A Preprocessor for the Treatment of Elastic Bodies in Multibody Systems

1991 ◽  
Author(s):  
Kai Sorge ◽  
Friedrich Pfeiffer
Keyword(s):  
Multibody Systems ◽  
Computational Effort ◽  
Elastic Ring ◽  
Elastic Bodies ◽  
Symbolic Calculator

Abstract A preprocessor providing the inertia data of elastic bodies for multibody algorithms is considered. The desired capability of including stress stiffening terms leads to a high computational effort. The method presented allows a straight forward implementation of the basic formulas by starting with the development of a special purpose symbolic calculator. A rotating elastic ring serves as an example.

scholarly journals Multibody Systems with Flexible Elements

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1359
Author(s):  
Marin Marin ◽  
Dumitru Băleanu ◽  
Sorin Vlase
Keyword(s):  
Multibody Systems ◽  
Computer Assisted ◽  
Elastic Bodies ◽  
Algorithmic Analysis

The formalism of multibody systems offers a means of computer-assisted algorithmic analysis and a means of simulating and optimizing an arbitrary movement of a possible high number of elastic bodies in the connection [...]

Contact Modeling in Multibody Systems with Elastic Bodies in High-Frequency Applications

PAMM ◽  
2014 ◽  
Vol 14 (1) ◽  
pp. 39-40
Author(s):  
Sebastian Schulze ◽  
Walter Sextro ◽  
Frank Grüter
Keyword(s):  
High Frequency ◽  
Multibody Systems ◽  
Contact Modeling ◽  
Elastic Bodies

Semi-Symbolical Equations of Motion for Flexible Multibody Systems

1993 ◽  
Author(s):  
Frank Melzer
Keyword(s):  
Data Model ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
General Purpose ◽  
Flexible Multibody Systems ◽  
Dynamical Analysis ◽  
Lightweight Structures ◽  
Elastic Bodies ◽  
Flexible Multibody ◽  
Increasing Demand

Abstract The need for computer aided engineering in the analysis of machines and mechanisms led to a wide variety of general purpose programs for the dynamical analysis of multibody systems. In the past few years the incorporation of flexible bodies in this methodology has evolved to one of the major research topics in the field of multibody dynamics, due to the use of more lightweight structures and an increasing demand for high-precision mechanisms such as robots. This paper presents a formalism for flexible multibody systems based on a minimum set of generalized coordinates and symbolic computation. A standardized object-oriented data model is used for the system matrices, describing the elastodynamic behaviour of the flexible body. Consequently, the equations of motion are derived in a form independent of the chosen modelling technique for the elastic bodies.

Elimination of Redundant Cut Joint Constraints for Multibody System Models

2003 ◽  
Vol 126 (3) ◽  
pp. 488-494 ◽  
Author(s):  
A. Mu¨ller
Keyword(s):  
Multibody Systems ◽  
Computational Effort ◽  
Basis Matrix ◽  
Constraint Equations ◽  
Kinematic Loops ◽  
Joint Constraints ◽  
Rigid Multibody Systems ◽  
Kinematic Loop ◽  
Rigid Multibody

The problem of dependent cut joint constraints for kinematic loops in rigid multibody systems is addressed. The constraints are reduced taking into account the subalgebra generated by the screw system of the kinematic loop. The elimination of dependent constraint equations is based on constructing a basis matrix of the screw algebra generated by loop’s screw system. This matrix is configuration independent and thus always valid. The determination of the sufficient constraints is achieved with a SVD or QR decomposition of this matrix. Unlike all other proposed approaches the presented method is singularity consistent because it is not the Jacobian which is decomposed, but instead a basis matrix for the loop algebra. Since this basis is obtained after a finite number of cross products the computational effort is negligible. Furthermore, because the elimination process is only necessary once in advance of the integration/simulation process, it proved valuable even if it does not remove all dependent constraints, as for paradoxical mechanisms.

Application of LCP Contact Formulation on Mechanical Systems With Nonrigid Coupled Unilateral Contact Points Illustrated With a Simple Model of a Windscreen Wiper

2009 ◽  
Author(s):  
S. Tatzko ◽  
P. Gro¨nefeld ◽  
M. Wangenheim
Keyword(s):  
Multibody Systems ◽  
Equations Of Motion ◽  
Equation System ◽  
Small Time ◽  
Computational Effort ◽  
Unilateral Contact ◽  
Contact Points ◽  
Contact Formulation ◽  
The Masses ◽  
Discrete Mass

Technical applications with unilateral contact are often modeled as multiple coupled discrete mass points. The transition between contact states is often described by transforming the contact formulation into a linear complementary problem (LCP). In case of compliant materials such as rubber, the LCP can be simplified so that no algorithm is needed to solve the equation system. Thus, computational effort can be reduced considerably. In this paper a windscreen wiper lip is modeled as a simple mechanical system with unilateral contact points. The system consists of masses which are coupled by linear springs and dampers. The masses can come into contact with a rigid surface. The equations of motion are derived and transformed into an LCP. The modeling of the coupled, compliant system leads to a simplification of the equation system. Therefore, it can be solved line by line as single independent scalar LCP’s. Also at the transition from separation to contact, when an impact occurs, the contact points can be considered individually. It will be shown, that the coupling can be neglected during the infinitesimal small time of impact. The LCP formulation in combination with simple models of compliant structures therefore yields an effective method for treating multibody systems or discretized continua with several unilateral contact points.

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.

A Recursive Algorithm for Solving the Generalized Velocities From the Momenta of Flexible Multibody Systems

2010 ◽  
Vol 5 (4) ◽  
Author(s):  
Martin M. Tong
Keyword(s):  
Multibody Systems ◽  
Recursive Algorithm ◽  
Time Derivative ◽  
Computational Effort ◽  
Open Loop ◽  
Flexible Multibody Systems ◽  
Arithmetic Operations ◽  
Flexible Multibody ◽  
Hamilton's Equations ◽  
Hamilton’S Equations

Hamilton’s equations can be used to define the dynamics of a tree configured flexible multibody system. Their states are the generalized coordinates and momenta (p,q). Numerical solution of these equations requires the time derivatives of the states be defined. Hamilton’s equations have the benefit that the time derivative of the system momenta are easy to compute. However, the generalized velocities q̇ need be solved from the system momenta as defined by p=J(q)q̇ to support the computation of ṗ and the propagation of q. Because of the size of J, the determination of q̇ by linear equation solution schemes requires order ([N+∑i=1Nni]3) arithmetic operations, where N is the number of bodies and ni is the number of mode shape functions used to model the ith body deformations. It has been shown that q̇ can be solved recursively from the momentum equations for rigid multibody systems (Naudet, Lefeber, and Terze, 2003, “Forward Dynamics of Open-Loop Multibody Mechanisms Using An Efficient Recursive Algorithm Based On Canonical Momenta,” Multibody Syst. Dyn., 10, pp. 45–59). This paper extends that result to flexible multibody systems. The overall arithmetic operations to solve for q̇ in this case is proportional to N if the effort to solve for the flexible coordinate rates for each body is weighted the same as that for the joint rate. However, each time the flexible coordinates rate of a body is solved an order (ni3) operations is incurred. Thus, the total computational effort for flexible multibody systems includes an additional order (∑i=1Nni3) operations.

Simulation Based Optimal Tolerancing for Multibody Systems

2007 ◽  
Author(s):  
Henry Arenbeck ◽  
Samy Missoum ◽  
Anirban Basudhar ◽  
Parviz E. Nikravesh
Keyword(s):  
Multibody Systems ◽  
Multibody System ◽  
Failure Detection ◽  
Optimization Method ◽  
Computational Effort ◽  
Efficient Estimation ◽  
Design Parameters ◽  
Support Vector ◽  
Manufacturing Cost ◽  
Analysis Scheme

This paper introduces a new methodology for probabilistic optimal design of multibody systems. Specifically, the effects of dimensional uncertainties on the behavior of a system are considered. The proposed reliability-based optimization method addresses difficulties such as high computational effort and non-smoothness of the system’s responses, for example, as a result of contact events. The approach is based on decomposition of the design space into regions, corresponding to either acceptable or non-acceptable system performance. The boundaries of these regions are defined using Support Vector Machines (SVMs), which are explicit in terms of the design parameters. A SVM can be trained based on a limited number of samples, obtained from a design of experiments, and allows a very efficient estimation of probability of failure, even when Monte Carlo Simulation (MCS) is used. A modularly structured tolerance analysis scheme for automatic estimation of system production cost and probability of system failure is presented. In this scheme, detection of failure is based on multibody system simulation, yielding high computational demand. A SVM-based replication of the failure detection process is derived, which ultimately allows for automatic optimization of tolerance assignments. A simple multibody system, whose performance usually shows high tolerance sensitivity, is chosen as an exemplary system for illustration of the proposed approach. The system is optimally designed for minimum manufacturing cost while satisfying a target performance level with a given probability.

scholarly journals Reduced-Order Observers for Nonlinear State Estimation in Flexible Multibody Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Ilaria Palomba ◽  
Dario Richiedei ◽  
Alberto Trevisani
Keyword(s):  
Model Reduction ◽  
Multibody Systems ◽  
Numerical Test ◽  
Computational Effort ◽  
Flexible Multibody Systems ◽  
Large Set ◽  
State Variables ◽  
Reduced Order ◽  
Flexible Multibody ◽  
Nonlinear State

Modern control schemes adopted in multibody systems take advantage of the knowledge of a large set of measurements of the most important state variables to improve system performances. In the case of flexible-link multibody systems, however, the direct measurement of these state variables is not usually possible or convenient. Hence, it is necessary to estimate them through accurate models and a reduced set of measurements ensuring observability. In order to cope with the large dimension of models adopted for flexible multibody systems, this paper exploits model reduction for synthesizing reduced-order nonlinear state observers. Model reduction is done through a modified Craig-Bampton strategy that handles effectively nonlinearities due to large displacements of the mechanism and through a wise selection of the most important coordinates to be retained in the model. Starting from such a reduced nonlinear model, a nonlinear state observer is developed through the extended Kalman filter (EKF). The method is applied to the numerical test case of a six-bar planar mechanism. The smaller size of the model, compared with the original one, preserves accuracy of the estimates while reducing the computational effort.

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