Abstract
In this paper, a method of modeling and simulatingflexible beam finite rotation is investigated. Based on theassumptions of low speed and small deformation, theANCF method is regarded as a finite element interpolationmethod to obtain the constant mass matrix of the flexiblebeam; the local coordinate system in the ANCF method isconsidered the floating coordinate system, and thestiffness matrix independent of the generalizedcoordinates is obtained. The split-iteration method is usedto expand the generalized coordinates that are notcontained in the constraint equations to the 2nd -orderTaylor series of the generalized coordinates that arecontained in the constraint equations and the Lagrangemultipliers. The nonlinear constraint equations arelinearized to the 1st -order Taylor series of the generalizedcoordinates. Then, the generalized coordinates andLagrange multipliers can be solved quickly. The resultsshow that the dynamic equations can be effectivelysimplified by combining the ANCF method with the FFRmethod for the small-deformation problems. Thelow-order Taylor approximation of generalizedcoordinates in both the dynamic equations and constrainedequations does not lose substantial computationalaccuracy but can significantly reduce computational time.The results of this investigation have important referencevalues for dynamic analysis of cranes, aerial workplatforms, and other engineering equipment. DOI: http://dx.doi.org/10.5755/j01.mech.24.5.20358
Highlights
The earliest method discovered for dealing with flexible body dynamic equations is the kineto-elasto-dynamic (KED) method [1,2,3]
The frame of reference (FFR) method decomposes the configuration of the flexible body into two parts: the large overall rigid motions of the floating coordinate system, and the elastic deformation of the flexible body with respect to the floating coordinate system
The selection of the floating coordinate system does not affect the analysis results, the mass matrix obtained by this method is a nonlinear function matrix of generalized coordinates, resulting in inertial coupling between the rigid motion and elastic deformation of the flexible body
Summary
The earliest method discovered for dealing with flexible body dynamic equations is the kineto-elasto-dynamic (KED) method [1,2,3]. At the end of the 20th century, Shabana and other scholars [10,11,12,13,14] proposed the absolute nodal coordinate formulation (ANCF) method This method is similar to that proposed by Simo: the dynamic equations of the beam are described in the global coordinate system; the cross-section local coordinate system of the beam is used to describe bending, shearing, and twisting; and the constant mass matrix can be obtained, so the centrifugal force and Coriolis force are zero. The shortcomings of these two methods are identical: the stiffness matrix becomes highly complicated. This algorithm guarantees a sufficiently accurate solution and improves the computational efficiency substantially
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