轴向可压缩两铰圆弧拱静水压力屈曲荷载研究

Research on buckling loads of compressible hinged-circular arch under uniform hydrostatic pressure

为了求得考虑轴向压缩变形的两铰圆弧拱的平面内临界屈曲荷载精确解,需将拱的轴向刚度作为影响其面内稳定性的重要因素,对两铰圆弧拱在径向静水压力作用下的轴向压缩变形加以考虑。基于经典理论解的求解过程,结合拱的平衡微分方程及边界条件,对承受均布静水压力且考虑轴向压缩变形的圆弧拱进行了分析,求得了该条件下拱的平面内反对称临界屈曲荷载计算式。为了验证该计算式的准确性,采用非线性有限元法对均布静水压力下的圆弧拱进行了分析,并将有限元分析结果与公式解及铁木辛柯解析解进行了对比。结果表明,相同条件下该方法与有限元分析结果及解析解均吻合良好。对不同矢跨比的拱进行了参数化的对比计算,结果表明,文中推导的计算式具有普遍适用性,能满足工程的计算精度需要。

To derive the accurate buckling loads of the compressible hinged-circular arch under uniform hydrostatic pressure,the axial stiffness of arch should be defined as an important factor to consider the axial compression. Based on the solving process of traditional buckling theory,the equilibrium differential equations and boundary conditions were utilized to analyze the circular arch under radial uniformly distributed load. The formula of anti-symmetric critical buckling load was deduced with the consideration of axial compression deformation. In order to verify the formula,the nonlinear finite element method was used to solve this problem. Through the comparison of numerical method,the proposed formula in this paper and the analytic solution of Timoshenko,it is shown that the solution of buckling load formula is close to that of numerical method and analytic method. By the comparison of arches with different rise-tospan ratios,it shows that the formula given by this work is of general application,and its accuracy can satisfy the demand of practical engineering.