Corotational total Lagrangian formulation for three-dimensional beamelement

Abstract

A corotational total Lagrangian formulation of beam element is presented for the nonlinear analysis of three-dimensional beam structures with large rotations but small strains. The nonlinear coupling among the bending, twisting, and stretching deformations is considered. All of the element deformations and equations are defined in body-attached element coordinates. Three rotation parameters are proposed to determine the orientation of the element cross section. Two sets of element nodal parameters termed explicit nodal parameters and implicit nodal parameters are introduced. The explicit nodal parameters are used in the assembly of the system equations from the element equations and chosen to be three components of the incremental translation vector and three components of the incremental rotation vector. The implicit nodal parameters are used to determine the deformations of the beam element and chosen to be three components of the total displacement vector and nodal values of the three rotation parameters. The element internal nodal forces corresponding to the implicit nodal parameters are obtained from the virtual work principle. Numerical examples are presented and compared with the numerical and experimental results reported in the literature to demonstrate the accuracy and efficiency of the proposed method. HREE-DIMENSIONAL beams are very important structural elements in all types of engineering systems. In many applications, these beam elements undergo finite rotations that require a nonlinear formulation to their structural analysis. The development of new and efficient formulations for nonlinear analysis of beam structures has attracted the study of many researchers in recent years. Based on different kinematic assumptions, different alternative formulation strategies and procedures to accommodate large rotation capability during the large deformation process have been presented.120 The kinematic assumptions used in Refs. 4, 5, 7, 11, and 17-19 are based on Timoshenko's hypothesis: the effect of stretching, bending, torsion, and transverse shear are taken into account.