抛物线拱面内位移近似解析方法

Approximate analytical method for in-plane deformation of parabolic arches

针对抛物线拱面内线性位移没有解析解的现状,提出一种高精度的近似解析方法用以解决这个问题。在非圆弧拱面内应变表达式的基础上,基于虚功原理推演了面内线性平衡微分方程,并使用泰勒展开近似得到微分方程的近似解析解;基于弹性压缩与压缩应变沿弧长积分相等的原理,推演得到水平反力的解析,进而得到满足所有边界的竖向位移、水平位移及面内转角的高精度近似解析。算例分析结果表明,本文方法与有限元数值解吻合较好,可以作为实用公式为工程界参考。

Because of no analytical solution for the in-plane linear deformation of parabolic arches,this paper proposed a high accurate approximate analytical method to solve this problem.The in-plane linear equilibrium differential equation was derived based on the strain-displacement expression for non-circular arches and the virtual work principle,and the approximate analytical solution of the differential equation was obtained by using the Taylor approximate method.The analytical solution for horizontal reaction force of fixed parabolic arches was deduced from the basic principle that the change of curve arc length of fixed parabolic arches can be calculated by using the axial force as well as the membrane strain,and then the approximate close-formed solutions for vertical displacement,horizontal displacement and rotation displacement were derived.Comparisons with the results of finite element method demonstrate that the calculation results of proposed method agree well with the finite element simulationresults,and the proposed approximate analytical solutions can be used for the practical expressions of arch bridges.