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Buckling mechanism of thin-walled arches with composite polyhedral shapes

机译：复合多面体形状的薄壁拱弯机机理

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摘要

The present work is concerned with the pressure capacity of the thin-walled composite arches with different polyhedral shapes. The analytical derivation process involves the employment of the energy theory, the thin-walled shell principle, and the assumed displacement field. The total potential energy formulae of the polyhedral arch are expressed analytically. By taking the first derivatives of the energy function to the two unknowns, it is effortless to obtain two equations of equilibrium. The critical buckling pressure and the equilibrium paths are expressed by solving these two equations of equilibrium simultaneously. Subsequently, good agreements are reached when the proposed buckling pressure is compared with other closed-form expressions for a circular arch with a constant radius. Finally, the effect of the geometric parameters on the critical buckling pressure is analyzed. An enhancement factor is introduced to express the ratio of the buckling pressure between the arch with the polyhedral shapes and the traditional circular cross-section. It is found the enhancement factor reduces when the values of N increases and the ratio of thickness-to-radius increases, respectively. Therefore, a polyhedral arch with a small value of N and a small ratio of thickness-to-radius is recommended in engineering applications.
机译：本作工作涉及薄壁复合拱的压力容量，具有不同的多面体形状。分析衍生过程涉及能量理论，薄壁壳体原理和假设的位移场的就业。多面体弓的总势能公式分析表达。通过将第一衍生物的能量函数占用到两个未知数，因此获得两种平衡方程是毫不费力的。通过同时求解这两个平衡方程来表达关键屈曲压力和平衡路径。随后，当建议的屈曲压力与具有恒定半径的圆形拱的其他闭合形式的表达式进行比较时，达到良好的协议。最后，分析了几何参数对关键屈曲压力的影响。引入增强因子以表达拱形与多面体形状与传统圆形横截面之间的弯曲压力的比率。当N增加的值增加并且厚度到半径的比例增加时，可以减少增强因子。因此，在工程应用中建议使用具有少值N值的多面体拱形和厚度到半径的小比例。

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