严格求解夹层圆柱壳在轴压下的轴对称失稳问题
A Rigorous Solution for the Axisymmetrical Buckling of Simply Supported Cylindrical Sandwich Shells under Axial Load
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摘要: 本文在文献[1]的基础上,用严格的方法求解两端简支的夹层圆柱壳在均匀轴压下的轴对称失稳问题.内、外表层很薄弹性模量又大,按薄壳理论处理;夹心较厚弹性模量又相当小,横向剪切变形的影响必须考虑,在研究夹层壳的整体失稳尤其是局部失稳时,横向的拉伸和压缩变形也不可忽略,用数学弹性力学的方法处理.本文导得了可求解轴对称整体失稳和局部失稳临界载荷的超越方程,用数值计算的方法可算得临界载荷的最小值.对于整体失稳的情况,给出算例,与夹层壳理论的解作了比较.Abstract: In this paper, based on Ref. [1] the axisymmetrical buckling of simply supported cylindrical sandwich shells under the action of uniform axial lood is solved by a rigorous method. The classical theory of shells is used for the two face sheets and the core is considered as a three-dimensional elastic body. A series of transcendental equations are obtained, from which the critical loads can be calculated by manericai methods. Numerical examples are given to compare with the solutions of sandwich shell theories.
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[1] 王震鸣,用数学弹性力学的方法研究弹性体的稳定问题.应用数学和力学,2, 1 (1981), 49-74. [2] 王震鸣.不对称构造的夹层圆柱壳在轴压下的稳定问题,中国科学院力学研究所研究生论文(1963年).中国科学院图书馆资料室和力学研究所资料室收藏. [3] Куршин Л.М.,Уравнения tрехслойных дилидрических оболочек, 3 (1958), 142-144. -
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