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

• 作者: Ahmed A.Shabana Lingmin Xu
• 来源期刊: 力学学报（英文版）
• 年，卷（期）: 2021,（1）
• 所属期刊栏目: DYNAMICS,VIBRATION,AND CONTROL
• 页码范围: 105-126
• 页数: 22页
• 语种: 英文

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 equa-tions.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 consist-ent(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.