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Kuo Mo Hsiao - One of the best experts on this subject based on the ideXlab platform.
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An explicit algorithm for geometrically nonlinear transient analysis of spatial beams using a corotational total Lagrangian finite Element formulation
Computers & Structures, 2018Co-Authors: Chu Chang Huang, Fumio Fujii, Kuo Mo HsiaoAbstract:Abstract An explicit method for nonlinear transient dynamic analysis of spatial beams with finite rotations using a corotational total Lagrangian finite Element formulation is presented. The kinematics of the beam Element is described in the current Element Coordinate System constructed in the current configuration of the beam Element. The Element deformation and inertia nodal forces are derived by the virtual work principle, the d'Alembert principle, and the consistent linearization of the geometrically nonlinear beam theory. A nodal rotation vector is used to represent the finite rotation of a base Coordinate System rigidly attached to each node of the discretized structure. A numerical procedure of explicit method is proposed for the solution of the nonlinear equations of motion. The standard central difference method is applied to the incremental displacement vector and the incremental rotation vector, and the time derivatives of displacement vector and rotation vector. The nodal orientations are updated by the incremental nodal rotation vectors. The values of nodal rotation vectors are reset to zero in the current configuration. In order to assess the efficiency and the accuracy of the proposed method, numerical examples are studied and compared with the results obtained using the implicit method based on the Newmark method.
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A buckling and postbuckling analysis of axially loaded thin-walled beams with point-symmetric open section using corotational finite Element formulation
Thin-Walled Structures, 2018Co-Authors: Chu Chang Huang, Shih Chung Peng, Wen Yi Lin, Fumio Fujii, Kuo Mo HsiaoAbstract:Abstract The axially loaded thin-walled beams with point symmetric open section are studied using a corotational finite Element formulation. The kinematics of the beam Element is described in the current Element Coordinate System. The Element nodal forces are derived using the virtual work principle, and consistent second order linearization of the fully geometrically non-linear beam theory. Different axial load Systems with the same centric resultant axial force but different resultant bimoments are considered. Numerical examples studied show that the effects of bimoments on the buckling and postbuckling behavior of point symmetric open section beams are remarked.
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Investigation on steady state deformation and free vibration of a rotating inclined Euler beam
International Journal of Mechanical Sciences, 2011Co-Authors: Ming-hsu Tsai, Yu Chun Zhou, Kuo Mo HsiaoAbstract:Abstract The steady state deformation and infinitesimal free vibration around the steady state deformation of a rotating inclined Euler beam at constant angular velocity are investigated by the corotational finite Element method combined with floating frame method. The Element nodal forces are derived using the consistent second order linearization of the nonlinear beam theory, the d'Alembert principle and the virtual work principle in a current inertia Element Coordinates, which is coincident with a rotating Element Coordinate System constructed at the current configuration of the beam Element. The rotating Element Coordinates rotate about the hub axis at the angular speed of the hub. The equations of motion of the System are defined in terms of an inertia global Coordinate System, which is coincident with a rotating global Coordinate System rigidly tied to the rotating hub. Numerical examples are studied to demonstrate the accuracy and efficiency of the proposed method and to investigate the steady state deformation and natural frequency of the rotating inclined beam.
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A Corotational Finite Element Method Combined with Floating Frame Method for Large Steady-State Deformation and Free Vibration Analysis of a Rotating-Inclined Beam
Mathematical Problems in Engineering, 2011Co-Authors: Ming-hsu Tsai, Yu Chun Zhou, Wen Yi Lin, Kuo Mo HsiaoAbstract:A corotational finite Element method combined with floating frame method and a numerical procedure is proposed to investigate large steady-state deformation and infinitesimal-free vibrationaround the steady-state deformation of a rotating-inclined Euler beam at constant angular velocity. The Element nodal forces are derived using the consistent second-order linearization of the nonlinear beam theory, the d'Alembert principle, and the virtual work principle in a current inertia Element Coordinates, which is coincident with a rotating Element Coordinate System constructed at the current configuration of the beam Element. The governing equations for linear vibration are obtained by the first-order Taylor series expansion of the equation of motion at the position of steady-state deformation. Numerical examples are studied to demonstrate the accuracy and efficiency of the proposed method and to investigate the steady-state deformation and natural frequency of the rotating beam with different inclined angle, angular velocities, radius of the hub, and slenderness ratios.
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Geometrically Non-Linear Dynamic Analysis of Thin-Walled Beams
2009Co-Authors: Kuo Mo Hsiao, Wen Yi Lin, Ren-haw ChenAbstract:A co-rotational finite Element formulation for the geometrically nonlinear dynamic analysis of thin-walled beam with large rotations but small strain is presented. The Element developed here has two nodes with seven degrees of freedom per node. The Element nodes are chosen to be located at the centroid of the end cross sections of the beam Element and the centroid axis is chosen to be the reference axis. The kinematics of the beam Element is described in the current Element Coordinate System constructed at the current configuration of the beam Element. The Element nodal forces are conventional forces, moments and bimoments. Both the Element deformation nodal forces and inertia nodal forces are Systematically derived by consistent linearization of the fully geometrically non-linear beam theory, the d'Alembert principle and the virtual work principle in the current Element Coordinates. An incremental-iterative method based on the Newmark direct integration method and the Newton-Raphson method is employed here for the solution of the nonlinear equations of motion. Numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method. rigidity has not been reported in the literature. The object of this paper is to present a co-rotational finite Element formulation for the geometric nonlinear dynamic analysis of thin-walled beams with open section. In order to capture correctly all coupling among bending, twisting, and stretching deformations of the beam Elements, the formulation of beam Elements might be derived by the fully geometrically non-linear beam theory. The exact expressions for the Element nodal forces, which are required in a total Lagrangian formulation for large displacement/small strain problems, are highly nonlinear functions of Element nodal parameters. However, the dominant factors in the geometrical nonlinearities of beam structures are attributable to finite rotations, the strains remaining small. For a beam structure discretized by finite Elements, this implies that the motion of the individual Elements to a large extent will consist of rigid body motion. If the rigid body motion part is eliminated from the total displacements and the Element size is properly chosen, the deformational part of the motion is always small relative to the local Element axes. Thus in conjunction with the co-rotational formulation, the higher order terms of nodal parameters in the Element nodal forces may be neglected by consistent linearization. The Element deformation and inertia nodal forces are Systematically derived by using the d'Alembert principle and the virtual work principle. An incremental-iterative method based on the Newmark direct integration method and the Newton-Raphson method is employed here for the solution of the nonlinear equations of motion. Numerical examples are presented and compared with the results reported in the literature to demonstrate the accuracy and efficiency of the proposed method.
Ahmed A. Shabana - One of the best experts on this subject based on the ideXlab platform.
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Prediction of dynamic stresses using flexible multibody System algorithms: Application to tracked vehicle upper structure
Proceedings of the Institution of Mechanical Engineers Part K: Journal of Multi-body Dynamics, 2014Co-Authors: Takeshi Sasaki, Ahmed A. ShabanaAbstract:The objective of this investigation is to develop a general procedure for predicting the dynamic stresses when the nonlinear floating frame of reference formulation is used to model flexible components in multibody System applications. The procedure utilizes the concept of the floating frame of reference intermediate finite Element Coordinate System and the general continuum mechanics approach to develop accurate definitions of the floating frame of reference kinematic equations that enter into the formulations of the strains. These general equations are used to design a computational algorithm for the calculation of the dynamic stresses. In order to demonstrate the use of the procedure developed in this investigation for the stress prediction, a tracked vehicle System is used as the study model. Taking into consideration the actual endurance test, a model for a bulldozer upper structure is developed using computer aided engineering solution framework which includes flexible multibody System algorithms. I...
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Numerical investigation of the slope discontinuities in large deformation finite Element formulations
Nonlinear Dynamics, 2009Co-Authors: Luis G. Maqueda, Ahmed A. ShabanaAbstract:In many multibody System applications, the System components are made of structural Elements that can have different orientations, leading to slope discontinuities. In this paper, a numerical investigation of a new procedure that can be used to model structures with slope discontinuities in the finite Element absolute nodal Coordinate formulation (ANCF) is presented. This procedure can be applied to model slope discontinuities in the case of commutative rotations of gradient deficient Elements that are used for modeling thin beam and plate structures. An important special case to which the proposed procedure can be applied is the case of all planar gradient deficient ANCF finite Elements. The use of the proposed method leads to a constant orthogonal Element transformation that describes an arbitrary initial configuration. As a consequence, one obtains, in the case of large commutative rotations and large deformations, a constant mass matrix for structures which have complex geometry. The procedure used in this investigation to model slope discontinuities requires the use of the concept of the intermediate finite Element Coordinate System . For each finite Element, a new set of gradient Coordinates that define, at the discontinuity node, the Element deformation with respect to the intermediate Element Coordinate System is introduced. These new gradient Coordinates are assumed to be equal for the two finite Elements at the point of intersection. That is, the change of the gradients of two Elements at the intersection point from their respective intermediate initial reference configuration is assumed to be the same. This procedure leads to a set of linear algebraic equations that define the orthogonal transformation matrix for the finite Element. Numerical examples are presented in order to demonstrate the use of the proposed procedure for modeling slope discontinuities.
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Slope discontinuities in the finite Element absolute nodal Coordinate formulation: gradient deficient Elements
Multibody System Dynamics, 2008Co-Authors: Ahmed A. Shabana, Luis G. MaquedaAbstract:In this paper, the treatment of the slope discontinuities in the finite Element absolute nodal Coordinate formulation (ANCF) is discussed. The paper explains the fundamental problems associated with developing a constant transformation that accounts for the slope discontinuities in the case of gradient deficient ANCF finite Elements. A procedure that allows for the treatment of slope discontinuities in the case of gradient deficient finite Elements which do not employ full parameterization is proposed for the special case of commutative rotations . The use of the proposed procedure leads to a constant orthogonal Element transformation that describes the Element initial configuration. As a consequence, one obtains in the case of large deformation and commutative rotations, a constant mass matrix for the structures. In order to achieve this goal, the concept of the intermediate finite Element Coordinate System is invoked. The intermediate finite Element Coordinate System used in this investigation serves to define the Element reference configuration, follows the rotation of the structure, and maintains a fixed orientation relative to the structure Coordinate System. Since planar rotations are always commutative, the procedure proposed in this investigation is applicable to all planar gradient deficient ANCF finite Elements.
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A Non-Incremental Nonlinear Finite Element Solution for Cable Problems
Journal of Mechanical Design, 2003Co-Authors: Hiroyuki Sugiyama, Aki Mikkola, Ahmed A. ShabanaAbstract:In this investigation, a nonlinear finite Element method for the large deformation and rotation of cable problems is presented. This method is based on finite Element absolute nodal Coordinate formulation that guarantees the continuity of all displacement gradients and leads to a constant mass matrix. The classical cable theory is first reviewed and the assumptions used in this linear theory are defined in order to demonstrate the basic differences between the linear theory and the nonlinear finite Element formulation proposed in this paper for cable applications. The elastic cable forces in the absolute nodal Coordinate formulation are obtained using a general continuum mechanics approach that accounts for the effect of all geometric nonlinearities. It is shown in this investigation that the use of the general continuum mechanics approach leads to a simpler and more efficient formulation as compared to the use of the assumptions of the linear theory that employs a local finite Element Coordinate System. The results obtained using the absolute nodal Coordinate formulation show a good agreement with the results obtained using the classical cable theory when linear cable problems are considered. In particular it is shown that the use of perturbation methods to linearize the finite Element equations of motion leads to modal characteristics results that are in a good agreement with the linear theory. The results of this investigation obtained using explicit numerical integration also show the potential of the proposed finite Element formulation in the nonlinear analysis of cables that experience large rotations and deformations. The generalization of the procedure presented in this paper to three-dimensional cable problems is demonstrated and the computer implementation in multibody algorithms is discussed.
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Use of the Finite Element Absolute Nodal Coordinate Formulation in Modeling Slope Discontinuity
Journal of Mechanical Design, 2003Co-Authors: Ahmed A. Shabana, Aki MikkolaAbstract:A large rigid body rotation of a finite Element can be described by rotating the axes of the Element Coordinate System or by keeping the axes unchanged and change the slopes or the position vector gradients. In the first method, the definition of the local Element parameters (spatial Coordinates) changes with respect to a body or a global Coordinate System. The use of this method will always lead to a nonlinear mass matrix and non-zero centrifugal and Coriolis forces. The second method, in which the axes of the Element Coordinate System do not rotate with respect to the body or the global Coordinate System, leads to a constant mass matrix and zero centrifugal and Coriolis forces when the absolute nodal Coordinate formulation is used. This important property remains in effect even in the case of flexible bodies with slope discontinuities. The concept employed to accomplish this goal resembles the concept of the intermediate Element Coordinate System previously adopted in the finite Element floating frame of reference formulation. It is shown in this paper that the absolute nodal Coordinate formulation that leads to exact representation of the rigid body dynamics can be effecitively used in the analysis of complex structures with slope discontinuities. The analysis presented in this paper also demonstrates that objectivity is not an issue when the absolute nodal Coordinate formulation is used due to the fact that this formulation automatically accounts for the proper Coordinate transformations.
Wen Yi Lin - One of the best experts on this subject based on the ideXlab platform.
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A buckling and postbuckling analysis of axially loaded thin-walled beams with point-symmetric open section using corotational finite Element formulation
Thin-Walled Structures, 2018Co-Authors: Chu Chang Huang, Shih Chung Peng, Wen Yi Lin, Fumio Fujii, Kuo Mo HsiaoAbstract:Abstract The axially loaded thin-walled beams with point symmetric open section are studied using a corotational finite Element formulation. The kinematics of the beam Element is described in the current Element Coordinate System. The Element nodal forces are derived using the virtual work principle, and consistent second order linearization of the fully geometrically non-linear beam theory. Different axial load Systems with the same centric resultant axial force but different resultant bimoments are considered. Numerical examples studied show that the effects of bimoments on the buckling and postbuckling behavior of point symmetric open section beams are remarked.
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A Corotational Finite Element Method Combined with Floating Frame Method for Large Steady-State Deformation and Free Vibration Analysis of a Rotating-Inclined Beam
Mathematical Problems in Engineering, 2011Co-Authors: Ming-hsu Tsai, Yu Chun Zhou, Wen Yi Lin, Kuo Mo HsiaoAbstract:A corotational finite Element method combined with floating frame method and a numerical procedure is proposed to investigate large steady-state deformation and infinitesimal-free vibrationaround the steady-state deformation of a rotating-inclined Euler beam at constant angular velocity. The Element nodal forces are derived using the consistent second-order linearization of the nonlinear beam theory, the d'Alembert principle, and the virtual work principle in a current inertia Element Coordinates, which is coincident with a rotating Element Coordinate System constructed at the current configuration of the beam Element. The governing equations for linear vibration are obtained by the first-order Taylor series expansion of the equation of motion at the position of steady-state deformation. Numerical examples are studied to demonstrate the accuracy and efficiency of the proposed method and to investigate the steady-state deformation and natural frequency of the rotating beam with different inclined angle, angular velocities, radius of the hub, and slenderness ratios.
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Geometrically Non-Linear Dynamic Analysis of Thin-Walled Beams
2009Co-Authors: Kuo Mo Hsiao, Wen Yi Lin, Ren-haw ChenAbstract:A co-rotational finite Element formulation for the geometrically nonlinear dynamic analysis of thin-walled beam with large rotations but small strain is presented. The Element developed here has two nodes with seven degrees of freedom per node. The Element nodes are chosen to be located at the centroid of the end cross sections of the beam Element and the centroid axis is chosen to be the reference axis. The kinematics of the beam Element is described in the current Element Coordinate System constructed at the current configuration of the beam Element. The Element nodal forces are conventional forces, moments and bimoments. Both the Element deformation nodal forces and inertia nodal forces are Systematically derived by consistent linearization of the fully geometrically non-linear beam theory, the d'Alembert principle and the virtual work principle in the current Element Coordinates. An incremental-iterative method based on the Newmark direct integration method and the Newton-Raphson method is employed here for the solution of the nonlinear equations of motion. Numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method. rigidity has not been reported in the literature. The object of this paper is to present a co-rotational finite Element formulation for the geometric nonlinear dynamic analysis of thin-walled beams with open section. In order to capture correctly all coupling among bending, twisting, and stretching deformations of the beam Elements, the formulation of beam Elements might be derived by the fully geometrically non-linear beam theory. The exact expressions for the Element nodal forces, which are required in a total Lagrangian formulation for large displacement/small strain problems, are highly nonlinear functions of Element nodal parameters. However, the dominant factors in the geometrical nonlinearities of beam structures are attributable to finite rotations, the strains remaining small. For a beam structure discretized by finite Elements, this implies that the motion of the individual Elements to a large extent will consist of rigid body motion. If the rigid body motion part is eliminated from the total displacements and the Element size is properly chosen, the deformational part of the motion is always small relative to the local Element axes. Thus in conjunction with the co-rotational formulation, the higher order terms of nodal parameters in the Element nodal forces may be neglected by consistent linearization. The Element deformation and inertia nodal forces are Systematically derived by using the d'Alembert principle and the virtual work principle. An incremental-iterative method based on the Newmark direct integration method and the Newton-Raphson method is employed here for the solution of the nonlinear equations of motion. Numerical examples are presented and compared with the results reported in the literature to demonstrate the accuracy and efficiency of the proposed method.
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co rotational finite Element formulation for thin walled beams with generic open section
Computer Methods in Applied Mechanics and Engineering, 2006Co-Authors: Hong Hu Chen, Wen Yi Lin, Kuo Mo HsiaoAbstract:A consistent co-rotational total Lagrangian finite Element formulation for the geometric nonlinear buckling and postbuckling analysis of thin-walled beams with generic open section is presented. The Element developed here has two nodes with seven degrees of freedom per node. The Element nodes are chosen to be located at the shear centers of the end cross-sections of the beam Element and the shear center axis is chosen to be the reference axis. The deformations of the beam Element are described in the current Element Coordinate System constructed at the current configuration of the beam Element. The Element nodal forces are derived using the virtual work principle. The virtual rigid body motion corresponding to the virtual nodal displacements is excluded in the derivation of the Element nodal forces. A procedure is proposed to determine the virtual rigid body motion. The way used to determine the Element Coordinate System and Element nodal deformations corresponding to the virtual nodal displacements and that corresponding to the incremental nodal displacement are consistent. In Element nodal forces, all coupling among bending, twisting, and stretching deformations of the beam Element is considered by consistent second-order linearization of the fully geometrically nonlinear beam theory. In the derivation of the Element tangent stiffness matrix, the change of Element nodal forces induced by the Element rigid body rotations should be considered for the present method. Thus, a stability matrix is included in the Element tangent stiffness matrix. An incremental-iterative method based on the Newton–Raphson method combined with constant arc length of incremental displacement vector is employed for the solution of nonlinear equilibrium equations. The zero value of the tangent stiffness matrix determinant of the structure is used as the criterion of the buckling state. Numerical examples are presented to investigate the accuracy and efficiency of the proposed method. The effect of the terms in the Element nodal force and tangent stiffness matrix, which will converge to zero with the decrease of Element size, on the convergence rate of solution and accuracy for the buckling load and nonlinear behavior of three dimensional beam structures are also investigated through numerical examples. � 2005 Elsevier B.V. All rights reserved.
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A co-rotational formulation for thin-walled beams with monosymmetric open section
Computer Methods in Applied Mechanics and Engineering, 2000Co-Authors: Kuo Mo Hsiao, Wen Yi LinAbstract:Abstract A consistent co-rotational total Lagrangian finite Element formulation and numerical procedure for the geometric nonlinear buckling and postbuckling analysis of thin-walled beams with monosymmetric open section is presented. The Element developed here has two nodes with seven degrees of freedom per node. The Element nodes are chosen to be located at the shear centers of the end cross-sections of the beam Element and the shear center axis is chosen to be the reference axis. The deformations of the beam Element are described in the current Element Coordinate System, which is constructed at the current configuration of the beam Element. In Element nodal forces, all coupling among bending, twisting, and stretching deformations of the beam Element is considered by consistent second-order linearization of the fully geometrically nonlinear beam theory. However, the third-order term of the twist rate of the beam axis is considered in Element nodal forces. An incremental-iterative method based on the Newton–Raphson method combined with constant arc length of incremental displacement vector is employed for the solution of nonlinear equilibrium equations. The zero value of the tangent stiffness matrix determinant of the structure is used as the criterion of the buckling state. A parabolic interpolation method of the arc length is used to find the buckling load. Numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method.
Aki Mikkola - One of the best experts on this subject based on the ideXlab platform.
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A Linear Beam Finite Element Based on the Absolute Nodal Coordinate Formulation
Journal of Mechanical Design, 2004Co-Authors: Kimmo Kerkkänen, Jussi Sopanen, Aki MikkolaAbstract:In this paper, a new two-dimensional shear deformable beam Element based on the absolute nodal Coordinate formulation is proposed. The nonlinear elastic forces of the beam Element are obtained using a continuum mechanics approach, without employing a local Element Coordinate System. In this study, linear polynomials are used to interpolate both the transverse and longitudinal components of the displacement. This is different from other absolute nodal-Coordinate-based beam Elements where cubic polynomials are used in the longitudinal direction. The use of linear interpolation polynomials leads to the phenomenon known as shear locking. This defect is avoided through the adoption of selective integration within the numerical integration method. The proposed Element is verified using several numerical examples. The results of the proposed Element are compared to analytical solutions and the results for an existing shear deformable beam Element. It is shown that by using the proposed Element, accurate linear and nonlinear static deformations, as well as realistic dynamic behavior including the capturing of the centrifugal stiffening effect, can be achieved with a smaller computational effort than by using existing shear deformable two-dimensional beam Elements.
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A Non-Incremental Nonlinear Finite Element Solution for Cable Problems
Journal of Mechanical Design, 2003Co-Authors: Hiroyuki Sugiyama, Aki Mikkola, Ahmed A. ShabanaAbstract:In this investigation, a nonlinear finite Element method for the large deformation and rotation of cable problems is presented. This method is based on finite Element absolute nodal Coordinate formulation that guarantees the continuity of all displacement gradients and leads to a constant mass matrix. The classical cable theory is first reviewed and the assumptions used in this linear theory are defined in order to demonstrate the basic differences between the linear theory and the nonlinear finite Element formulation proposed in this paper for cable applications. The elastic cable forces in the absolute nodal Coordinate formulation are obtained using a general continuum mechanics approach that accounts for the effect of all geometric nonlinearities. It is shown in this investigation that the use of the general continuum mechanics approach leads to a simpler and more efficient formulation as compared to the use of the assumptions of the linear theory that employs a local finite Element Coordinate System. The results obtained using the absolute nodal Coordinate formulation show a good agreement with the results obtained using the classical cable theory when linear cable problems are considered. In particular it is shown that the use of perturbation methods to linearize the finite Element equations of motion leads to modal characteristics results that are in a good agreement with the linear theory. The results of this investigation obtained using explicit numerical integration also show the potential of the proposed finite Element formulation in the nonlinear analysis of cables that experience large rotations and deformations. The generalization of the procedure presented in this paper to three-dimensional cable problems is demonstrated and the computer implementation in multibody algorithms is discussed.
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Use of the Finite Element Absolute Nodal Coordinate Formulation in Modeling Slope Discontinuity
Journal of Mechanical Design, 2003Co-Authors: Ahmed A. Shabana, Aki MikkolaAbstract:A large rigid body rotation of a finite Element can be described by rotating the axes of the Element Coordinate System or by keeping the axes unchanged and change the slopes or the position vector gradients. In the first method, the definition of the local Element parameters (spatial Coordinates) changes with respect to a body or a global Coordinate System. The use of this method will always lead to a nonlinear mass matrix and non-zero centrifugal and Coriolis forces. The second method, in which the axes of the Element Coordinate System do not rotate with respect to the body or the global Coordinate System, leads to a constant mass matrix and zero centrifugal and Coriolis forces when the absolute nodal Coordinate formulation is used. This important property remains in effect even in the case of flexible bodies with slope discontinuities. The concept employed to accomplish this goal resembles the concept of the intermediate Element Coordinate System previously adopted in the finite Element floating frame of reference formulation. It is shown in this paper that the absolute nodal Coordinate formulation that leads to exact representation of the rigid body dynamics can be effecitively used in the analysis of complex structures with slope discontinuities. The analysis presented in this paper also demonstrates that objectivity is not an issue when the absolute nodal Coordinate formulation is used due to the fact that this formulation automatically accounts for the proper Coordinate transformations.
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A computationally efficient shear deformable beam Element for large deformation multibody applications
2003Co-Authors: Kimmo Kerkkänen, Jussi Sopanen, Aki MikkolaAbstract:In this paper, a new two-dimensional shear deformable beam Element based on the absolute nodal Coordinate formulation is proposed. The nonlinear elastic forces of the beam Element are obtained using a continuum mechanics approach without employing a local Element Coordinate System. In this study, linear polynomials are used to interpolate both the transverse and longitudinal components of the displacement. This is different from other absolute nodal-Coordinate-based beam Elements where cubic polynomials are used in the longitudinal direction. The accompanying defects of the phenomenon known as shear locking are avoided through the adoption of selective integration within the numerical integration method. The proposed Element is verified using several numerical examples, and the results are compared to analytical solutions and the results for an existing shear deformable beam Element. It is shown that by using the proposed Element, accurate linear and nonlinear static deformations, as well as realistic dynamic behavior, can be achieved with a smaller computational effort than by using existing shear deformable two-dimensional beam Elements.
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A non-incremental nonlinear finite Element solution for cable problems
Volume 5: 19th Biennial Conference on Mechanical Vibration and Noise Parts A B and C, 2003Co-Authors: Hiroyuki Sugiyama, Aki Mikkola, Ahmed A. ShabanaAbstract:In this investigation, a nonlinear finite Element method for the large deformation and rotation of cable problems is presented. This method is based on the finite Element absolute nodal Coordinate formulation that guarantees the continuity of all the displacement gradients and leads to a constant mass matrix. The classical cable theory is first reviewed and the assumptions used in this linear theory are defined in order to demonstrate the basic differences between the linear theory and the nonlinear finite Element formulation proposed in this paper for cable applications. The elastic cable forces in the absolute nodal Coordinate formulation are obtained in this investigation using a general continuum mechanics approach that accounts for the effect of all geometric nonlinearities. It is shown in this investigation that the use of the general continuum mechanics approach leads to a simpler and more efficient formulation as compared to the use of the assumptions of the linear theory that employs a local finite Element Coordinate System. The results obtained using the absolute nodal Coordinate formulation show a good agreement with the results obtained using the classical cable theory when linear cable problems are considered. The results of this investigation obtained using explicit numerical integration also show the potential of the proposed finite Element formulation in the nonlinear analysis of cables that experience large rotations and large deformations. It is also shown that the use of perturbation methods to linearize the finite Element equations of motion leads to modal characteristics results that are in a good agreement with the linear theory. The generalization of the procedure presented in this paper to three-dimensional cable problems is demonstrated and the computer implementation in multibody algorithms is discussed.Copyright © 2003 by ASME
Ming-hsu Tsai - One of the best experts on this subject based on the ideXlab platform.
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Investigation on steady state deformation and free vibration of a rotating inclined Euler beam
International Journal of Mechanical Sciences, 2011Co-Authors: Ming-hsu Tsai, Yu Chun Zhou, Kuo Mo HsiaoAbstract:Abstract The steady state deformation and infinitesimal free vibration around the steady state deformation of a rotating inclined Euler beam at constant angular velocity are investigated by the corotational finite Element method combined with floating frame method. The Element nodal forces are derived using the consistent second order linearization of the nonlinear beam theory, the d'Alembert principle and the virtual work principle in a current inertia Element Coordinates, which is coincident with a rotating Element Coordinate System constructed at the current configuration of the beam Element. The rotating Element Coordinates rotate about the hub axis at the angular speed of the hub. The equations of motion of the System are defined in terms of an inertia global Coordinate System, which is coincident with a rotating global Coordinate System rigidly tied to the rotating hub. Numerical examples are studied to demonstrate the accuracy and efficiency of the proposed method and to investigate the steady state deformation and natural frequency of the rotating inclined beam.
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A Corotational Finite Element Method Combined with Floating Frame Method for Large Steady-State Deformation and Free Vibration Analysis of a Rotating-Inclined Beam
Mathematical Problems in Engineering, 2011Co-Authors: Ming-hsu Tsai, Yu Chun Zhou, Wen Yi Lin, Kuo Mo HsiaoAbstract:A corotational finite Element method combined with floating frame method and a numerical procedure is proposed to investigate large steady-state deformation and infinitesimal-free vibrationaround the steady-state deformation of a rotating-inclined Euler beam at constant angular velocity. The Element nodal forces are derived using the consistent second-order linearization of the nonlinear beam theory, the d'Alembert principle, and the virtual work principle in a current inertia Element Coordinates, which is coincident with a rotating Element Coordinate System constructed at the current configuration of the beam Element. The governing equations for linear vibration are obtained by the first-order Taylor series expansion of the equation of motion at the position of steady-state deformation. Numerical examples are studied to demonstrate the accuracy and efficiency of the proposed method and to investigate the steady-state deformation and natural frequency of the rotating beam with different inclined angle, angular velocities, radius of the hub, and slenderness ratios.