Formulation of Three-Dimensional Rigid-Flexible Multibody Systems

2007 ◽  
Author(s):  
Daniel Garci´a-Vallejo ◽  
Jose´ L. Escalona ◽  
Juana M. Mayo ◽  
Jaime Domi´nguez
Keyword(s):  
Multibody Systems ◽  
Multibody System ◽  
Three Dimensional ◽  
Natural Coordinates ◽  
Flexible Multibody System ◽  
Absolute Nodal Coordinates ◽  
Constraint Equations ◽  
Flexible Multibody ◽  
The Matrix ◽  
Nodal Coordinates

Multibody systems generally contain solids the deformations of which are appreciable and which decisively influence the dynamics of the system. These solids have to be modeled by means of special formulations for flexible solids. At the same time, other solids are of such a high stiffness that they may be considered rigid, which simplifies their modeling. For these reasons, for a rigid-flexible multibody system, two types of formulations co-exist in the equations of the system. Among the different possibilities provided in bibliography on the material, the formulation in natural coordinates and the formulation in absolute nodal coordinates are utilized in this article to model the rigid and flexible solids, respectively. This article contains a mixed formulation based on the possibility of sharing coordinates between a rigid solid and a flexible solid. In addition, the fact that the matrix of the global mass of the system is shown to be constant and that many of the constraint equations obtained upon utilizing these formulations are linear and can be eliminated. In this work, the formulation presented is utilized to simulate a mechanism with both rigid and flexible components.

Flexible Multibody Dynamics Formulation by Hamilton’s Equations

2010 ◽  
Author(s):  
Martin M. Tong
Keyword(s):  
Multibody Dynamics ◽  
Multibody System ◽  
Mass Matrix ◽  
Equations Of Motion ◽  
Flexible Multibody Dynamics ◽  
Flexible Body ◽  
Flexible Multibody System ◽  
Generalized Coordinates ◽  
Flexible Multibody ◽  
The Matrix

Numerical solution of the dynamics equations of a flexible multibody system as represented by Hamilton’s canonical equations requires that its generalized velocities q˙ be solved from the generalized momenta p. The relation between them is p = J(q)q˙, where J is the system mass matrix and q is the generalized coordinates. This paper presents the dynamics equations for a generic flexible multibody system as represented by p˙ and gives emphasis to a systematic way of constructing the matrix J for solving q˙. The mass matrix is shown to be separable into four submatrices Jrr, Jrf, Jfr and Jff relating the joint momenta and flexible body mementa to the joint coordinate rates and the flexible body deformation coordinate rates. Explicit formulas are given for these submatrices. The equations of motion presented here lend insight to the structure of the flexible multibody dynamics equations. They are also a versatile alternative to the acceleration-based dynamics equations for modeling mechanical systems.

Monte Carlo Simulation of Flexible Multibody System with Uncertainties

2011 ◽  
Vol 55-57 ◽  
pp. 1382-1385
Author(s):  
Ting Pi ◽  
Yun Qing Zhang
Keyword(s):  
Monte Carlo ◽  
Multibody Systems ◽  
Multibody System ◽  
Absolute Nodal Coordinate Formulation ◽  
Flexible Multibody Systems ◽  
Flexible Multibody System ◽  
System Behavior ◽  
Flexible Multibody ◽  
And Performance ◽  
Crank Mechanism

Practical mechanical systems often contain several flexible components and uncertain parameters which makes it hard to predict the system behavior and performance exactly. This research presents the uncertainty analysis of flexible multibody systems with random variables. Absolute nodal coordinate formulation (ANCF), which is different from the traditional finite element method, is employed to model the flexibility here. Monte Carlo method is successfully used to simulate flexible multibody systems of index-3. The method proposed is demonstrated by an example of flexible slider-crank mechanism.

A New Sparse Solver for Kinematics Simulation of Multibody Systems in Natural Coordinates Based on Tearing Methods

2001 ◽  
Author(s):  
Francisco Javier Funes ◽  
José Manuel Jiménez ◽  
José Ignacio Rodríguez ◽  
Javier García de Jalón
Keyword(s):  
Multibody Systems ◽  
Linear Equations ◽  
New Method ◽  
Natural Coordinates ◽  
Open Chain ◽  
Triangular Form ◽  
Constraint Equations ◽  
Closed Loop Systems ◽  
Kinematics Simulation ◽  
The Matrix

Abstract This paper presents a new method for the factorization of the sparse system of linear equations arising from the kinematic simulation of multibody systems using natural coordinates. A special reordering of the jacobian matrix of the mechanism constraint equations will be described. This reordering depends only on the topology of the mechanism. In open-chain systems the matrix can be reordered to a block triangular form. For closed-loop systems this matrix can take a bordered block triangular form, with very few columns in the border. A modification of the Harwell’s implementation of the P5 algorithm from Erisman et al. [1] is used for reordering the rows and columns of the matrix. A new method of factorization is described. This method reduces the number of floating-point operations and the fill-ins. An efficient way for solving the least-squares problem arising from over-determined systems is explained.

Topology Optimization of a Three-Dimensional Flexible Multibody System Via Moving Morphable Components

2017 ◽  
Vol 13 (2) ◽  
Author(s):  
Jialiang Sun ◽  
Qiang Tian ◽  
Haiyan Hu
Keyword(s):  
Topology Optimization ◽  
Multibody System ◽  
Three Dimensional ◽  
Building Blocks ◽  
Optimization Approach ◽  
Flexible Multibody System ◽  
Topology Optimization Problem ◽  
Solid Element ◽  
Flexible Multibody ◽  
Moving Morphable Components

In this work, an efficient topology optimization approach is proposed for a three-dimensional (3D) flexible multibody system (FMBS) undergoing both large overall motion and large deformation. The FMBS of concern is accurately modeled first via the solid element of the absolute nodal coordinate formulation (ANCF), which utilizes both nodal positions and nodal slopes as the generalized coordinates. Furthermore, the analytical formulae of the elastic force vector and the corresponding Jacobian are derived for efficient computation. To deal with the dynamics in the optimization process, the equivalent static load (ESL) method is employed to transform the topology optimization problem of dynamic response into a static one. Besides, the newly developed topology optimization method by moving morphable components (MMC) is used and reevaluated to optimize the 3D FMBS. In the MMC-based framework, a set of morphable structural components serves as the building blocks of optimization and hence greatly reduces the number of design variables. Therefore, the topology optimization approach has a potential to efficiently optimize an FMBS of large scale, especially in 3D cases. Two numerical examples are presented to validate the accuracy of the solid element of ANCF and the efficiency of the proposed optimization methodology, respectively.

The Study on 3D Incompatible Element in Flexible Multibody System Dynamics

2014 ◽  
Vol 543-547 ◽  
pp. 1282-1285
Author(s):  
Su Bing Liu ◽  
Da Zhi Cao ◽  
Zhi Hui Zhao
Keyword(s):  
Incompatible Element ◽  
Multibody System ◽  
Three Dimensional ◽  
Computational Time ◽  
Flexible Multibody System ◽  
Robust Performance ◽  
Excellent Performance ◽  
Incompatible Elements ◽  
Flexible Multibody ◽  
Standard Linear

In this study the performance of three-dimensional tetrahedron elements has been compared with the background of the simulation of Flexible Multibody System (FMBS). The standard linear tetrahedron element has the least number of nodes, however it has the locking problem. The standard quadratic element has shown precise result and robust performance in many applications, but its high nodes also means large computational time. The incompatible elements integrates the excellence of the linear and quadratic elements and its excellent performance in term of accuracy and time efficiency is presented.

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