Browsing by Author "Lin, WY"

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A buckling and postbuckling analysis of rods under end torque and compressive load
(2003-04-01)
Lin, WY
;
Hsiao, KM
;
機械工程學系
;
Department of Mechanical Engineering
The buckling and postbuckling behavior of spatial rods under different types of end torque and compressive axial force is investigated using finite element method. All coupling among bending, twisting, and stretching deformations for 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 is also considered. An incremental-iterative method based on the NewtonRaphson 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 effect of aspect ratio of the rectangular cross section and compressive force on the buckling torque and postbuckling behavior of spatial rods under different types of end torque.
A case study of the five-point double-toggle mould clamping mechanism
(2006-04-01)
Lin, WY
;
Shen, CL
;
Hsiao, KM
;
機械工程學系
;
Department of Mechanical Engineering
This work attempts to enhance the performances of the stroke ratio and/or thrust saving of the conventional and Fanuc five-point double-toggle mould clamping mechanisms, at the cost of increasing the offset and varying the cross-head height and loosening the initial transmission performance within an acceptable extent, on condition that the overall horizontal length cannot exceed the one of the original design in the work of Lin and Hsiao [1]. In addition, to show the effect of the initial transmission performance and the effect of the combination of the offset and the crosshead height individually, the present and previous designs in the work of Lin and Hsiao without loosening the initial transmission performance are also presented. The parameter study in the work of Lin and Hsiao is extended to synthesize the conventional and Fanuc linkages and to find the optimal dimensions in the programming discrete domain. The kinematic stick diagrams in the open and closed positions for the original and present designs are shown, which may see some features of the profiles of the toggle linkages with the larger stroke ratio and/or thrust saving and the difference between the two designs.
A co-rotational finite element formulation for buckling and postbuckling analyses of spatial beams
(2000)
Hsiao, KM
;
Lin, WY
;
機械工程學系
;
Department of Mechanical Engineering
A consistent co-rotational finite element formulation and numerical procedure for the buckling and postbuckling analyses of three-dimensional elastic Euler beam is presented. All coupling among bending, twisting, and stretching deformations for a beam element is considered by consistent second-order linearization of the fully geometrically nonlinear beam theory. However, the third-order terms, which are relevant to the twist rate and curvature of the beam axis, are also considered. An incremental-iterative method based on the Newton-Raphson method combined with constant are 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 bisection method of the are length is proposed to find the buckling load. Numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method and to investigate the effect of third-order terms on the buckling load and postbuckling behavior of three-dimensional beams. (C) 2000 Elsevier Science S.A. All rights reserved.
A co-rotational formulation for thin-walled beams with monosymmetric open section
(2000)
Hsiao, KM
;
Lin, WY
;
機械工程學系
;
Department of Mechanical Engineering
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 are 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 are length is used to find the buckling load. Numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method. (C) 2000 Elsevier Science S.A. All rights reserved.
A consistent co-rotational finite element formulation for geometrically nonlinear dynamic analysis of 3-D beams
(1999-01-29)
Hsiao, KM
;
Lin, JY
;
Lin, WY
;
機械工程學系
;
Department of Mechanical Engineering
A co-rotational total Lagrangian finite element formulation for the geometrically nonlinear dynamic analysis of spatial Euler beam with large rotations but small strain, is presented. The nodal coordinates, displacements, rotations, velocities, accelerations, and the equations of motion of the structure are defined in a fixed global set of coordinates. The beam element has two nodes with six degrees of freedom per node. The element nodal forces are conventional forces and moments. The kinematics of beam element are defined in terms of element coordinates, which are constructed at the current configuration of the beam element. Both the element deformation nodal forces and inertia nodal forces are systematically derived by consistent linearization of the fully geometrically nonlinear beam theory using 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. (C) 1999 Elsevier Science S.A. All rights reserved.
A consistent finite element formulation for linear buckling analysis of spatial beams
(1998-04-14)
Hsiao, KM
;
Yang, RT
;
Lin, WY
;
機械工程學系
;
Department of Mechanical Engineering
A consistent co-rotational finite element formulation and numerical procedure for the linear buckling analysis of three-dimensional elastic Euler beam is presented. A mechanism for generating configuration dependent conservative moment is proposed and the corresponding load stiffness matrix is derived. It is assumed that the prebuckling displacements and rotations of the structure and the corresponding deformations of the elements are linearly proportional to the external loading. The prebuckling rotations of the structure are fixed axis rotations or small rotations, and the effect of the prebuckling displacement on transformation matrix for the coordinates transformation can be ignored. All coupling among bending, twisting and stretching deformations for beam element is considered by consistent linearization of the fully geometrically nonlinear beam theory. An inverse power method for the solution of the generalized eigenvalue problem is used to find the buckling load and buckling mode. Numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method. (C) 1998 Elsevier Science S.A.
Co-rotational finite element formulation for thin-walled beams with generic open section
(2006)
Chen, HH
;
Lin, WY
;
Hsiao, KM
;
機械工程學系
;
Department of Mechanical Engineering
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. (c) 2005 Elsevier B.V. All rights reserved.
Co-rotational formulation for geometric nonlinear analysis of doubly symmetric thin-walled beams
(2001)
Lin, WY
;
Hsiao, KM
;
機械工程學系
;
Department of Mechanical Engineering
A doubly symmetric thin-walled beam element with open section is derived using co-rotational (CR) total Lagrangian (TL) formulation. The effects of deformation-dependent third-order terms of element nodal forces on the buckling load and post-buckling behavior are investigated. All coupling among bending, twisting, and stretching deformations for beam element is considered by consistent second-order linearization of the fully geometrically nonlinear beam theory. However, all third-order terms of nodal forces, which are relevant to the twist rate, rate of twist rate and curvature of the beam axis are also considered. An incremental-iterative method based on the Newton-Raphson method combined with constant are 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 element and to investigate the effect of third-order terms of element nodal forces on the buckling load and post-buckling behavior of doubly symmetric thin-walled beams. (C) 2001 Elsevier Science B.V. All rights reserved.
Investigation of the friction effect at pin joints for the five-point double-toggle clamping mechanisms of injection molding machines
(2003-11-01)
Lin, WY
;
Hsiao, KM
;
機械工程學系
;
Department of Mechanical Engineering
In this study, an analytical formulation for the necessary thrust of the crosshead of the five-point double-toggle clamping mechanism during real-mold clamping operation is proposed in order to investigate the effect of the friction at pin joints. The friction is considered to be a Coulomb friction. The inertia effects are not considered. Numerical examples are studied for different values of coefficient of friction to investigate the effects of friction at pin joints. In order to estimate the kinetic friction coefficient at pin joints, the motor torques required for real-mold clamping obtained by the present study are adjusted by using different values of coefficient of friction and mechanical efficiency to fit the experimental data. (C) 2003 Elsevier Ltd. All rights reserved.
More general expression for the torsional warping of a thin-walled open-section beam
(2003-05-01)
Lin, WY
;
Hsiao, KM
;
機械工程學系
;
Department of Mechanical Engineering
In this study, an analytical formulation for the torsional warping function of a thin-walled open-section beam is built based on the combination of the Vlasov assumption and the Kirchhoff assumption of plate/shell theory, essentially due to Goodier and Gjelsvik. Vlasov, Timoshenko and many authors (follow Vlasov) only consider the contour warping function as the real warping function. Goodier and Gjelsvik (follow Goodier) not only consider the contour warping but also the thickness warping. For some cross-sectional constants related to the warping function such as the torsional constant, the adoption of the warping function based on Vlasov's theory or Timoshenko's theory may cause them incorrectness. On the other hand, the torsional constant based on the Goodier's theory is consistent with the one based on the membrane analogy. Thus, Goodier's theory is a good approximation for the torsional warping of a thin-walled open-section beam. To the authors' limited knowledge, the analytical expression for the complete torsional warping of a thin-walled open-section beam has not been found in the literature. in this study, a more general expression for the torsional warping of a thin-walled open-section beam is presented. The position formulas to determine the twist center are also given. (C) 2003 Elsevier Ltd. All rights reserved.
Study on improvements of the five-point double-toggle mould clamping mechanism
(2004-07-01)
Lin, WY
;
Hsiao, KM
;
機械工程學系
;
Department of Mechanical Engineering
In current designs of the conventional and Fanuc five-point double-toggle mechanisms, the lengths of moving-platen side links are greater than the lengths of tail stock-platen side links in order to provide enough horizontal space for the ejector unit and to avoid the unsound transmission characteristic. In this study, another method to provide such a space is adopted. From a parametric study, the method can be proved practicable and the individual profiles of toggle linkages for the two types of mechanism with the characteristics of time saving or a larger opening stroke and/or thrust saving can be found. Moreover, objective comparisons of the performances between the two types of mechanism are also given.