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.

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.

Flexible Multibody Dynamics Based on a Fully Cartesian System of Support Coordinates

1993 ◽  
Vol 115 (2) ◽  
pp. 294-299 ◽  
Author(s):  
N. Vukasovic ◽  
J. T. Celigu¨eta ◽  
J. Garci´a de Jalo´n ◽  
E. Bayo
Keyword(s):  
Multibody Dynamics ◽  
Reference Frames ◽  
Deformable Body ◽  
Equations Of Motion ◽  
Flexible Multibody Dynamics ◽  
Body Motion ◽  
Cartesian System ◽  
Flexible Multibody ◽  
Local Reference ◽  
Rigid Multibody

In this paper we present an extension to flexible multibody systems of a system of fully cartesian coordinates previously used in rigid multibody dynamics. This method is fully compatible with the previous one, keeping most of its advantages in kinematics and dynamics. The deformation in each deformable body is expressed as a linear combination of Ritz vectors with respect to a local frame whose motion is defined by a series of points and vectors that move according to the rigid body motion. Joint constraint equations are formulated through the points and vectors that define each link. These are chosen so that a minimum use of local reference frames is done. The resulting equations of motion are integrated using the trapezoidal rule combined with fixed point iteration. An illustrative example that corresponds to a satellite deployment is presented.

Nonlinear three-dimensional beam theory for flexible multibody dynamics

2014 ◽  
Vol 34 (3) ◽  
pp. 211-242 ◽  
Author(s):  
Shilei Han ◽  
Olivier A. Bauchau
Keyword(s):  
Multibody Dynamics ◽  
Three Dimensional ◽  
Flexible Multibody Dynamics ◽  
Beam Theory ◽  
Flexible Multibody

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.

Discontinuous Galerkin Method and Dual-SLERP for Time Integration of Flexible Multibody Dynamics

2020 ◽  
Vol 15 (9) ◽  
Author(s):  
Shilei Han ◽  
Olivier A. Bauchau
Keyword(s):  
Discontinuous Galerkin ◽  
Multibody Dynamics ◽  
Time Integration ◽  
Flexible Multibody Dynamics ◽  
Differential Algebraic Equations ◽  
Body Motion ◽  
Motion Field ◽  
Algebraic Equations ◽  
Time Step ◽  
Flexible Multibody

Abstract A novel time-discontinuous Galerkin (DG) method is introduced for the time integration of the differential-algebraic equations governing the dynamic response of flexible multibody systems. In contrast to traditional Galerkin methods, the rigid-body motion field is interpolated using the dual spherical linear scheme. Furthermore, the jumps inherent to time-DG methods are expressed in terms of a parameterization of the relative motion from one time-step to the next. The proposed scheme is third-order accurate for initial value problems of both rigid and flexible multibody dynamics.

Procedure for non-smooth contact for planar flexible beams with cone complementarity problem

2020 ◽  
pp. 146441932095745 ◽  
Author(s):  
Xinxin Yu ◽  
Marko K Matikainen ◽  
Ajay B Harish ◽  
Aki Mikkola
Keyword(s):  
Rigid Body ◽  
Multibody Dynamics ◽  
Complementarity Problem ◽  
Arbitrary Shape ◽  
Penalty Method ◽  
Nonlinear Complementarity Problem ◽  
Flexible Multibody Dynamics ◽  
Detection Algorithm ◽  
Contact Detection ◽  
Flexible Multibody

Contact description plays an important role in modeling of applications involving flexible multibody dynamics. Example of such applications include contact between a belt and pulley, crash-worthiness analysis in aerospace and automotive engineering. Approaches such as the linear complementarity problem (LCP), nonlinear complementarity problem (NCP) and penalty method have been proposed for contact detection and imposition of contact constraints. Contact description within multibody dynamics, however, continues to be a challenging topic, particularly in the case of flexible bodies. This paper describes and compares the use of two contact descriptions in the framework of flexible multibody dynamics; (1) the use of nonlinear cone complementarity approach (CCP) and (2) the penalty method. Both contact models are presented together with a master-slave detection algorithm. The modified form of node-to-node approach presented facilitates creation of pseudo-nodes where gap function can be calculated. This reduces the cumbersome effort of contact search. Since large deformations can be an important phenomenon in flexible multibody applications, beam elements based on the absolute nodal coordinate formulation (ANCF) are implemented in this study. To make a comparison of two approaches, the damping component is included in the penalty method by using the continuous contact model introduced by Hunt and Crossley. Numerical results are based on the simulation of ANCF beam contact with rigid ground, rigid body with an arbitrary shape and pendulum contact. Although kinematic results show a good agreement between both approaches when the coefficient of restitution is zero, the unphysical interpenetration appears in the penalty method. Nonlinear minimization problem solved by CCP approach helps to prevent the penetration during contact event. Furthermore, the proposed contact detection algorithm is proved to be capable of being used for multiple contact between beam and arbitrary shape rigid body; different contact types, such as side-by-side and corner-by-side, can be performed without prediction.

Stability Analysis of Periodic Solutions for Flexible Multibody Dynamics

2019 ◽  
Author(s):  
Shilei Han ◽  
Olivier A. Bauchau
Keyword(s):  
Periodic Solution ◽  
Stability Analysis ◽  
Rigid Body ◽  
Periodic Solutions ◽  
Multibody Dynamics ◽  
Flexible Multibody Dynamics ◽  
Linear Interpolation ◽  
Periodic Linear ◽  
Flexible Multibody ◽  
Rigid Body Motions

Abstract Discontinuous Galerkin formulation is developed for stability analysis of periodic solutions of flexible multibody dynamics. The proposed approach takes rigid-body motions of each structural nodes as the unknowns. The rigid-body motions are interpolated by using dual spherical linear interpolation (dual-SLERP). The analysis is composed of two steps: (1) the periodic solution is obtained by solving nonlinear equations resulting from Galerkin method; (2) a linearization about the periodic solution leads to a periodic linear system and its stability is assessed by using Floquet’s method.

Integrating 3D Stress Analysis With Flexible Multibody Dynamics Simulation

2017 ◽  
Author(s):  
Olivier A. Bauchau ◽  
Shilei Han
Keyword(s):  
Multibody Dynamics ◽  
Axial Stress ◽  
Three Dimensional ◽  
Flexible Multibody Dynamics ◽  
Beam Theory ◽  
Torsional Stiffness ◽  
Dynamics Simulation ◽  
Numerical Examples ◽  
Axial Forces ◽  
Flexible Multibody

This paper presents an approach toward the integration of 3D stress computation with the tools used for the simulation of flexible multibody dynamics. Due to the low accuracy of the floating frame of reference approach, the the multibody dynamics community has turned its attention to comprehensive analysis tools based on beam theory. These tools evaluate sectional stress resultants, not 3D stress fields. The proposed approach decomposes the 3D problem into two simpler problems: a linear 2D analysis of the cross-section of the beam and a nonlinear, 1D of the beam. This procedure is described in details. For static problems, the proposed approach provides exact solutions of three-dimensional elasticity for uniform beams of arbitrary geometric configuration and made of anisotropic composite materials. While this strategy has been applied to dynamic problems, little attention has been devoted to inertial effects. This paper assesses the range of validity of the proposed beam theory when applied to dynamics problems. When beams are subjected to large axial forces, the induced axial stress components become inclined, generating a net torque that opposes further rotation of the section and leading to an increased effective torsional stiffness. This behavior, referred to as the Wagner or trapeze effect, cannot be captured by beam formulations that assume strain components to remain small, although arbitrarily large motions are taken into account properly. A formulation of beam theory that includes higher-order strain effects in an approximate manner is developed and numerical examples are presented. The “Saint-Venant problem” refers to a three-dimensional beam loaded at its end sections only. The “Almansi-Michell problem” refers to a three-dimensional beam loaded by distributed body forces, lateral surface tractions, and forces and moments at its end sections. Numerical examples of beams subjected to distributed loads will be presented and compared with 3D finite element solutions.

Further approximations in flexible multibody dynamics

1991 ◽  
Author(s):  
CARLOS PADILLA ◽  
ANDREAS VON FLOTOW
Keyword(s):  
Multibody Dynamics ◽  
Flexible Multibody Dynamics ◽  
Flexible Multibody
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