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Rotation-based finite elements:reference-configuration geometry and motion description

Acta Mechanica Sinica 2021年第1期37卷 105-126,I0004页

作者： Ahmed A.Shabana Lingmin Xu Department of Mechanical and Industrial Engineering University of Illinois At ChicagoChicagoIL60607USA Faculty of Mechanical Engineering and Automation Zhejiang Sci-Tech UniversityHangzhou310018China

Infinitesimal-rotation finite elements allow creating a linear problem that can be exploited to systematically reduce the number of coordinates and obtain efficient solutions for a wide range of applications,including those governed by nonlinear equations.This paper discusses the limitations of conventional infinitesimal-rotation finite elements(FE)in capturing correctly the initial stress-free reference-configuration geometry,and explains the effect of these limitations on the definition of the inertia used in the motion description.An alternative to conventional infinitesimal-rotation finite elements is a new class of elements that allow developing inertia expressions written explicitly in terms of constant coefficients that define accurately the reference-configuration geometry.It is shown that using a geometrically inconsistent(GI)approach that introduces the infinitesimal-rotation coordinates from the outset to replace the interpolation-polynomial coefficients is the main source of the failure to capture correctly the reference-configuration geometry.On the other hand,by using a geometrically consistent(GC)approach that employs the position gradients of the absolute nodal coordinate formulation(ANCF)to define the infinitesimal-rotation coordinates,the reference-configuration geometry can be preserved.Two simple examples of straight and tapered beams are used to demonstrate the basic differences between the two fundamentally different approaches used to introduce the infinitesimal-rotation coordinates.The analysis presented in this study sheds light on the differences between the incremental co-rotational solution procedure,widely used in computational structural mechanics,and the non-incremental floating frame of reference formulation(FFR),widely used in multibody system(MBS)dynamics.

关键词： reference-configuration geometry Infinitesimal-rotation finite elements Rigid-body inertia floating frame of reference Absolute nodal coordinate formulation Co-rotational procedure

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