Geometric Nonlinear Analysis of AngleSection Elements Based on Updated Lagrangian Formulation and Rigid Body Rule

Abstract

Angle cross-section members are widely used in various transmission towers owing to their convenient connections, easy availability, simple production processes, and high efficiency. Such members are very susceptible to nonlinear behavior when subjected to abnormal or extreme loads. In this work, a new geometric stiffness matrix for thin-walled steel members with an angle cross-section is derived based on the principle of virtual displacement, rigid body rule and updated Lagrangian equations. The generalized displacement control (GDC) method is employed to deal with the issues of non-convergence at the extreme value point and rebound point in the geometric nonlinear analysis, which offers clear physical meaning and can adjust the loading direction. The geometric and the traditional elastic stiffness matrices derived in this work are applied during the prediction phase, while only the traditional elastic stiffness matrix is used in the correction phase. The comparisons of the results obtained by the proposed method with those in the previous literature and ANSYS numerical solutions show that the proposed method is sufficient to ensure the accuracy and applicability for addressing the structural geometrically nonlinear issues.