中文摘要：

为了进行不均匀壁厚圆环和圆管的临界外压计算,从研究壁厚关于2个正交轴对称且波动变化的圆环在均匀静水压力作用下的平面内稳定性入手,采用傅里叶级数逼近圆环屈曲的变系数常微分方程的解,导出圆环屈曲的特征方程,分别求得圆环对称屈曲和反对称屈曲的临界外压系数.用最小相对误差拟合法得到了精度较高的临界外压系数拟合公式,其最大相对误差仅为±0.68%.分析表明,壁厚不均匀度越大,临界外压越小.采用平面应变假设,推广得到超长变壁厚圆管在均匀静水压力作用下的临界外压计算公式,并应用于某煤矿工程中超长圆钢管的局部稳定性计算,算例中当壁厚在公称壁厚和最小允许壁厚之间波动变化时,临界外压降低18.21%.

英文摘要：

The critical pressure calculation of circular rings and pipes with non-uniform wall thickness is investigated.The in-plane buckling problem of a circular ring with double symmetrically fluctuated non-uniform thickness under external uniform hydrostatic pressure is approximated with Fourier series,and the critical pressure coefficients of symmetric buckling and anti-symmetric buckling are solved,respectively.High precision formulas,the relative errors of which are within±0.68%,of the critical pressure coefficients are obtained by minimum-relative-error data fitting.Formulas show that the greater the unevenness of wall thickness,the smaller the critical pressure.Based on the plane strain hypothesis,the critical pressure formulas are extended to be suitable for a long circular pipe with fluctuantly non-uniform thickness under external uniform hydrostatic pressure.The formulas are applied to the calculation of local buckling of a long circular steel pipe in a coal project,and the critical pressure reduced by 18.21% for the wall thickness fluctuating between the nominal thickness and the allowable minimum thickness.