一种基于Fourier-Bessel级数求解FRP筋粘结锚固径向反应的解析方法

根据FRP筋表面沿纵向呈周期的特性,提出了一种基于Fourier-Bessel级数求解FRP筋粘结锚固径向反应的实用解析方法。从轴对称问题的基本方程出发,利用标准化Fourier-Bessel级数三角函数等式,推导了修正贝塞尔方程,得到了各向同性材料和横观各向同性材料的解析解,最后针对FRP筋粘结式锚具的边界条件,得到了钢套筒约束的粘结介质以及FRP筋在径向应力作用下的位移和应力计算公式。解析解与有限元解基本一致,验证了基于Fourier-Bessel级数求解FRP筋粘结锚固的径向反应是一种可靠的、实用的解析方法。计算表明,在径向应力作用下,对于钢套筒约束的粘结介质和CFRP筋,轴向位移在粘结界面的径向应力中心位置处最大;钢套筒外壁的径向位移仅为粘结界面处的径向位移1/8;CFRP筋的径向位移在中心轴为零,并向筋材表面线性增加。

Solutions of Radial Response of Anchorage Performance of FRP Tendon Based on Fourier-Bessel Series

According to the characteristic of periodic intended surface along longitudinal direction of Fiber Reinforced Polymer/Plastics(FRP) tendon,a reliable analytical method was developed for radial response of bond-type anchorage system based on Fourier-Bessel series solutions.Using the governing equations for a general axisymmetric problem and the trigonometric functions as the orthonormal basis in the Fourier series,the modified Bessel equations were presented,and the analytic solutions were subsequently obtained for isotropic and transversely isotropic media.Finally combining with the boundary conditions of bond-type anchorage system for FRP tendons,the calculation formulas of stresses and displacements were obtained for hollow cylinder medium and FRP tendon whose walls are subjected to a concentrated distribution of radial traction.The agreement between the analytical and numerical solutions suggests that the analytical solution is correct.In other words,the reliability of the presented approaches was proved.The analytical results show that the maximum axial displacement is found at the position of radial stress center in bond interface for hollow cylinder medium and CFRP tendon.The investigations show that(1) the ratio of the radial displacements of hollow cylinder and bond medium is 1/8;(2) the radial displacement is zero in center axis of solid cylinder CFRP tendon and increases with radial radius of solid cylinder CFRP tendon increasing.