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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 medium-thick cylindrical shell theory, considering the in-plane stiffness of the sandwich layer, according to the geometric equation, constitutive relation and balance equation of the medium-thickness cylindrical flat shell, a small-deflection buckling mid-thickness cylindrical flat shell was established. Differential equations; Applying the generalized Fourier series solution method, we obtain the expression of the critical load for the buckling of a mid-thick sandwiched cylindrical flat shell under the condition of simple support. This expression can be degenerated into an expression of a hard sandwich sandwich plate, indicating the correctness of the derivation process in this paper. The paper also discusses the influence of the elastic modulus and Poisson’s ratio of the sandwich layer and the aspect ratio and thickness of the medium-thickness cylindrical flat shell on the buckling load of the flat shell. The results show that the critical load is proportional to the elastic modulus and Poisson’s ratio of the sandwich layer and inversely proportional to the aspect ratio and thickness of the flat shell.