. P. FriesAbstract:The Kirchhoff–Love Shell Theory is recasted in the frame of the tangential differential calculus (TDC) where differential operators on surfaces are formulated based on global, three-dimensional coordinates. As a consequence, there is no need for a parametrization of the Shell geometry implying curvilinear surface coordinates as used in the classical Shell Theory. Therefore, the proposed TDC-based formulation also applies to Shell geometries which are zero-isosurfaces as in the level-set method where no parametrization is available in general. For the discretization, the TDC-based formulation may be used based on surface meshes implying element-wise parametrizations. Then, the results are equivalent to those obtained based on the classical Theory. However, it may also be used in recent finite element approaches as the TraceFEM and CutFEM where shape functions are generated on a background mesh without any need for a parametrization. Numerical results presented herein are achieved with isogeometric analysis for classical and new benchmark tests. Higher-order convergence rates in the residual errors are achieved when the physical fields are sufficiently smooth.
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kirchhoff love Shell Theory based on tangential differential calculus
Computational Mechanics, 2019Co-Authors: D. Schöllhammer, Thomaspeter FriesAbstract:The Kirchhoff–Love Shell Theory is recasted in the frame of the tangential differential calculus (TDC) where differential operators on surfaces are formulated based on global, three-dimensional coordinates. As a consequence, there is no need for a parametrization of the Shell geometry implying curvilinear surface coordinates as used in the classical Shell Theory. Therefore, the proposed TDC-based formulation also applies to Shell geometries which are zero-isosurfaces as in the level-set method where no parametrization is available in general. For the discretization, the TDC-based formulation may be used based on surface meshes implying element-wise parametrizations. Then, the results are equivalent to those obtained based on the classical Theory. However, it may also be used in recent finite element approaches as the TraceFEM and CutFEM where shape functions are generated on a background mesh without any need for a parametrization. Numerical results presented herein are achieved with isogeometric analysis for classical and new benchmark tests. Higher-order convergence rates in the residual errors are achieved when the physical fields are sufficiently smooth.
Jian Wu - One of the best experts on this subject based on the ideXlab platform.
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an atomistic based finite deformation Shell Theory for single wall carbon nanotubes
Journal of The Mechanics and Physics of Solids, 2008Co-Authors: Jian Wu, Kehchih Hwang, Yonggang HuangAbstract:A finite-deformation Shell Theory is developed for single-wall carbon nanotubes (CNTs) based on the interatomic potential. The modified Born rule for Bravais multi-lattice is used to link the continuum strain energy density to the interatomic potential. The Theory incorporates the effect of bending moment and curvature for a curved surface, and accurately accounts for the nonlinear, multi-body atomistic interactions as well as the CNT chirality. It avoids the amibiguous definition of nanotube thickness, and provides the constitutive relations among stress, moment, strain and curvature in terms of the interatomic potential.
