Finite element formulation of rigid body motion in dynamic analysis of mechanisms

1995 ◽  
Vol 57 (2) ◽  
pp. 213-217 ◽  
Author(s):  
M. Hać ◽  
J. Osiński
Keyword(s):  
Finite Element ◽  
Rigid Body ◽  
Dynamic Analysis ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Finite Element Formulation ◽  
Element Formulation

Full Beam Formulation for Coupled Elastic and Rigid Body Motion

1991 ◽  
Author(s):  
C. Venkatakrishnan ◽  
B. Fallahi ◽  
H. Y. Lai
Keyword(s):  
Finite Element ◽  
Rigid Body ◽  
Coordinate System ◽  
Numerical Solution ◽  
Body Motion ◽  
Finite Element Formulation ◽  
Rotary Inertia ◽  
Element Formulation ◽  
Rotating Beam ◽  
Moving Coordinate

Abstract The need for higher operating speeds has led to the study of flexibility in mechanisms. In most of the previous works, rotary inertia, normal, tangential and coriolis terms are neglected. These assumptions are valid at lower speeds and for slender links. In this paper, a procedure to include all inertia terms in a local moving coordinate system is introduced. It is shown that the inertia terms lead to the introduction of three element matrices in the finite element formulation. The proposed approach is used to model the rotating beam problem. The results of a numerical solution is reported and validated.

Substructure analysis of complex systems using rigid body information of components

2002 ◽  
Vol 216 (10) ◽  
pp. 811-817 ◽  
Author(s):  
W S Hwang ◽  
D H Lee
Keyword(s):  
Finite Element ◽  
Complex Systems ◽  
Rigid Body ◽  
Computer Aided Design ◽  
Element Model ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Element Analysis ◽  
Design Data ◽  
Substructure Analysis

Frequency response function (FRF) based substructure analysis can predict the response of complex systems using the FRFs of substructures. It combines the FRFs of each substructure derived from finite element analysis or experiments depending on the situation. In general, the substructure with the excitation is separated from the others by rubber bushes to prevent the transmission of vibration from the source to the main structure. In this case, the substructure with the excitation shows rigid body motion up to the mid-frequency region. This paper presents a new FRF-based substructure analysis that uses the FRFs from the rigid body information not from the complex finite element model of the substructure with rigid body motion. The rigid body information including the mass, the moment of inertia and the coordinates of the mass centre comes from the computer-aided design data. Since the mechanism of this technique is very similar to the finite element formation, it can be applied to complex systems with ease. Through a simple example of a ladder structure and a practical example of the interior noise in a car, the accuracy and efficiency of this approach is proven.

Hamiltonian Nodal Position Finite Element Method for Cable Dynamics

2017 ◽  
Vol 09 (08) ◽  
pp. 1750109 ◽  
Author(s):  
Huaiping Ding ◽  
Zheng H. Zhu ◽  
Xiaochun Yin ◽  
Lin Zhang ◽  
Gangqiang Li ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Rigid Body ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Frequency Mode ◽  
Integration Scheme ◽  
Long Period ◽  
Nodal Position ◽  
Element Method

This paper developed a new Hamiltonian nodal position finite element method (FEM) to treat the nonlinear dynamics of cable system in which the large rigid-body motion is coupled with small elastic cable elongation. The FEM is derived from the Hamiltonian theory using canonical coordinates. The resulting Hamiltonian finite element model of cable contains low frequency mode of rigid-body motion and high frequency mode of axial elastic deformation, which is prone to numerical instability due to error accumulation over a very long period. A second-order explicit Symplectic integration scheme is used naturally to enforce the conservation of energy and momentum of the Hamiltonian finite element system. Numerical analyses are conducted and compared with theoretical and experimental results as well as the commercial software LS-DYNA. The comparisons demonstrate that the new Hamiltonian nodal position FEM is numerically efficient, stable and robust for simulation of long-period motion of cable systems.

Nonlinear Finite Element Formulation for the Large Displacement Analysis of Plates

1990 ◽  
Vol 57 (3) ◽  
pp. 707-718 ◽  
Author(s):  
Bilin Chang ◽  
A. A. Shabana
Keyword(s):  
Finite Element ◽  
Rigid Body ◽  
Coordinate System ◽  
Deformable Body ◽  
Finite Element Formulation ◽  
Deformation Analysis ◽  
Element Formulation ◽  
Rectangular Plates ◽  
Shape Functions ◽  
Intermediate Element

In this investigation a nonlinear total Lagrangian finite element formulation is developed for the dynamic analysis of plates that undergo large rigid body displacements. In this formulation shape functions are required to include rigid body modes that describe only large translational displacements. This does not represent any limitation on the technique presented in this study, since most of commonly used shape functions satisfy this requirement. For each finite plate element an intermediate element coordinate system, whose axes are initially parallel to the axes of the element coordinate system, is introduced. This intermediate element coordinate system, which has an origin which is rigidly attached to the origin of the deformable body, is used for the convenience of describing the configuration of the element with respect to the deformable body coordinate system in the undeformed state. The nonlinear dynamic equations developed in this investigation for the large rigid body displacement and small elastic deformation analysis of the rectangular plates are expressed in terms of a unique set of time invariant element matrices that depend on the assumed displacement field. The invariants of motion of the deformable body discretized using the plate elements are obtained by assembling the invariants of its elements using a standard finite element procedure.

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