刘树堂　朱文正

摘要：基于曲杆单元应力弦长关系和矩阵微分理论，推导出曲杆单元在弹性与弹塑性状态下的切线刚度矩阵精确公式。研究构件取理想弹塑性材料，结构支座取固定铰支座和可动铰支座2种约束情况，考虑构件具有初弯曲，采用曲杆单元切线刚度矩阵和广义位移控制法，取结构自重为参考荷载，对节点铰接的K8大跨单层网壳结构进行弹塑性后屈曲分析。结果表明：曲杆单元切线刚度矩阵公式精确性很高，可有效用于大型铰接单层网壳弹塑性后屈曲分析。

关键词：曲杆单元；切线刚度矩阵；单层网壳；后屈曲分析；弹塑性屈曲；广义位移控制法

中图分类号：TU393.3文献标志码：A

Abstract： The accurate tangent stiffness matrix formula of curved lever unit at elastic and elasticplastic states was derived based on stresschord length relation and matrix differential theory. The research component was ideal elastic plastic material. The structure support included 2 kinds of constraint conditions of the fixed hinge support and the movable hinge support. The initial bending of the component was considered， the tangent stiffness matrix of curved lever unit and the generalized displacement control method were adopted， and the structure weight was taken as the reference load. The elastic and plastic postbuckling analysis of K8 largespan single layer reticulated shell structures was carried out. The results show that the tangent stiffness matrix of curved lever unit is accurate， and can be used to the elasticplastic postbuckling analysis of large hinged single layer reticulated shells.

Key words： curved lever unit； tangent stiffness matrix； singlelayer reticulated shell； postbuckling analysis； elasticplastic buckling； generalized displacement control method

0引言

单层网壳结构力学性能好、重量轻、造型优美，在大型体育场馆屋盖结构中得到广泛应用。从20世纪60年代以来，关于单层网壳结构稳定性及极限荷载的研究一直备受关注，已开展了大量理论与试验研究。单层网壳结构矢跨比较小，构件长细比较大，在垂直荷载作用下结构几何非线性特别显著，往往在构件还没有屈服时结构就发生失稳破坏。目前在单层网壳结构极限荷载分析中，构件力学特性常用直杆单元来模拟，因为直杆单元的应力应变关系简单，易于完成结构极限荷载分析。然而，实际构件并非直杆，其在轧制、加工制作、运输和安装等机械作用过程中已产生微小初弯曲，基于直杆单元的结构极限荷载分析忽略了构件初弯曲对极限荷载降低的影响。……