TY - JOUR

T1 - Accuracy of Co-rotational formulation for 3-D Timoshenko's beam

AU - Iura, M.

AU - Suetake, Y.

AU - Atluri, S. N.

N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.

PY - 2003

Y1 - 2003

N2 - An accuracy of finite element solutions for 3-D Timoshenko's beams, obtained using a co-rotational formulation, is discussed. The co-rotational formulation has often been used with an assumption that the relative deformations are small. A fundamental question, therefore, has been raised as to whether or not the numerical solutions obtained approach the solutions of the exact theory. In this paper, from theoretical point of view, we investigate the accuracy of the co-rotational formulation for 3-D Timoshenko's beam undergoing finite strains and finite rotations. It is shown that the use of the conventional secant coordinates fails to give satisfactory numerical solutions. We introduce a new local coordinate system in which a linear beam theory is used to construct the strain energy function. It is shown that the finite element solutions obtained converge to those of the exact beam theory as the number of element increases.

AB - An accuracy of finite element solutions for 3-D Timoshenko's beams, obtained using a co-rotational formulation, is discussed. The co-rotational formulation has often been used with an assumption that the relative deformations are small. A fundamental question, therefore, has been raised as to whether or not the numerical solutions obtained approach the solutions of the exact theory. In this paper, from theoretical point of view, we investigate the accuracy of the co-rotational formulation for 3-D Timoshenko's beam undergoing finite strains and finite rotations. It is shown that the use of the conventional secant coordinates fails to give satisfactory numerical solutions. We introduce a new local coordinate system in which a linear beam theory is used to construct the strain energy function. It is shown that the finite element solutions obtained converge to those of the exact beam theory as the number of element increases.

KW - Co-rotational formulation

KW - Finite element method

KW - Finite rotations

KW - Timoshenko's beam

UR - http://www.scopus.com/inward/record.url?scp=8344286308&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:8344286308

VL - 4

SP - 249

EP - 258

JO - CMES - Computer Modeling in Engineering and Sciences

JF - CMES - Computer Modeling in Engineering and Sciences

SN - 1526-1492

IS - 2

ER -