均布外压下弹性支撑扁球壳的非线性稳定性分析

均匀腐蚀减薄的扁球壳被简化为边缘弹性支撑的扁球壳,应用大挠度板壳理论的修正迭代法,对均匀外压作用下的弹性支撑扁球壳的非线性稳定性问题进行了求解,得到了二次近似的解析解。与极限边界下的经典理论解和弹性支撑条件下的非线性有限元解的对比结果表明了该方法的准确性。

Approximate Critical Load in Analytic Form of Uniformly Corroded Shallow Spherical Shell under Uniform External Pressure

Aim.Oil storage tank roofs,which have been observed to undergo corrosion under service conditions,are usually designed as shallow spherical shells subjected to uniform external pressure,and it is necessary to determine the critical load of this locally thinned shallow spherical roof.We now present our approximate but very quick way of calculating this critical load.In this paper,we explain how to simplify the locally thinned spherical roof into a shallow spherical shell with elastic support(Fig.2).In this abstract,we add some pertinent remarks to listing the following three topics of explanation:(1) fundamental equations,(2) solutions by modified iteration method,(3) contrastive analysis;under topics one and two,based on the above-mentioned simplification,we deduce a second-order algebraic equation to compute approximate critical deflection(eq.18),which is substituted into eqs.(17) and(19) in the full paper, thus obtaining the upper critical load of the shallow spherical shell;under topic three,to examine the effectiveness of the method proposed in this paper,we do the contrastive analysis of two scenarios(Fig.3 and Table 1).The contrast results preliminarily show that the average error of the four upper critical loads calculated is less than 10%,indicating that the present method is effective.