Buckling patterns of complete spherical shells filled with an elastic medium under external pressure
Buckling patterns of complete spherical shells filled with an elastic medium under external pressure
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DOI：
10.1016/j.ijmecsci.2012.02.001
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发表时间：
2011-03
期刊：
影响因子：
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通讯作者：
Motohiro Sato;M. Wadee;Kohtaroh Iiboshi;Takafumi Sekizawa;H. Shima
中科院分区：
文献类型：
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作者：
Motohiro Sato;M. Wadee;Kohtaroh Iiboshi;Takafumi Sekizawa;H. Shima
研究了充液充压球壳的临界屈曲特性。本文提出了一个基于小挠度薄壳理论的模型，并结合变分原理求解了该模型的方程。在精确公式中最初不使用轴对称和非延伸假设，弹性介质被建模为Winkler地基，即使用具有与壳体屈曲模式的波数无关的恒定地基模量的非耦合径向弹簧。基于瑞利-里兹方法的简化近似也被引入临界屈曲压力和模态数，具有相当程度的准确性。特性模态形状证明了广泛的材料和几何参数。建立相图，以获得所需的厚度半径，刚度比为所需的模式配置文件。本文的精确公式可以很容易地推广到更一般的非轴对称屈曲问题，而近似方法可以推广到后屈曲范围。
The critical buckling characteristics of hydrostatically pressurized complete spherical shells filled with an elastic medium are demonstrated. A model based on small deflection thin shell theory, the equations of which are solved in conjunction with variational principles, is presented. Axisymmetric and inextensional assumptions are not used initially in the exact formulation and the elastic medium is modelled as a Winkler foundation, i.e. using uncoupled radial springs with a constant foundation modulus that is independent of wave numbers of shell buckling modes. Simplified approximations based on a Rayleigh–Ritz approach are also introduced for the critical buckling pressure and the mode number with a considerable degree of accuracy. Characteristic modal shapes are demonstrated for a wide range of material and geometric parameters. A phase diagram is established to obtain the requisite thickness to radius, and stiffness ratios for a desired mode profile. The present exact formulation can be readily extended to apply to more general cases of non-axisymmetric buckling problems and the approximate method can be extended to the post-buckling range.