薄壁悬臂构件的弹性弯-扭屈曲作用

Elastic Flexural-Torsional Buckling of Thin-Walled Cantilevers

以往的研究表明,广泛用于分析薄壁梁的弯-扭屈曲作用的两个差异不大的具有代表性的理论,用于评估具有单轴对称横截面的简支梁的临界荷载时,会导致两种不同的解决方案。这两种解决方案可能会导致在这些单轴对称梁中出现有明显差异的临界荷载。基于屈曲分析中所采用的经典变分原理,作者提出一个新的理论,用于分析薄壁构件的弯-扭屈曲作用。文中采用了这三个理论来分析悬臂结构的弯-扭屈曲作用。首先进行简短回顾,并使用三种不同理论对薄壁悬臂结构的弯-扭屈曲作用进行详细的对比分析。在纯弯曲和两种典型的横向分布荷载作用下对悬臂结构的屈曲进行分析,表明三种理论的确存在差异。采用第三种理论,考虑梁长度的变化和沿梁横截面纵轴的加载位置,对两种典型的横向分布荷载下双向对称悬臂结构的临界荷载进行预测,与现有解决方案和有限元分析所得到的关键结果进行对比,可知将新方法具有:良好的准确性和易用性等优点。

Previous studies by the authors revealed .that the two representative theories with slight differences between, widely used in investigating the flexural-torsional buckling of thin-walled beams, have led to two different solutions in well-known literature for assessing critical loads of simply supported beams of monosymmetric cross section. With these two solutions, significant differences in critical loads may be found for these monosymmetric beams. Based on the classical variational principle for buck-ling analyses, a new theory on the flexural-torsional buck-ling of thin-walled members was proposed by the authors. In this paper, this new theory as well as the other two typical theories is employed to investigate the flexural-torsional buckling of cantilevers. This paper first gives a brief review and a careful comparative study on the flexural-torsional buckling of thin-walled cantilevers employing three different buckling theories. Differences between these theories are demonstrated with investigations on buckling of cantilevers under pure bending and two typical transverse loads. Explicit solutions, capable of considering variations of beam length and loading position along the vertical axis of cross section, are presented for predicting the critical loads of doubly symmetric cantilevers under two typical transverse loads. Advantages of presented solutions, such as good accuracy and ease of use, are exploited through the comparisons of critical results with those from existing solutions and finite element analyses.