Utilizing Tait-Bryan Angles for Large Displacement Corotational Finite Element Static Analysis of Spatial Beams

Abstract

In this work, a corotational finite element formulation is suggested for spatial beams with geometrically nonlinear behavior subjected to static loads. We returned to the three successive rotation angle procedure, mainly the Tait-Bryan angles. By carefully defining the trigonometric rules for all rotation angles, the singularity problem, that had limited the use of these angles, is avoided. Three different types of coordinate systems are used: a fixed global coordinate system that stays fixed throughout the analysis, a fixed local coordinate system that is fixed and precisely attached to each element, and a corotational local frame for each element that moves and rotates together with the element throughout the analysis. The rigid body motion can easily be separated from the overall deformation since the deformation is always tiny relative to the corotational frame. An incremental-iterative method is used for the solution based upon the Newton-Raphson method. Different examples are solved to demonstrate the practicality, correctness, and accuracy of the proposed method. The solutions converge at a relatively quick rate.