scholarly journals Modeling Flexible Bodies in Multibody Systems in Joint-Coordinates Formulation Using Spatial Algebra

2014 ◽  
Vol 6 ◽  
pp. 468986 ◽  
Author(s):  
Mohamed A. Omar
Keyword(s):  
Multibody Systems ◽  
Flexible Bodies ◽  
Joint Coordinates

Recursive Method for the Dynamic Analysis of Open-Loop Flexible Multibody Systems

2003 ◽  
Author(s):  
Yunn-Lin Hwang
Keyword(s):  
Dynamic Analysis ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Open Loop ◽  
Flexible Multibody Systems ◽  
Recursive Method ◽  
Flexible Bodies ◽  
System Equations ◽  
Generalized Newton ◽  
Time Invariant

The main objective of this paper is to develop a recursive method for the dynamic analysis of open-loop flexible multibody systems. The nonlinear generalized Newton-Euler equations are used for flexible bodies that undergo large translational and rotational displacements. These equations are formulated in terms of a set of time invariant scalars, vectors and matrices that depend on the spatial coordinates as well as the assumed displacement fields, and these time invariant quantities represent the dynamic coupling between the rigid body motion and elastic deformation. The method to solve for the equations of motion for open-loop systems consisting of interconnected rigid and flexible bodies is presented in this investigation. This method applies recursive method with the generalized Newton-Euler method for flexible bodies to obtain a large, loosely coupled system equations of motion. The solution techniques used to solve for the system equations of motion can be more efficiently implemented in the vector or digital computer systems. The algorithms presented in this investigation are illustrated by using cylindrical joints that can be easily extended to revolute, slider and rigid joints. The basic recursive formulations developed in this paper are demonstrated by two numerical examples.

Spatial Dynamics of Deformable Multibody Systems With Variable Kinematic Structure: Part 2—Velocity Transformation

1990 ◽  
Vol 112 (2) ◽  
pp. 160-167 ◽  
Author(s):  
C. W. Chang ◽  
A. A. Shabana
Keyword(s):  
Multibody Systems ◽  
Robot Manipulator ◽  
Spatial Dynamics ◽  
Dynamic Equations ◽  
Velocity Transformation ◽  
Joint Forces ◽  
Joint Coordinates ◽  
Deformable Bodies ◽  
Spatial System ◽  
Velocity Transformation Technique

In Part 1 of these two companion papers, the spatial system kinematic and dynamic equations are developed using the Cartesian and elastic coordinates in order to maintain the generality of the formulation. This allows introducing general forcing functions and adding and/or deleting kinematic constraints. In control applications, however, it is desirable to determine the joint forces associated with the joint variables. On the other hand the use of the joint coordinates to formulate the dynamic equations leads to a complex recursive formulation based on loop closure equations. In this paper a velocity transformation technique applicable to spatial multibody systems that consist of interconnected rigid and deformable bodies is developed. The Cartesian variables are expressed in terms of the joint and elastic variables. The resulting kinematic relationships are then employed to determine the joint forces associated with the joint variables. A spatial robot manipulator that manipulates an object is presented as a numerical example to exemplify the development presented in this paper.

An Open Code for the Dynamic Simulation of Multibody Systems

2004 ◽  
Author(s):  
Pietro Fanghella ◽  
Carlo Galletti ◽  
Giorgio Torre
Keyword(s):  
Control Systems ◽  
Multibody Systems ◽  
Object Oriented ◽  
General Purpose ◽  
External Control ◽  
Common Environment ◽  
Flexible Bodies ◽  
Kinematic Chains ◽  
Dynamic Simulator ◽  
User Friendly

The paper presents several features of a dynamic simulator for multibody systems. Its main characteristics are the following: it can deal with mechanisms with open and closed kinematic chains, allows definitions of rigid and flexible bodies, permits definitions of complex non-standard dynamic actions by a powerful and well-known general-purpose simulation package, and provides links to user-friendly interfaces for result displaying and interfacing with external control systems. In order to perform all these actions, a common environment based on Matlab has been established. The software is implemented using the Matlab object-oriented language. The first part of the paper provides a basic discussion of the mathematical approach followed to model multibody systems, then the actual software implementation is described. The designed software architecture is open and allows great model generality; moreover, the software can be optimized and tailored to specific multibody models in order to obtain good computational efficiency. Integration aspects in Simulink and VRML environments are analyzed.

Non-Linear Effects in Transient Dynamic Analysis of Flexible Multibody Systems

1995 ◽  
Author(s):  
Madeleine Pascal
Keyword(s):  
Multibody Systems ◽  
Transient Dynamic Analysis ◽  
Flexible Bodies ◽  
Open Questions ◽  
Centrifugal Stiffening ◽  
Higher Order Terms ◽  
Geometric Stiffening ◽  
Slender Bodies ◽  
Linear Effects ◽  
Rigid Body Motions

Abstract Some open questions arising in the dynamical formulation of systems of hinge-connected flexible bodies are discussed. The first one deals with the choice of the “floating reference frame” associated to a body under-going large rigid body motions but small elastic deformations. The second one is concerned by the so-called geometric stiffening (or centrifugal stiffening) effects. It is shown that in the most cases, these effects have to be taken into account only for slender bodies like beams or plates when they are subjected to axial or inplane forces. The last problem is concerned by the eventual appearance of higher order terms in the kinetic energy of the system for large rates and large accelerations.

scholarly journals On design sensitivities in the structural analysis and optimization of flexible multibody systems

2021 ◽  
Author(s):  
Alexander Held
Keyword(s):  
Structural Analysis ◽  
Multibody Systems ◽  
The Body ◽  
Flexible Multibody Systems ◽  
Adjoint Variable ◽  
Flexible Bodies ◽  
Design Sensitivities ◽  
Flexible Multibody ◽  
Data Files ◽  
Floating Frame

AbstractThe structural analysis and optimization of flexible multibody systems become more and more popular due to the ability to efficiently compute gradients using sophisticated approaches such as the adjoint variable method and the adoption of powerful methods from static structural optimization. To drive the improvement of the optimization process, this work addresses the computation of design sensitivities for multibody systems with arbitrarily parameterized rigid and flexible bodies that are modeled using the floating frame of reference formulation. It is shown that it is useful to augment the body describing standard input data files by their design derivatives. In this way, a clear separation can be achieved between the body modeling and parameterization and the system simulation and analysis.

Formulation and Implementation of Nonholonomic Constraints in the Analysis of Multibody Systems Using Joint Coordinates

1996 ◽  
Author(s):  
Claus Balling
Keyword(s):  
Multibody Systems ◽  
Relative Velocity ◽  
Nonholonomic Constraint ◽  
Nonholonomic Constraints ◽  
General Purpose ◽  
Mutual Interaction ◽  
Cartesian Coordinates ◽  
Joint Coordinates ◽  
Moving Points ◽  
Two Bodies

Abstract A general formulation for analysis of spatial multibody systems subjected to nonholonomic constraints is presented. Nonholonomic constraints are usually formulated in Cartesian coordinates constraining the relative velocity or acceleration between some (fixed or moving) points on two bodies in mutual interaction or a point on one body with respect to ground. The formulation involves a specific type of nonholonomic constraint (rolling disk on a surface) in terms of joint coordinates and perform the implementation in a general purpose program.

Aspects of Symbolic Formulations in Flexible Multibody Systems

2014 ◽  
Vol 9 (4) ◽  
Author(s):  
Markus Burkhardt ◽  
Robert Seifried ◽  
Peter Eberhard
Keyword(s):  
Multibody Systems ◽  
Multibody System ◽  
Dynamic Properties ◽  
Equations Of Motion ◽  
Flexible Multibody Systems ◽  
Fem Model ◽  
Local Shape ◽  
Flexible Bodies ◽  
Elastic Bodies ◽  
Flexible Multibody

The symbolic modeling of flexible multibody systems is a challenging task. This is especially the case for complex-shaped elastic bodies, which are described by a numerical model, e.g., an FEM model. The kinematic and dynamic properties of the flexible body are in this case numerical and the elastic deformations are described with a certain number of local shape functions, which results in a large amount of data that have to be handled. Both attributes do not suggest the usage of symbolic tools to model a flexible multibody system. Nevertheless, there are several symbolic multibody codes that can treat flexible multibody systems in a very efficient way. In this paper, we present some of the modifications of the symbolic research code Neweul-M2 which are needed to support flexible bodies. On the basis of these modifications, the mentioned restrictions due to the numerical flexible bodies can be eliminated. Furthermore, it is possible to re-establish the symbolic character of the created equations of motion even in the presence of these solely numerical flexible bodies.

Modeling of Impact in Multibody Systems: An Overview

2012 ◽  
Vol 8 (2) ◽  
Author(s):  
Y. A. Khulief
Keyword(s):  
Multibody Systems ◽  
Mechanical Systems ◽  
Current Status ◽  
Flexible Bodies ◽  
Rigid Multibody

This paper appraises the current status of research devoted to the problem of modeling impact in multibody systems. The paper presents a focused, yet coherent overview of the problem of modeling impulsive motions initiated by impacts in multibody systems in light of the reported literature, while highlighting the key research accomplishments, unresolved problems, and pending challenges. The paper begins with a brief overview of the mechanics of contact in two-body collisions, and then proceeds to review different approaches for modeling the dynamics of impact in rigid multibody mechanical systems and multibody systems of interconnected rigid and flexible bodies. The review concludes by shedding light on some pertinent computational considerations.

Bond Graphs for Flexible Multibody Systems

1979 ◽  
Vol 101 (1) ◽  
pp. 50-57 ◽  
Author(s):  
D. L. Margolis ◽  
D. C. Karnopp
Keyword(s):  
Rigid Body ◽  
Multibody Systems ◽  
Rigid Body Dynamics ◽  
Bond Graphs ◽  
Flexible Bodies ◽  
Actuator Dynamics ◽  
Bending Mode ◽  
Body Dynamics ◽  
Rigid Body Modes ◽  
Bending Modes

A method is presented for the analysis and simulation of the dynamic response of systems containing several long, flexible bodies driven by actuators at joints and attachment points. Applications include remote manipulators, cranes, and complex spacecraft. The geometric nonlinearities of rigid body dynamics are retained as well as small bending mode vibrations based upon linearized analysis. Since bond graphs are used, the actuator dynamics are readily incorporated. The results of simulation of a two body system with electrical actuators and up to three bending modes per body in addition to the rigid body modes are shown.

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