单双层球面扁网壳连续化方法非线性稳定理论临界荷载的确定

NON-LINEAR STABILITY CRITICAL LOADS OF SINGLE-LAYER AND DOUBLE-LAYER RETICULATED SPHERICAL SHALLOW SHELLS BASED ON CONTINUUM ANALOGY METHOD

连续化方法是研究网壳结构稳定问题的一种重要途径,目前用连续化理论分析球面扁网壳的稳定问题还存在欠缺和不足。运用经典的壳体理论,将单层和双层球面扁网壳等代为实体薄壳并建立非线性稳定理论混合法基本方程,再用李兹法求出球面扁网壳上下临界荷载计算公式。通过参数分析,首次从1000多个算例中得出了正三角形网格单层和双层常用球面扁网壳临界荷载系数的精确解。与国内外现有文献的计算公式相比,结果更为完善和正确。即便在有限元技术日益成熟的今天,用连续化方法计算的网壳结构临界荷载仍然对工程设计有重要指导作用,也是有限元方法分析网壳稳定性的对比和补充。

Continuum analogy method is an important approach for the stability analysis of reticulated shells, but there still exist imperfections in applying this method to reticulated spherical shallow shells. Based on the classical shell theory, single-layer and double-layer reticulated spherical shallow shells were treated as equivalent thin solid shells. Governing equations for the equivalent shells were established based on the non-linear stability theory and then solved by the Ritz method to provide theoretical upper and lower critical loads. Through a major parametric study (more than 1000 numerical examples), theoretical solutions for the critical load coefficients of reticulated spherical shallow shells with normal triangle grids were obtained. Compared with existing solutions, the proposed formulae are more perfect and accurate. Though the finite element technology becomes quite popular today, the continuum analogy method still provides an important guidance to the determination of critical loads of reticulated shells, and is also a supplement to the finite element method in the stability design of reticulated shells.