曲线梁研究进展

曲线梁在工程中的应用非常广泛, 但由于曲率的影响, 导致梁内弯矩和扭矩的耦合, 使得 曲线梁的研究相对直梁非常复杂. 本文从4个方面较为详细地评述了近年来国内外曲线梁的 研究进展情况. 从曲线梁的平衡方程、几何方程和基本微分方程出发, 概述了曲线梁静动力 学的基本理论、建模及分析方法; 面内面外振动及分析方法; 非线性问题及分析方法; 特别 评述了有限元单元法在曲线梁研究中的应用, 论述了各种曲梁单元的优缺点; 对复合曲线梁 的发展及理论研究进行介绍; 推导了空间曲线梁非线性动力学方程; 最后提出了值得进一步 研究的方向及采用的方法.

ADVANCES OF RESEARCH ON CURVED BEAMS

Curved beams are widely used in space engineering, mechanical engineering and civil engineering. Due to the coupling of flexure and torsion, the research on curved beams is difficult as compared with that on straight beams. Some recent advances of research on curved beams are reviewed in this paper. Based on a discussion on equilibrium equations, strain-displacement relations and governing equations of curved beams, a summary of basic static theories and dynamic theories, and modeling methods for curved beams, and inplane vibrations and out-plane vibrations is given in this paper. In addition, the nonlinear problems and the finite element methods for curved beams, and recent advances of research on curved composite beams are also reviewed. Then, the nonlinear equations of motion are given. Finally, the promising future developments in this area are discussed.