不圆度对圆环和圆管静水压力下临界荷载的影响  

Influence of out-of-roundness on the critical loads of circular rings and circular tubes under hydrostatic pressure

作　　者：邓长根[1] 

机构地区：[1]同济大学建筑工程系,上海200092

出　　处：《计算力学学报》2011年第6期851-857,共7页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(50478107)资助项目

摘　　要：采用最小二乘法求解曲率半径对称波动变化的非理想圆环在均匀静水压力作用下的平面内稳定性问题,分别求得了反对称屈曲和对称屈曲的临界荷载系数。当不圆度参数β=0.4时,反对称屈曲的临界荷载系数降低67.71%。用最小相对误差拟合法得到了精度较高的临界荷载系数拟合公式,其最大相对误差仅为±0.76%。采用平面应变假设,推广得到非理想长圆管在均匀静水压力作用下的临界荷载计算公式,并应用于某工程中长圆钢管的局部稳定性计算,算例中当外径在最大允许外径和公称外径之间波动变化时,临界荷载降低2.58%。The in-plane buckling problem of a circular ring with symmetric fluctuant radius of curvature under uniform hydrostatic pressure is solved with Least Squares Method, and the critical load coeffi- cients of antisymmetric buckling and symmetric buckling are calculated, respectively. The critical load coefficient of antisymmetric buckling is reduced by 67.71% for out-of-roundness parameter β=0. 4. High precision formulas, the relative errors of which are within ±0. 76%, of the critical load coefficients are obtained by minimum-relative-error data fitting. Based on the plane strain hypothesis, the critical load formulas are extended to a long circular tube with fluctuant radius of curvature under uniform hydrostatic pressure. The formulas are applied to the calculation of local buckling of a long circular steel tube, and the critical load is reduced only by 2.58 % for the diameter fluctuating between the allowable maximum diameter and the nominal diameter.

关 键 词：圆环 临界荷载 不圆度 静水压力 最小二乘法 

分 类 号：TU311.2[建筑科学—结构工程]