Joint Modeling Method for Higher-order Beam-based Models of Thin-walled Frame Structures

Abstract

Higher-order sectional modes of a thin-walled beam such as distortion and warping significantly affect structural stiffness levels. Because this higher-order effect becomes even greater near the joints of a beam frame structure, finding the correct connection conditions of sectional modes at beam joints is crucial for an accurate analysis. For conventional beam elements based on the Euler-Bernoulli/Timoshenko beam theory, the joint connection conditions are obtained by component-wise matching of the force and moment vectors at the joint node. However, this simple approach is no longer valid for the joints of higher-order beam elements because warping and distortion modes have zero force/moment resultants on the beam cross-section and therefore cannot be considered through the equilibrium condition of their resultants. In this investigation, three-dimensional displacements and rotation angles are set to be continuous at the connection points on a so-called joint section, which is defined as a virtual plane shared by joining beams. We propose to comprise the connection points using the vertices of the joint section and intersection points on the joint axis and impose the continuity conditions at these points using Lagrange multipliers. The proposed joint connection conditions can be applied to a beam frame structure with general section shapes without requiring any geometry-dependent conditions as done in earlier studies. The validity of the proposed method is demonstrated by conducting static and vibration analyses of two-beam joint structures, a T-joint structure, and a vehicle frame structure.