Use of independent rotation field in the large displacement analysis of beams

Ding, Jieyu; Wallin, Michael; Wei, Cheng; Recuero, Antonio M.; Shabana, Ahmed A.

doi:10.1007/s11071-014-1252-1

Cited by 45 publications

(14 citation statements)

References 15 publications

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“…For 2D problems, equations (24) are replaced by x r Á n ¼ 0, where n is a vector perpendicular to k. Equation 23is used to obtain the current estimate of the unknown location of the point of contact kþ1 nþ1 at the current iteration k þ 1 of the current time step n þ 1. Linearizing this equation with respect to , we have…”

Section: Modeling Jointsmentioning

confidence: 99%

A hybrid finite element formulation for flexible multibody dynamics

Singh

Jog

2015

Proceedings of the Institution of Mechanical Engineers, Part K:

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This work deals with the transient analysis of flexible multibody systems within a hybrid finite element framework. Hybrid finite elements are based on a two-field variational formulation in which the displacements and stresses are interpolated separately yielding very good coarse mesh accuracy. Most of the literature on flexible multibody systems uses beam-theory-based formulations. In contrast, the use of hybrid finite elements uses continuum-based elements, thus avoiding the problems associated with rotational degrees of freedom. In particular, any given three-dimensional constitutive relations can be directly used within the framework of this formulation. Since the coarse mesh accuracy as compared to a conventional displacement-based formulation is very high, the scheme is cost effective as well. A general formulation is developed for the constrained motion of a given point on a line manifold, using a total Lagrangian method. The multipoint constraint equations are implemented using Lagrange multipliers. Various kinds of joints such as cylindrical, prismatic, and screw joints are implemented within this general framework. Hinge joints such as spherical, universal, and revolute joints are obtained simply by using shared nodes between the bodies. In addition to joints, the formulation and implementation details for a DC motor actuator and for prescribed relative rotation are also presented. Several example problems illustrate the efficacy of the developed formulation.

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Section: Modeling Jointsmentioning

confidence: 99%

A hybrid finite element formulation for flexible multibody dynamics

Singh

Jog

2015

Proceedings of the Institution of Mechanical Engineers, Part K:

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“…[25][26][27] The MK method is based on the canonical coordinates of the first kind (CCFK) which is discrete pseudo-rotation angle increment and is applied in the Runge-Kutta method for index 1 DAEs. 28,29 The basic approaches in solving the matrix differential equations are similar to the developed methods of multibody dynamics in Park and Chung 30 and Ding et al 31 The aforementioned methods do not involve the constraint stabilization.…”

Section: Introductionmentioning

confidence: 99%

The constraint-stabilized implicit methods on Lie group for differential-algebraic equations of multibody system dynamics

Ding

Pan

Zhang

2019

Advances in Mechanical Engineering

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The implicit methods on Lie group are developed for multibody system dynamics. To avoid the violation of the displacement, velocity and acceleration constraints of the nonlinear differential-algebraic equations, the constraint-stabilized equations on Lie group are formulated. The implicit method for the Euler-Lagrange equations and the symplectic Euler method for the constrained Hamilton equations are presented. These methods can keep the stability of the displacement, velocity and acceleration constraints at the same time during the longer simulation. A three-dimensional single pendulum and a three-dimensional double pendulum are used to verify the accuracy of the constraint-stabilized Euler methods on Lie group and the orthogonality preservation of the rotation matrix.

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“…At present, many formulations can be used to describe the FMBS, such as the floating frame of reference formulation (FFRF), the absolute nodal coordinate formulation (ANCF) [20] and the large rotation vector formulation (LRVF) [21]. Ding et al [22] has clearly illustrated the performance of the LRVF. For the simulation of an FMBS with variable-length bodies, however, only two formulations are available.…”

Section: Introductionmentioning

confidence: 99%

Topology optimization of a flexible multibody system with variable-length bodies described by ALE–ANCF

Sun

Tian

et al. 2018

Nonlinear Dyn

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Use of independent rotation field in the large displacement analysis of beams

Cited by 45 publications

References 15 publications

A hybrid finite element formulation for flexible multibody dynamics

A hybrid finite element formulation for flexible multibody dynamics

The constraint-stabilized implicit methods on Lie group for differential-algebraic equations of multibody system dynamics

Topology optimization of a flexible multibody system with variable-length bodies described by ALE–ANCF

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