Accuracy and Efficiency Analysis of the Beam Elements for Nonlinear Large Deformation

Purpose: The purpose of this paper is to study that which beam element should be adopted to achieve the required high accuracy and efficiency in different projects. Three kinds of beam elements commonly used to analyze the nonlinear dynamics of flexible multibody systems are compared and analyzed, which are fully parameterized beam and gradient-deficient beam elements based on the absolute nodal coordinate formulation, and geometrically exact beam element, respectively. Methods: The governing equations are established based on the fully parameterized beam element, the gradient-deficient beam element and the geometrically exact beam element, and the generalized-α implicit time stepping algorithm is used to study the dynamic responses of system. Results and Conclusion: In this study, the solution accuracy and efficiency of the three kinds of element are analyzed in both statics and dynamics in detail and compared with each other. It is found that the geometrically exact beam element is superior to other two elements when the discretized element is subjected to axial deformation and torsion. Both gradient-deficient beam element and geometrically exact beam element show the high accuracy and efficiency when the element is bent. Moreover, the Young’s modulus and time step have a great effect on displacement responses when the beam element is in dynamic state. All the results should be helpful for selection of a high-precision calculation method in engineering applications.