A co-rotational updated Lagrangian formulation for a 2D beam element with consideration of the deformed curvature

摘要

A tensor-based updated Lagrangian (UL) formulation for the geometrically nonlinear analysis of 2D beam-column structures is developed by using curvilinear coordinates, which has considered the effects of the deformed curvature. Between the known configuration C1 and the desired configuration C2, a configuration C2* derived by rigid-body motion of C1 is introduced to eliminate the element-end transverse displacements between C2* and C2. A stiffness matrix is obtained in C2*; and then by a transformation defined by the element-end displacements, the stiffness matrix in C2* is transformed into that in C1. Comparing the stiffness matrix with that in the conventional UL formulation for a 2D beam element, the initial displacement stiffness matrix emerges, which results from the deformed curvature within the element. Numerical examples have verified the accuracy and efficiency of the present formulation, and the results show that the deformed curvatures have significant effects when deformations are large.