考虑翘曲效应的薄壁曲梁几何非线性分析

EFFECT OF WARPING IN GEOMETRIC NONLINEAR ANALYSIS OF CURVED THIN-WALLED BEAMS

利用UL法研究了开口薄壁曲线梁几何非线性分析问题。采用多项式插值函数表示位移场。考虑了翘曲自由度及曲率效应模拟开口薄壁曲梁的结构行为。所有位移参数定义于截面形心以便在弹性应变能中包括弯扭耦合项。利用修正的弧长法求解非线性方程,跟踪荷载位移曲线。用算例对提出的方法进行了验证,表明了薄壁曲梁的分析中翘曲变形不可忽略。

The geometric nonlinear analysis of curved beams with thin-walled open sections is performed. With the updated Lagrange formulation, a Hermitian polynomial is adopted to describe the displacement field. Warping degree of freedom and curvature effects are taken into consideration to simulate the structural behavior of curved thin-walled beams with open sections. In this formulation, all displacement parameters are defined at centroid axis so that the couple terms of bending and torsion are added to elastic strain energy. The improved arc-length method is adopted to trace the nonlinear load-deflection path. Numerical examples are presented to illustrate the validity and the accuracy of the proposed numerical approach. It is found that warping deformation is not negligible in the analysis of thin-walled beams.