Objectivity of strain measures in the geometrically exact three-dimensional beam theory and its finite-element implementation

被引：272

作者：

Crisfield, MA ^{[1
]}

Jelenic, G ^{[1
]}

机构：

[1] Univ London Imperial Coll Sci Technol & Med, Dept Aeronaut, London SW7 2BY, England

来源：

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 1999年 / 455卷 / 1983期

关键词：

nonlinear beam theory; large (3D) rotations; strain invariance; finite-element method; interpolation of rotations;

D O I：

10.1098/rspa.1999.0352

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

The paper discusses the issue of discretization of the strain-configuration relationships in the geometrically exact theory of three-dimensional (3D) beams, which has been at the heart of most recent nonlinear finite-element formulations. It is demonstrated that the usual discretization procedures for implementing these strain measures within a finite-element framework violate the important property of objectivity: invariance to rigid-body rotations. A method is proposed for overcoming this limitation, which paves the way for an objective finite-element formulation of the geometrically exact 3D beam theory. For a two-noded element, this method involves obtaining the relative rotation matrix that rotates one nodal triad onto the other and then interpolating the resulting rotation vector.

引用

页码：1125 / 1147

页数：23

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