双模量悬臂梁在线性分布荷载作用下的Kantorovich解

来源期刊:中南大学学报(自然科学版)2014年第1期

论文作者:吴晓 杨立军 黄翀 孙晋

文章页码:306 - 312

关键词:双模量;悬臂梁;分布载荷;Kantorovich法;弯曲

Key words:bimodulous; cantilever beam; distributed loads; Kantorovich method; bending

摘    要:基于双模量悬臂梁在分布载荷作用下发生弯曲变形时,会形成各向同性的拉伸区和压缩区,为此,将双模量悬臂梁看成2种各向同性材料组成的层合梁,采用弹性理论建立双模量悬臂梁在均布载荷作用下的静力平衡方程,利用静力平衡方程确定双模量悬臂梁的中性面位置。在此基础上,利用Kantorovich法研究分布载荷作用下双模量悬臂梁的平面应力问题,推导出悬臂梁的应力公式,并将该应力公式计算结果与有限元法计算结果进行比较,以验证双模量悬臂梁的应力公式的可靠性。研究结果表明:在分布载荷作用下,双模量悬臂梁的平面应力问题不宜采用相同弹性模量弹性理论计算,而应该采用双模量弹性理论计算。

Abstract: Considering that the bimodulous cantilever can form isotropic compression and tensile area under distributed load, bimodulous cantilever was regarded as laminated beam composed of two kinds of otropic material. Static equilibrium equation of bimodulous cantilever under uniform load was established by using elastic mechanics theory. The location of neutral plane in bimodulous cantilever was determined by using static equilibrium equation. Plane stress problem of bimodulous cantilever under distributed loads was studied by Kantorovich method, and the stress formula was derived. The calculation results obtained by finite element were compared to verify the reliability of this method. The results show that the plane stress problem of bimodulous cantilever under distributed loads can not be computed using the same elastic modulus theory, and the bimodulous elastic theory should be used.

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