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首页> 外文期刊>Journal of Engineering Mechanics >Lateral-torsional buckling of singly symmetric tapered beams: Theory and applications
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Lateral-torsional buckling of singly symmetric tapered beams: Theory and applications

机译：单对称锥形梁的横向扭转屈曲：理论与应用

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摘要

A general variational formulation to analyze the elastic lateral-torsional buckling (LTB) behavior of singly symmetric thin-walled tapered beams is presented, numerically implemented, validated and illustrated. It (1) begins with a precise geometrical definition of a tapered beam; (2) extends the kinematical assumptions traditionally adopted to study the LTB of prismatic beams; (3) includes a careful derivation of the beam total potential energy; and (4) employs Trefftz's criterion to ensure the beam adjacent equilibrium. In order to validate and illustrate the application and capabilities of the proposed formulation, several numerical results are presented, discussed and, when possible, also compared with values reported by other authors. These results (1) are obtained by means of the Rayleigh-Ritz method, using trigonometric functions to approximate the beam critical buckling mode, and (2) concern the critical moments of doubly and singly symmetric web-tapered I-section simply supported beams and cantilevers acted by point loads. In particular, one shows that modeling a tapered beam as an assembly of prismatic beam segments is conceptually inconsistent and may lead to rather inaccurate (safe or unsafe) results. Finally, it is worth mentioning that the paper includes a state-of-the-art review concerning one-dimensional analytical formulations for the LTB behavior of tapered beams.
机译：提出，数值实现，验证和说明了一种用于分析单对称薄壁锥形梁的弹性横向扭转屈曲（LTB）行为的通用变分公式。它（1）从锥形束的精确几何定义开始; （2）扩展了传统上用于研究棱柱光束LTB的运动学假设; （3）包括仔细推导电子束的总势能; （4）采用Trefftz准则来确保光束邻近平衡。为了验证和说明所提出配方的应用和功能，提出，讨论了一些数值结果，并在可能的情况下，还与其他作者报告的值进行了比较。这些结果（1）是通过瑞利-里兹（Rayleigh-Ritz）方法获得的，使用三角函数逼近了梁的临界屈曲模式，并且（2）关注了双对称和单对称腹板I型截面简支梁的临界弯矩，以及悬臂受点荷载作用。特别地，显示出将锥形光束建模为棱柱形光束段的组合在概念上是不一致的，并且可能导致相当不准确的结果（安全或不安全）。最后，值得一提的是，本文包括有关锥束LTB行为的一维分析公式的最新技术综述。

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