非圆弧深拱稳定承载力的随机性研究

受参数随机性的影响，拱结构的稳定承载力也具有随机性。蒙特卡洛方法是承载力随机分析的可靠方法，但计算量巨大，选取合适的数学模型替代耗时的稳定承载力有限元模型，是降低计算成本的关键。解析解是最优的替代模型，但拱结构稳定解析解研究主要集中于圆弧拱与抛物线浅拱，而拱桥中常用的抛物线、悬链线等非圆弧深拱的研究未见报道，该问题是稳定理论由裸拱向拱桥发展的瓶颈。本项目以非圆弧深拱为研究对象，提出屈曲实用解析解的近似曲线积分法、极限承载力实用表达式的特殊响应面法，将得到的实用公式用以替代有限元模型并进行随机分析；提出统计特征参数响应面法，回归承载力的均值方差表达式；最后，通过稳定承载力随机性的模型试验，来验证理论研究的成果。通过本项目的研究，能得到非圆弧深拱稳定承载力的近似解、均值方差的实用公式，研究成果可用于实际拱桥承载力评估，所用方法可推广至一般裸拱和拱桥稳定分析，具有较大的理论意义与工程实用价值。

Because it has stochasticity in arch structure parameters, its buckling and ultimate load carrying capacity also has some randomness. The reliable method of stochastic analysis was Monte Carlo simulation method, but it need high calculation cost, so, using appropriate mathematical model to replace the time-consuming finite element model became the key technology. The best mathematical model was analytical solution, but only circular and parabolic shallow arch analytical solution was researched, non-circular deep arch fruits was not published until now, though it was most used in arch bridge and a bottleneck problems from arch structure to arch bridge stability theory. It takes non-circular deep arch as research object in this project, and proposes an approximate curve integration method for practical buckling analytical solution, a special response surface method for load carrying capacity practical expression; These practical expressions will replace finite element model in stochastic analysis, and a basic statistical characteristic response surface method will proposed for mean and variance practical expression regression; In the end, a non-circular deep arch stochastic model test will be done for verify theoretical stochastic analysis fruits. Through this project, it can obtain buckling and ultimate load carrying capacity approximate expression, mean and variance practical expression in non-circular deep arch, the research fruits can be applied to actual arch bridge load carrying capacity assessment, the research methods can be used in normal arch structure and arch bridge stability analysis, in this mean, the project has both significant theoretical value and engineering application value.