刘建林^*

（  中国石油大学（华东）工程力学系；  ）

摘要： 本文研究了悬臂梁、Arc型梁以及S型梁随着一无量纲参数的变化而逐渐演化的过程。求得了悬臂梁与基底接触形成Arc型梁以及S型梁的条件。并且通过最小势能原理，采用两种方法推导出了S型梁的临界悬空长度。通过叠加原理，求得了形成Arc型梁时基底的支持力。给出了随着无量纲参数的变化各种梁的挠曲线。这些分析对于工程设计，以及MEMS、生物的毛细黏附等有一定的参考价值。
关键词： Arc型梁；S型梁；变分法；横截条件；临界悬空长度

Liu Jianlin^*

（  Department of Engineering Mechanics, China University of Petroleum；  ）

Abstract： The evolution process with the change of a non-dimensional variable about the cantilever, Arc shaped beam and S shaped beam is investigated in this paper. The condition of the cantilever contacting the substrate and becoming the Arc shaped beam or the S shaped beam is presented. The critical hanging length of the S shaped beam is derived with two methods, which are based upon the principle of least potential energy. The constraint force of the substrate for the Arc shaped beam is also solved through the principle of superposition. Finally, all kinds of deflection curves are given with the change of the non-dimensional variable. These analyses may be beneficial to engineering design, MEMS and capillary adhesion in biology, etc.

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