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.

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]

System-Level Modal Representation of Flexible Multibody Systems

2009 ◽  
Author(s):  
Gert H. K. Heirman ◽  
Wim Desmet
Keyword(s):  
Model Reduction ◽  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Flexible Multibody Systems ◽  
System Level ◽  
Algebraic Equations ◽  
Flexible Multibody ◽  
Simulation Results ◽  
Model Equations ◽  
Model Reduction Technique

The presence of both differential and algebraic equations in the model equations, as well as the number of degrees of freedom needed to accurately represent flexibility, prohibit fast simulation of flexible multibody systems (e.g. real-time). In this research, Global Modal Parametrization, a model reduction technique for flexible multibody systems is further developed to speed up simulation of flexible multibody systems. The reduction of the model is achieved by projection on a curvilinear subspace instead of a fixed vector space, requiring significantly less degrees of freedom to represent the system dynamics with the same level of accuracy. The complexity of simulation of the reduced model equations is estimated. In a numerical experiment, simulation results for the original model equations are compared with simulation results for the model equations obtained after model reduction, showing a good match. The dominant sources of error of the proposed methodology are illustrated and explained.

scholarly journals Formulation of Shell Elements Based on the Motion Formalism

2021 ◽  
Vol 2 (4) ◽  
pp. 1009-1036
Author(s):  
Olivier Bauchau ◽  
Valentin Sonneville
Keyword(s):  
Multibody Systems ◽  
Equations Of Motion ◽  
Solution Process ◽  
Flexible Multibody Systems ◽  
Governing Equations ◽  
Euclidean Group ◽  
Shell Elements ◽  
Reduced Order ◽  
Flexible Multibody ◽  
Plates And Shells

This paper presents a finite element implementation of plates and shells for the analysis of flexible multibody systems. The developments are set within the framework of the motion formalism that (1) uses configuration and motion to describe the kinematics of flexible multibody systems, (2) couples their displacement and rotation components by recognizing that configuration and motion are members of the Special Euclidean group, and (3) resolves all tensors components in local frames. The formulation based on the motion formalism (1) provides a theoretical framework that streamlines the formulation of shell elements, (2) leads to governing equations of motion that are objective, intrinsic, and present a reduced order of nonlinearity, (3) improves the efficiency of the solution process, (4) circumvents the shear locking phenomenon that plagues shell formulations based on classical kinematic descriptions, and (5) prevents the occurrence of singularities in the treatment of finite rotation. Numerical examples are presented to illustrate the advantageous features of the proposed formulation.

Approximate End-Effector Tracking Control of Flexible Multibody Systems Using Singular Perturbations

2013 ◽  
Vol 9 (1) ◽  
Author(s):  
Thomas Gorius ◽  
Robert Seifried ◽  
Peter Eberhard
Keyword(s):  
Tracking Control ◽  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Multibody System ◽  
Feedforward Control ◽  
Flexible Multibody Systems ◽  
Flexible Manipulator ◽  
End Effector ◽  
Nonminimum Phase ◽  
Flexible Multibody

In many cases, the design of a tracking controller can be significantly simplified by the use of a 2-degrees of freedom (DOF) control structure, including a feedforward control (i.e., the inversion of the nominal system dynamics). Unfortunately, the computation of this feedforward control is not easy if the system is nonminimum-phase. Important examples of such systems are flexible multibody systems, such as lightweight manipulators. There are several approaches to the numerical computation of the exact inversion of a flexible multibody system. In this paper, the singularly perturbed form of such mechanical systems is used to give a semianalytic solution to the tracking control design. The control makes the end-effector to even though not exactly, but approximately track a certain trajectory. Thereby, the control signal is computed as a series expansion in terms of an overall flexibility of the bodies of the multibody system. Due to the use of symbolic computations, the main calculations are independent of given parameters (e.g., the desired trajectories), such that the feedforward control can be calculated online. The effectiveness of this approach is shown by the simulation of a two-link flexible manipulator.

Reduced Isogeometric Analysis Models for Impact Simulations

2021 ◽  
Author(s):  
Tobias Rückwald ◽  
Alexander Held ◽  
Robert Seifried
Keyword(s):  
Isogeometric Analysis ◽  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Computation Time ◽  
Flexible Multibody Systems ◽  
Shape Functions ◽  
Elastic Rod ◽  
Flexible Multibody ◽  
Impact Simulations ◽  
The Impact

Abstract Detailed impact simulations in flexible multibody systems are usually based on isoparametric finite element models. For modeling the dynamics of an impact, a precise representation of the geometry is essential. However, isoparametric finite elements involve the discretization of the geometry. This work tests the isogeometric analysis (IGA) as an alternative approach in flexible multibody systems. The IGA enables the exact representation of the geometry by using non-uniform rational basis splines (NURBS) as element shape functions. In the context of an efficient impact simulation a model reduction and a possible inclusion of the floating frame of reference formulation is beneficial. The degrees of freedom of the flexible bodies are reduced using component mode synthesis to save computation time in the multibody simulation. For the precise description of deformations and stresses in the contact area as well as elastodynamic effects, a large number of global shape functions is required. As testing examples, the impact of two elastic spheres and a multibody multicontact problem including wave propagation in a long elastic rod are simulated and compared to reference solutions.

Describing Rigid-Flexible Multibody Systems Using Absolute Coordinates

2003 ◽  
Vol 34 (1/2) ◽  
pp. 75-94 ◽  
Author(s):  
D. García-Vallejo ◽  
J. L. Escalona ◽  
J. Mayo ◽  
J. Domínguez
Keyword(s):  
Multibody Systems ◽  
Flexible Multibody Systems ◽  
Flexible Multibody ◽  
Absolute Coordinates

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.

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.

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