桁架结构稳定分析的几何非线性欧拉稳定理论

目前,桁架结构稳定分析有两个理论:经典的特征值理论和几何非线性临界点理论。前者发展较早,在许多结构力学书中都有叙述。但是经过工程应用检验,它过高地估计了结构抗稳定的能力。后者是20年前提出的,提出者认为适用于所有的扁桁架。经过几年的研究,作者连续提出三个稳定理论:线性与非线性欧拉理论;非线性临界点-欧拉理论和两个计算方法,进行桁架结构的线性和非线性截面优化设计。经过理论研究和对前人文献中数值例题的计算和比较,发现特征值理论不符合实际,临界点理论只适用于大扁度的桁架,而不适用于一切扁桁架。研究结果提供了若干有用的结论,给出了各种稳定理论的适用范围,指出了国际文献中若干例题的正确和错误,补充了桁架结构的稳定分析理论,使之更为完整和实用了。

Geometric nonlinear Eulerian stability theory for the stability analysis of shallow truss structures

Currently,there are two theories of stability: one is the classical eigenvalue theory,the other is nonlinear critical point theory.The former overestimated the stability resisting capacity of truss structures through examination of engineering application.The latter was presented to be suitable for all shallow truss structures.During the past years,the authors developed successively three theories of stability: linear and nonlinear Eulerian theories and critical point-Eulerian theory,and two algorithms for finding the critical load and optimum solution of cross-sectional area for truss structures undergoing small or large deformation.Through theoretical research and computation,and comparising some examples in international journals,the authors discovere that the eigenvalue theory is wrong;the critical point theory is only suitable for the shallow truss with large oblateness in the region of high-level load and large cross-sectional area,but it is wrong extended to all shallow truss structures.Research results of this paper provide us some useful conclusions: 1.the capabilities of various theories are given out,2.the correctness and incorrectness for some examples in international journals are pointed out.Thus,the theories of stability for truss structures are supplemented and become more complete and practical.