具有初始缺陷扁球面网壳在大挠度下的非线性动力学特性  

Non-linear stability of the shallow reticulated spherical shell considering initial imperfect with stationary and dynamic load

作　　者：栗蕾[1] 黄义[1,2] 

机构地区：[1]西安建筑科技大学土木工程学院,陕西西安710055 [2]西部建筑科技国家重点实验室(筹),陕西西安710055

出　　处：《西安建筑科技大学学报（自然科学版）》2009年第1期32-36,共5页Journal of Xi'an University of Architecture & Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目(59978038)

摘　　要：根据薄壳非线性动力学理论和网格结构拟壳法,研究了扁球面网壳在动、静荷载协同作用下的混合边值问题,先由大挠度非线性控制方程,在夹紧固定的边界条件下,给出了扁球面网壳大挠度及张力的解.然后把该大挠度解看作系统的初始缺陷并利用扁球面网壳的非线性动力学变分方程和协调方程,在同样的边界条件下,应用Galerkin方法得到一个含二次和三次的非线性动力学方程,采用Floquet指数方法研究了扁球面网壳在大挠度下的分岔问题,讨论了平衡点(奇点)邻域的稳定性问题.绘出有、无静载荷时平衡点的相对位置,数值结果表明静变形的变形对其中一个平衡点的位置影响较大.According to the nonlinear dynamical theory of plate-shell and ideology of continuous quasi-shell method, the mixed boundary value problems were discussed the shallow reticulated spherical shell under the load of both dynamic and static. Firstly, large deflection of the system was given by nonlinear governing equations and under the fixed edges boundary condition. Sewndly then the large deflection was taken as initial imperfect and using nonlinear dynamical variation equations and compatible equations of the shallow reticulated spherical shells. A nonlinear differential equation including quadric and cubic items was obtained by the Galerkin method under the fixed edges boundary condition. The problem of bifurcation of system was studied; the problem of statistic at the equilibrium of the system was discussed by exponent Floquet. Lastly the relative positions of the equilibrium point of the system with or without the static load were plotted. Especially, it is evident that the initial imferfect impacts greatly on one of the equilibriums.

关 键 词：初始缺陷 扁球壳 非线性 分叉 

分 类 号：O343.5[理学—固体力学]