A Uniform Rotationless Formulation of Flexible Multibody Dynamics: Conserving Integration of Rigid Bodies, Nonlinear Beams and Shells

2007 ◽  
Author(s):  
Peter Betsch ◽  
Nicolas Sa¨nger
Keyword(s):  
Multibody Dynamics ◽  
Flexible Multibody Dynamics ◽  
Rigid Bodies ◽  
Rigid Body Dynamics ◽  
Flexible Bodies ◽  
Finite Dimensional ◽  
Nonlinear Beams ◽  
Body Dynamics ◽  
Flexible Multibody ◽  
Additional Constraints

A uniform framework for rigid body dynamics and nonlinear structural dynamics is presented. The advocated approach is based on a rotationless formulation of rigid bodies, nonlinear beams and shells. In this connection, the specific kinematic assumptions are taken into account by the explicit incorporation of holonomic constraints. This approach facilitates the straightforward extension to flexible multibody dynamics by including additional constraints due to the interconnection of rigid and flexible bodies. We further address the design of energy-momentum schemes for the stable numerical integration of the underlying finite-dimensional mechanical systems.

A Virtual Body and Joint for Constrained Flexible Multibody Dynamics

1999 ◽  
Author(s):  
D. S. Bae ◽  
J. M. Han ◽  
J. H. Choi
Keyword(s):  
Rigid Body ◽  
Multibody Dynamics ◽  
Reference Frames ◽  
Flexible Multibody Dynamics ◽  
General Purpose ◽  
Rigid Body Dynamics ◽  
Flexible Body ◽  
Body Dynamics ◽  
Flexible Multibody ◽  
Flexible Body Dynamics

Abstract A convenient implementation method for constrained flexible multibody dynamics is presented by introducing virtual rigid body and joint. The general purpose program for rigid and flexible multibody dynamics consists of three major parts of a set of inertia modules, a set of force modules, and a set of joint modules. Whenever a new force or joint module is added to the general purpose program, the modules for the rigid body dynamics are not reusable for the flexible body dynamics. Consequently, the corresponding modules for the flexible body dynamics must be formulated and programmed again. Since the flexible body dynamics handles more degrees of freedom than the rigid body dynamics does, implementation of the module is generally complicated and prone to coding mistakes. In order to overcome these difficulties, a virtual rigid body is introduced at every joint and force reference frames. New kinematic admissibility conditions are imposed on two body reference frames of the virtual and original bodies by introducing a virtual flexible body joint. There are some computational overheads due to the additional bodies and joints. However, since computation time is mainly depended on the frequency of flexible body dynamics, the computational overhead of the presented method could not be a critical problem, while implementation convenience is dramatically improved.

Modeling Controlled Articulated Flexible Systems Using Assumed Modes: Part II — Numerical Investigation

2001 ◽  
Author(s):  
Theodore G. Mordfin ◽  
Sivakumar S. K. Tadikonda
Keyword(s):  
Multibody Dynamics ◽  
Dynamic Systems ◽  
Flexible Multibody Dynamics ◽  
Companion Paper ◽  
Parameter Variation ◽  
Flexible Bodies ◽  
Simulation Efficiency ◽  
Multibody Dynamic ◽  
Flexible Multibody ◽  
Assumed Mode

Abstract Guidelines are sought for generating component body models for use in controlled, articulated, flexible multibody dynamics system simulations. In support of this effort, exact truth models and linearized large-articulation models are developed in a companion paper. The purpose of the truth models is to aid in evaluating the use of various types of component body assumed modes in the large-articulation models. The assumed mode models are analytically evaluated from the perspectives of both structural dynamics and multibody dynamics. In this paper, component body assumed modes are tested in a linearized large-articulation model. The numerical behavior of the model and its performance in the presence of parameter variation is investigated and explained. The results show that high accuracy, high simulation efficiency, and numerical robustness cannot be simultaneously achieved. However, in many cases, satisfactory levels of all three are achievable. Guidelines are proposed for modeling the flexible bodies in controlled-articulation flexible multibody dynamic systems.

Real-Time Explicit Flexible Multibody Dynamics Solver With Application to Virtual-Reality Based E-Learning

2011 ◽  
Author(s):  
Tamer M. Wasfy ◽  
Hatem M. Wasfy ◽  
Jeanne M. Peters
Keyword(s):  
Virtual Reality ◽  
Finite Elements ◽  
Rigid Body ◽  
Real Time ◽  
Multibody Dynamics ◽  
Flexible Multibody Dynamics ◽  
Rigid Bodies ◽  
Flexible Bodies ◽  
Joint Contact ◽  
E Learning

A flexible multibody dynamics explicit time-integration parallel solver suitable for real-time virtual-reality applications is presented. The hierarchical “scene-graph” representation of the model used for display and user-interaction with the model is also used in the solver. The multibody system includes rigid bodies, flexible bodies, joints, frictional contact constraints, actuators and prescribed motion constraints. The rigid bodies rotational equations of motion are written in a body-fixed frame with the total rigid body rotation matrix updated each time step using incremental rotations. Flexible bodies are modeled using total-Lagrangian spring, truss, beam and hexahedral finite elements. The motion of the elements is referred to a global inertial Cartesian reference frame. A penalty technique is used to impose joint/contact constraints. An asperity-based friction model is used to model joint/contact friction. A bounding box binary tree contact search algorithm is used to allow fast contact detection between finite elements and other elements as well as general triangular/quadrilateral rigid-body surfaces. The real-time solver is used to model virtual-reality based experiments (including mass-spring systems, pendulums, pulley-rope-mass systems, billiards, air-hockey and a solar system) for a freshman university physics e-learning course.

Translational Joints in Flexible Multibody Dynamics

1988 ◽  
Author(s):  
R. S. Hwang ◽  
E. J. Haug
Keyword(s):  
Multibody Dynamics ◽  
Flexible Multibody Dynamics ◽  
Local Deformation ◽  
Kinematic Constraints ◽  
Flexible Bodies ◽  
Numerical Examples ◽  
Flexible Multibody ◽  
Global Deformation ◽  
Deformation Modes ◽  
Joint Formulations

Abstract Formulations of translational kinematic constraints between flexible bodies are developed to model deformatioin of flexible surfaces that move relative to one another. Three types of flexible translational articulated joints are presented The joint formulations are illustrated in analysis of prototype systems with translational joints. Global deformation modes and substructure local deformation modes are used and compared in numerical examples.

A TUTORIAL PRESENTATION OF ALTERNATIVE SOLUTIONS TO THE FLEXIBLE BEAM ON RIGID CART PROBLEM

2005 ◽  
Vol 29 (3) ◽  
pp. 357-373 ◽  
Author(s):  
R. G. Langlois ◽  
R. J. Anderson
Keyword(s):  
Rigid Body ◽  
Multibody Dynamics ◽  
Flexible Multibody Dynamics ◽  
Beam Theory ◽  
General Purpose ◽  
Rigid Body Dynamics ◽  
Body Motion ◽  
Flexible Beam ◽  
Euler Beam ◽  
Flexible Multibody

A classical planar problem in forward flexible multibody dynamics is thoroughly investigated. The system consists of a damped flexible beam cantilevered to a rigid translating cart. The problem is solved using three distinctly different conventional approaches presented in roughly the chronological order in which they have been applied to flexible dynamic systems. First, a modal superposition formulation based on Bernoulli-Euler beam theory is developed. Second, an alternative solution is developed drawing exclusively on methods for rigid body dynamics combined with a knowledge of the theoretical modal behaviour of continuous beams. Third, a formulation based on the conventional finite element method using four-degree-of-freedom planar beam elements is adapted to include the rigid body motion of the cart. The relative merits of the three formulations are discussed and numerical simulation results generated using each of the three formulations are compared with each other and with a solution from a general-purpose flexible multibody dynamics formulation that is briefly outlined. The relative accuracy and efficiency of the methods and the challenges associated with generalizing each formulation are discussed.

scholarly journals Iterative Coordinate Reduction Algorithm of Flexible Multibody Dynamics Using a Posteriori Eigenvalue Error Estimation

2020 ◽  
Vol 10 (20) ◽  
pp. 7143
Author(s):  
Seongji Han ◽  
Jin-Gyun Kim ◽  
Juhwan Choi ◽  
Jin Hwan Choi
Keyword(s):  
Multibody Dynamics ◽  
Reduction Process ◽  
Flexible Multibody Dynamics ◽  
Dynamics Simulation ◽  
Iteration Step ◽  
Error Estimator ◽  
A Posteriori ◽  
Flexible Bodies ◽  
Flexible Multibody ◽  
Coordinate Reduction

Coordinate reduction has been widely used for efficient simulation of flexible multibody dynamics. To achieve the reduction of flexible bodies with reasonable accuracy, the appropriate number of dominant modes used for the reduction process must be selected. To handle this issue, an iterative coordinate reduction strategy is introduced. In the iteration step, more dominant modes of flexible bodies are selected than the ones in the previous step. Among the various methods, the conventional frequency cut-off rule is here considered. As a stop criterion, a novel a posteriori error estimator that can evaluate the relative eigenvalue error between full and reduced flexible bodies is proposed. Through the estimated relative eigenvalue error obtained, the number of dominant modes is automatically selected to satisfy the error tolerance up to the desired mode range. The applicability to the automation process is verified through numerical examples. It is also evaluated that efficient and accurate flexible multibody dynamics simulation is available with the reduced flexible body, generated by the proposed algorithm.

Systematic Integration of Finite Element Methods Into Multibody Dynamics Considering Hyperelasticity and Plasticity

2014 ◽  
Vol 9 (4) ◽  
Author(s):  
Graham Sanborn ◽  
Juhwan Choi ◽  
Joon Shik Yoon ◽  
Sungsoo Rhim ◽  
Jin Hwan Choi
Keyword(s):  
Finite Element ◽  
Plastic Material ◽  
Shell Element ◽  
Rigid Bodies ◽  
Rigid Body Dynamics ◽  
Nonlinear Material ◽  
Element Formulation ◽  
Material Models ◽  
Flexible Bodies ◽  
Body Dynamics

This study proposes a systematic extension of a multiflexible-body dynamics (MFBD) formulation that is based on a recursive formulation for rigid body dynamics. It is extended to include nonlinear plastic and hyperelastic material models for the flexible bodies. The flexible bodies in the existing MFBD formulation use a finite element formulation based on corotational elements. The rigid bodies and flexible bodies are coupled using the method of Lagrange multipliers. The extensions to add plasticity and hyperelasticity are outlined. A solid, brick-type element and a shell element are adapted from the literature for use with the plastic material, and a constant volume constraint is introduced to enforce the approximation of incompressibility with the hyperelastic materials. A brief overview of the MFBD formulation and the details required to extend the formulation to incorporate these nonlinear material models are presented. Numerical examples are presented to demonstrate the feasibility of the model.

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