中心分布压力作用下圆底扁球壳的变形和稳定性*
Deformations and Stability of Spherical Caps under Centrally Distributed Pressures
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摘要: 本文研究圆底扁薄球壳在中心分布压力作用下的轴对称大挠度变形和稳定性.提出了求解圆底扁球壳非线性方程的牛顿-样条函数方法.分别讨论了当几何参数λ固定时,载荷作用半径的变化对壳体失稳的影响,以及当载荷作用半径固定时,几何参数λ的变化对壳体稳定性的影响.分析了临界载荷曲线与屈曲模式之间的关系.并就v=0.3的情形给出了数值分析结果.Abstract: In this paper the deformations and stability in large axisymmetric deflection of spherical caps under centrally distributed pressures are investigated. The Newton-spline method for solving the nonlinear equations governing large axisymmetric deflection of spherical caps is presented. The buckling behavior is studied for a cap with fixed geometry when the size of the loaded radius is allowed to vary, and for a fixed loaded radius when the shell geometry is allowed to vary. The influence of the buckling modes on the critical loads is analysed. Numerical results are given for v=0.3.
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[1] Stephens, W.B. and R.E. Fulton, Axisymmetric static and dynamic buckling of spherical caps due to centrally distributed pressures, AIAA J., 7, 11(1969), 2120-2126. [2] Mescall, J.F., Large deflections of spherical shells under concentrated, distributed and ring loadings, Proc. 4th Southeastern Conf. on Theo. Appl. Mech.(1968), 183-197. [3] Fitch, J.R. and B. Budiansky, Buckling and postbuckling behavior of spherical caps under axisymmetric load, AIAA J., 8, 4(1970), 686-693. [4] 宋卫平,圆平板的轴对称非线性弯曲,兰州大学学报(自然科学版),22, 1, (1986), 14-23. [5] 李岳生、齐东旭, 《样条函数方法》,科学出版社(1979). [6] Mescall, J.F., Large deflections of spherical shells under concentrated loads, J. Appl. Mech., 32, 4(1965), 936-938. -
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