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

作　　者：Ahmed A.Shabana Lingmin Xu 

机构地区：[1]Department of Mechanical and Industrial Engineering,University of Illinois At Chicago,Chicago,IL,60607,USA [2]Faculty of Mechanical Engineering and Automation,Zhejiang Sci-Tech University,Hangzhou,310018,China

出　　处：《Acta Mechanica Sinica》2021年第1期105-126,I0004,共23页力学学报（英文版）

基　　金：supported,in part,by the National Science Foundation(Grant 1852510).

摘　　要：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 

分 类 号：O343[理学—固体力学]