摘要
球面薄壳结构在建筑和其他工程领域应用广泛。这类结构的工作性能往往取决于其稳定特性,因此如何正确地预测其稳定承载力,一直是科研和工程设计人员十分关注的问题。本文首先采用ABAQUS对球面薄壳结构进行了非线性有限元分析。结果显示,球面薄壳的荷载-位移曲线存在一个近似水平的后屈曲“平台”,其所对应的即为球壳结构的后屈曲承载力。进而根据壳体屈曲后的变形特点和应变能分布特点并结合能量守恒原理,推导了球面薄壳在径向和竖向两种均布荷载作用下的后屈曲承载力计算公式,并作为考察其实际承载力的参考值。通过对典型算例进行非线性有限元分析,证明了该公式的正确性。
单层球面网壳结构受力合理、覆盖跨度大,兼有杆系结构和薄壳结构的优点,亦广泛应用于建筑工程中。本文对单层球面网壳结构进行了拟壳化处理,将离散的网壳转化为等效的连续壳体。然后把预测连续球壳的后屈曲荷载计算公式应用于单层球面网壳结构,用以预测球面网壳结构的稳定承载力。典型算例的有限元分析结果显示,离散的网壳结构的后屈曲荷载-位移曲线的下限与等效连续壳的荷载-位移曲线的“平台”是相当接近的,说明所推导公式确能用以预测球面网壳结构的稳定承载力。这不仅扩大了所推导公式的应用范围,而且提供了一种除借助计算机和复杂的有限元分析程序以外的,更准确地预测球面网壳结构稳定承载力的有效途径。
Thin spherical shells are widely used in civil engineering and other engineering branches. The structural behaviour of these structures is usually dominated by the buckling characteristics. To predict correctly the buckling load of these structures has long been a primary concern of researchers and the design engineers. In this study, nonlinear finite element modelling of the buckling behaviour of thin spherical shells was conducted using ABAQUS. It was revealed that there is a nearly-horizontal plateau in the post-bucked load-deflection curves, corresponding to a nearly-constant post-buckling load. Based on the deformation of the shell and the strain energy distribution in the deformed shell body, and combined with the theorem of work and energy, an empirical formula for the post-bucking load was derived, which can be used to predict the load-carrying capability of thin spherical shells under uniform radial load or vertical load. By means of nonlinear finite element modelling, the formula was validated.
Single-layer reticulated spherical shells, integrating the advantages of both trusses and thin shell structures, are also widely used in civil engineering to cover large spaces, with load being transferred in ideal manners. The continuum analogy method was applied to single-layer reticulated spherical shells, and the formula derived was thus extended to these structures. Nonlinear finite element modelling also showed close correlation between the lower bound of the post-buckling load-deflection curves of the discrete single-layer reticulated spherical shells and the post-buckling plateau of the equivalent continuous spherical shells. This proves the feasibility of using the derived formula for thin spherical shells to predict the load-carrying capability of single-layer reticulated spherical shells. By using the idea of post-buckling load, this study provides a way to predict the load-carrying capability of both thin spherical shells and single-layer reticulated spherical shells correctly, without resorting to computer and the rather complicated software.
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