A Generalized Component Mode Synthesis Approach for Flexible Multibody Systems With a Constant Mass Matrix

2012 ◽  
Vol 8 (1) ◽  
Author(s):  
Astrid Pechstein ◽  
Daniel Reischl ◽  
Johannes Gerstmayr
Keyword(s):  
Rigid Body ◽  
Multibody Systems ◽  
Mass Matrix ◽  
Rigid Body Motion ◽  
Flexible Multibody Systems ◽  
Component Mode Synthesis ◽  
Body Motion ◽  
Mode Shapes ◽  
Flexible Multibody ◽  
Flexible Deformation

A standard technique to reduce the system size of flexible multibody systems is the component mode synthesis. Selected mode shapes are used to approximate the flexible deformation of each single body numerically. Conventionally, the (small) flexible deformation is added relatively to a body-local reference frame which results in the floating frame of reference formulation (FFRF). The coupling between large rigid body motion and small relative deformation is nonlinear, which leads to computationally expensive nonconstant mass matrices and quadratic velocity vectors. In the present work, the total (absolute) displacements are directly approximated by means of global (inertial) mode shapes, without a splitting into rigid body motion and superimposed flexible deformation. As the main advantage of the proposed method, the mass matrix is constant, the quadratic velocity vector vanishes, and the stiffness matrix is a co-rotated constant matrix. Numerical experiments show the equivalence of the proposed method to the FFRF approach.

A Generalized Component Mode Synthesis Approach for Multibody System Dynamics Leading to Constant Mass and Stiffness Matrices

2011 ◽  
Author(s):  
Johannes Gerstmayr ◽  
Astrid Pechstein
Keyword(s):  
Rigid Body ◽  
Mass Matrix ◽  
Rigid Body Motion ◽  
Component Mode Synthesis ◽  
Body Motion ◽  
Mode Shapes ◽  
Relative Deformation ◽  
Constant Mass ◽  
Constant Matrix ◽  
Flexible Deformation

A standard technique to reduce the system size of flexible multibody systems is the component mode synthesis. Selected mode shapes are used to approximate the flexible deformation of each single body numerically. Conventionally, the (small) flexible deformation is added relatively to a body-local reference frame, which results in the floating frame of reference formulation (FFRF). The coupling between large rigid body motion and small relative deformation is nonlinear, which leads to computationally expensive non-constant mass matrices and quadratic velocity vectors. In the present work, the total (absolute) displacements are directly approximated by means of mode shapes, without a splitting into rigid body motion and superimposed flexible deformation. As the main advantage of the proposed method, the mass matrix is constant, the quadratic velocity vector vanishes and the stiffness matrix is a co-rotated constant matrix. Numerical experiments show the equivalence of the proposed method to the FFRF approach.

A Partitioned Iteration Method Employing CG-Following Reference Frames for Distributed Simulation of Flexible Multibody Systems

2007 ◽  
Author(s):  
Geunsoo Ryu ◽  
Zheng-Dong Ma ◽  
Gregory M. Hulbert
Keyword(s):  
Rigid Body ◽  
Elastic Deformation ◽  
Iteration Method ◽  
Multibody Systems ◽  
Distributed Simulation ◽  
Rigid Body Motion ◽  
Flexible Multibody Systems ◽  
Body Motion ◽  
Flexible Multibody ◽  
Gluing Algorithm

A distributed simulation platform, denoted as D-Sim, has been developed previously by our research group, which comprises three essential attributes: a general XML description for models suitable for both leaf and integrated models, a gluing algorithm, which only relies on the interface information to integrate subsystem models, and a logical distributed simulation architecture that can be realized using any connection-oriented distributed technology. The overarching research focus is to integrate heterogeneous subsystem models, e.g., multibody dynamics subsystems models and finite element subsystems models and to conduct seamlessly integrated simulation and design tasks in a distributed computing environment. A Partitioned Iteration Method (PIM) is proposed in this paper, which decouples the rigid body motion from elastic deformation of the simulated system using an iteration scheme. The method employs a CG-following reference frame for each deformable body in the distributed simulation of flexible multibody systems. The resultant simulation system can be used to integrate distributed deformable bodies D-Sim, while allowing large rigid body motions among the bodies or subsystems. It also enables using independent simulation servers; where each server can run commercially available or research-based MBD and/or FEM codes. Examples are provided that demonstrate the performance of the method and also how to decouple and integrate rigid body motion and elastic deformation using the developed gluing algorithm.

Vibration of Moving Flexible Bodies (Formulation of Dynamics by Using Normal Modes and a Local Observer Frame)

1999 ◽  
Author(s):  
Atsushi Kawamoto ◽  
Mizuho Inagaki ◽  
Takayuki Aoyama ◽  
Nobuyuki Mori ◽  
Kimihiko Yasuda
Keyword(s):  
Rigid Body ◽  
Elastic Deformation ◽  
Multibody Systems ◽  
Elastic Vibration ◽  
Rigid Body Motion ◽  
Flexible Multibody Systems ◽  
Body Motion ◽  
Flexible Multibody ◽  
Local Observer ◽  
New Formulation

Abstract This paper deals with the formulation that can analyze vibration noise problems practically in the flexible multibody systems. Many kinds of formulations have been proposed on the flexible multibody systems so far. They are categorized into several groups according to their purposes and coordinate systems. The floating frame of reference formulation is at present the most popular method for general purpose simulations among them. The formulation uses Cartesian coordinates for the position of a body, Euler angles or Euler parameters for the orientations, and modal coordinates for the elastic degrees of freedom. The equations of motion with these different kinds of coordinates are complicated because of coupling between rigid body motion and elastic vibration. On the other hand, the linear theory of elasto-dynamics appears to be simple and could be practical for some limited uses. But it neglects the effect of the elastic deformation on the rigid body motion. In many cases, the effect is significant and essential. In this paper, we propose a new formulation with rigid body modes and a local observer frame (LOF) for large amplitude rigid body motion, and with elastic modes for small amplitude elastic vibration. The LOF is updated properly to compensate the gap between rigid body motion and the LOF motion. The new formulation makes the coupling terms as simple as possible without any loss of the effect of the elastic deformation on the rigid body motion and gives the uniform description in each modal coordinate.

Generalized Component Mode Synthesis for the Spatial Motion of Flexible Bodies With Large Rotations About One Axis1

2016 ◽  
Vol 11 (4) ◽  
Author(s):  
Pascal Ziegler ◽  
Alexander Humer ◽  
Astrid Pechstein ◽  
Johannes Gerstmayr
Keyword(s):  
Multibody Systems ◽  
Velocity Vector ◽  
Degrees Of Freedom ◽  
Mass Matrix ◽  
Component Mode Synthesis ◽  
Mode Shapes ◽  
State Dependency ◽  
Large Rotations ◽  
Flexible Deformation ◽  
Quadratic Velocity Vector

In industrial practice, the floating frame of reference formulation (FFRF)—often combined with the component mode synthesis (CMS) in order to reduce the number of flexible degrees-of-freedom—is the common approach to describe arbitrarily shaped bodies in flexible multibody systems. Owed to the relative formulation of the flexible deformation with respect to the reference frame, the equations of motion show state-dependent nonconstant inertia terms. Such relative description, however, comes along with considerable numerical costs, since both the mass matrix and gyroscopic forces, i.e., the quadratic velocity vector, need to be evaluated in every integration step. The state dependency of the inertia terms can be avoided by employing an alternative formulation based on the mode shapes as in the classical CMS approach. In this approach, which is referred to as generalized component mode synthesis (GCMS), the total (absolute) displacements are approximated directly. Consequently, the mass matrix is constant, no quadratic velocity vector appears, and the stiffness matrix is a corotated but otherwise constant matrix. In order to represent the same flexible deformation as in the classical FFRF-based CMS, however, a comparatively large number of degrees-of-freedom is required. The approach described in the present paper makes use of the fact that a majority of components in technical systems are constrained to motions showing large rotations only about a single spatially fixed axis. For this reason, the GCMS is adapted for multibody systems that are subjected to small flexible deformations and undergo a rigid body motion showing large translations, large rotations about one axis, but small rotations otherwise. Thereby, the number of shape functions representing the flexible deformation is reduced, which further increases numerical efficiency compared to the original GCMS formulation for arbitrary rotations.

Performance of the Incremental and Non-Incremental Finite Element Formulations in Flexible Multibody Problems

1999 ◽  
Vol 122 (4) ◽  
pp. 498-507 ◽  
Author(s):  
Marcello Campanelli ◽  
Marcello Berzeri ◽  
Ahmed A. Shabana
Keyword(s):  
Finite Element ◽  
Multibody Systems ◽  
Absolute Nodal Coordinate Formulation ◽  
Flexible Multibody Systems ◽  
Large Displacement ◽  
Body Motion ◽  
Absolute Nodal Coordinate ◽  
Flexible Multibody ◽  
The Absolute ◽  
Finite Element Formulations

Many flexible multibody applications are characterized by high inertia forces and motion discontinuities. Because of these characteristics, problems can be encountered when large displacement finite element formulations are used in the simulation of flexible multibody systems. In this investigation, the performance of two different large displacement finite element formulations in the analysis of flexible multibody systems is investigated. These are the incremental corotational procedure proposed in an earlier article (Rankin, C. C., and Brogan, F. A., 1986, ASME J. Pressure Vessel Technol., 108, pp. 165–174) and the non-incremental absolute nodal coordinate formulation recently proposed (Shabana, A. A., 1998, Dynamics of Multibody Systems, 2nd ed., Cambridge University Press, Cambridge). It is demonstrated in this investigation that the limitation resulting from the use of the infinitesmal nodal rotations in the incremental corotational procedure can lead to simulation problems even when simple flexible multibody applications are considered. The absolute nodal coordinate formulation, on the other hand, does not employ infinitesimal or finite rotation coordinates and leads to a constant mass matrix. Despite the fact that the absolute nodal coordinate formulation leads to a non-linear expression for the elastic forces, the results presented in this study, surprisingly, demonstrate that such a formulation is efficient in static problems as compared to the incremental corotational procedure. The excellent performance of the absolute nodal coordinate formulation in static and dynamic problems can be attributed to the fact that such a formulation does not employ rotations and leads to exact representation of the rigid body motion of the finite element. [S1050-0472(00)00604-8]

Flexible Multibody Systems With Large Deformations Using Absolute Nodal Coordinates for Isoparametric Solid Brick Elements

2003 ◽  
Author(s):  
Lars Ku¨bler ◽  
Peter Eberhard ◽  
Johannes Geisler
Keyword(s):  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Large Deformations ◽  
Flexible Multibody Systems ◽  
Body Motion ◽  
Absolute Nodal Coordinates ◽  
Shell Elements ◽  
Flexible Multibody ◽  
Absolute Coordinates ◽  
Solid Bodies

In this paper a formulation for flexible Multibody Systems (MBS) is proposed where flexible bodies are described using absolute coordinates for isoparametric brick elements. The use of absolute coordinates allows for large deformations and provides an accurate description of rigid body motion and inertia in the case of large rotations without additional considerations. Further, constant mass matrices are obtained for isoparametric elements. Brick elements are important, e. g. if general solid bodies with low stiffness, i. e. not negligible large deformations, are part of the MBS and cannot be modeled using beam, plate, or shell elements. Since only nodal translational degrees of freedom are used for brick elements additional questions arise. For example, imposing joint constraints for relative rotations between two bodies requires a nodal reference frame at connection points. An approach is proposed to define such a reference system utilizing displacement information of three finite element nodes.

Compliant Interface in Component Mode Synthesis

2020 ◽  
Author(s):  
Pierangelo Masarati ◽  
Fanny Darbas ◽  
Israël Wander
Keyword(s):  
Rigid Body ◽  
Structural Component ◽  
Strain Energy ◽  
Rigid Body Motion ◽  
Component Mode Synthesis ◽  
Body Motion ◽  
Structural Components ◽  
Definition Of ◽  
Flexible Models

Abstract Substructuring, or component mode synthesis, requires components to share interface regions. When components modeled with rather different, often incompatible levels of refinement need to be connected, correctly defining the interfaces may be important. This work proposes the definition of the reduction of interface regions to the equivalent rigid-body motion which minimizes the strain energy in the structural component. The proposed formulation provides a natural and physically sound solution for the connection of detailed structural components within coarse, multi-rigid-body and 1D flexible models.

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

2008 ◽  
Author(s):  
Martin M. Tong
Keyword(s):  
Numerical Solution ◽  
Multibody Systems ◽  
Multibody System ◽  
Recursive Algorithm ◽  
Mass Matrix ◽  
Direct Methods ◽  
Flexible Multibody Systems ◽  
Hamiltonian Form ◽  
Generalized Coordinates ◽  
Flexible Multibody

The computation of the generalized velocities from the generalized momenta of a multibody system is a part of the numerical solution of the dynamics equations when they are given in the Hamiltonian form. The states of these equations are the generalized coordinates and momenta, (q, p). The generalized velocity, q˙, is defined by q˙ = J−1p, where J is the system mass matrix. The effort in solving q˙ by direct methods is order(N3) where N is the number of bodies in the system. This paper presents an order(N) recursive algorithm to compute q˙ for flexible multibody systems.

Sign in / Sign up

Export Citation Format

Share Document