Advanced analysis of arbitrarily shaped axially loaded beams including axial warping and distortion

摘要

In this paper, a higher order beam theory is developed for the analysis of beams of homogeneous cross-section, taking into account warping and distortional phenomena due to axial, shear, flexural and torsional behavior. The beam can be subjected to arbitrary axial, transverse and/or torsional concentrated or distributed load, while its edges are restrained by the most general linear boundary conditions. The analysis consists of two stages. In the first stage, where the Boundary Element Method is employed, a cross sectional analysis is performed based on the so-called sequential equilibrium scheme establishing the possible in-plane (distortion) and out-of-plane (warping) deformation patterns of the cross-section. In the second stage, where the Finite Element Method is employed, the extracted deformation patterns are included in the beam analysis multiplied by respective independent parameters expressing their contribution to the beam deformation. The four rigid body displacements of the cross-section together with the aforementioned independent parameters consist the degrees of freedom of the beam. The finite element equations are formulated with respect to the displacements and the independent warping and distortional parameters. Numerical examples of axially loaded beams are solved to emphasize the importance of axial mode. In addition, numerical examples of various loading combinations are presented to demonstrate the range of application of the proposed method.