Exact Beam Element and Algorithms for Stability Analysis of Frame Structures Including Transverse Shear Deformation

Abstract

Based on the general solutions of the governing equation for linear buckling of Timoshenko beam under axial force, exact shape functions for transverse shear deformable beam are constructed and corresponding exact element stifiness matrix and geometrical stifiness matrix are formulated for stability analysis of frame structures. Two new algorithms are developed for the determination of a given number of critical load factors or all critical load factors in a given range. In addition to the conventional eigenvalue extraction method, the well-known Wittrick-Williams method is employed in both algorithms. Numerical examples are presented to demonstrate the efiectiveness of the proposed element and algorithms.