中厚夹层圆柱扁壳的屈曲分析  

Bucking analysis of moderate thickness sandwich cylindrical shallow shells

作　　者：肖勇刚[1] 郭鑫[1] 戴业 

机构地区：[1]长沙理工大学土木与建筑学院,长沙410004

出　　处：《应用力学学报》2017年第4期710-715,共6页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(51108047)

摘　　要：基于一阶剪切变形中厚圆柱壳理论,考虑夹心层的面内刚度,根据中厚夹层圆柱扁壳的几何方程、本构关系、平衡方程,建立了中厚夹层圆柱扁壳小挠度屈曲的微分方程;应用广义傅里叶级数解法,得到了四边简支条件下中厚夹层圆柱扁壳屈曲的临界荷载表达式。该表达式可以退化为硬夹心夹层板的表达式,表明本文推导过程的正确性。本文还讨论了夹心层的弹性模量和泊松比以及中厚夹心圆柱扁壳的长宽比和厚度对扁壳屈曲荷载的影响。结果表明:临界荷载与夹心层的弹性模量和泊松比成正比,与扁壳的长宽比和厚度成反比。Based on the first-order shear deformation of thick cylindrical shell theory and considering the in-plane stiffness of sandwich layer, the thick sandwich cylindrical shallow shell small deflection buckling differential equation are established according to the geometric equation of thick sandwich cylindrical shallow shell, constitutive relation and the equilibrium equations. The application of generalized Fourier series method to get the critical load expressions the for buckling of moderately thick sandwich circular cylindrical shells under boundary condition of simply supported on four sides. The equations can degenerate to the expression of rectangular sandwich plates with hard core which demonstrates the correctness of the method. Effects of the elastic modulus and Poisson's ratio of the sandwich layer, the ratio of length to width and thickness ratio on the buckling load of the shallow shell are discussed. Result show that the critical load varies directly as the elastic modulus and Poisson's ratio of the sandwich layer and inversely as the ratio of length to width and thickness ratio.

关 键 词：中厚夹层圆柱扁壳 一阶剪切变形 广义傅里叶级数 临界荷载 小挠度屈曲 

分 类 号：TU33[建筑科学—结构工程]