The using a co-rotating Timoshenko beam element in nonlinear analysis of beams, plane frames and 2D arches

Abstract

The present work describes a co-rotating shear flexible beam element without shear locking using Timoshenko’s beam theories. The co-rotational kinematics separates rigid body motion from pure deformation. The paper details the deduction of the elastic stiffness matrix, geometric stiffness matrix, and co-rotational stiffness matrix, applying the unified beam element in the nonlinear analysis of beams, plane frames, and 2D arches. Numerical results reveal the effectiveness of the beam element in performing nonlinear structural analysis.