摘要
随着工程结构的轻型化、薄壁化,薄板结构稳定问题越来越受到重视,针对不同条件下薄板屈曲问题开展了大量研究。弹性支承上的薄板屈曲、边界弹性转动约束的薄板屈曲和刚性支承上边界转动约束的薄板屈曲问题已有相关文献,关于非加载边弹性转动约束、弹性支承上薄板屈曲问题的研究尚不充分。该文研究了非加载边弹性转动约束、均匀受压弹性支承矩形薄板弹性屈曲问题。由Ritz能量变分法得到了临界载荷计算公式,应用有限元分析证实了理论解的适用性。得到了屈曲半波数与板的纵横比、边界转动约束系数及支承刚度之间的关系式,支承刚度增加使屈曲半波数和屈曲系数增大。
The elastic stability of thin plate has been paid much attention to with the increasing application of light and thin-walled structures.Elastic buckling of thin plates under various kinds of boundary conditions have been studied,such as plates on elastic support,plates with elastic rotation restraint and plates on rigid support with rotation restraint.The elastic buckling of rectangle plate on elastic support with rotation restraint along unloaded edges is not thoroughly studied yet and is complemented in this paper.A set of formulas for critical load is obtained by Ritz variation method,and the applicability of theoretic solution is verified through FEM（Finite Element Method） simulation.Factors affecting buckling modes as ratio,stiffness of rotation restraint and elastic support are formulated explicitly.Results show that the increase of support stiffness leads to the rise of both buckling half-wave number and buckling coefficient.
出处
《工程力学》
EI
CSCD
北大核心
2010年第12期59-63,76,共6页
Engineering Mechanics
关键词
变分法
有限元分析
弹性屈曲
矩形薄板
弹性支承
转动约束
variation method
FEM simulation
elastic buckling
rectangle thin plates
elastic support
rotation restraint
