考虑轴力二阶效应的损伤梁弯曲摄动解

将损伤梁等效为阶梯型变刚度Euler-Bernoulli梁，利用Heaviside广义函数，给出了阶梯型变刚度梁抗弯刚度的统一表达式．在此基础上，考虑轴向压力二阶效应，并以损伤为摄动参数，得到了均布横向载荷作用下，简支损伤梁弯曲挠度的一阶和二阶摄动解析解，并数值分析了摄动解析解的精度和损伤梁的弯曲变形特性，结果表明：随着轴向压力和刚度损伤参数的增加，挠度一阶和二阶摄动解析解误差增加，挠度二阶摄动解析解误差通常小于其一阶摄动解析解误差，且二阶摄动解的误差很小，满足工程应用的精度．同时，损伤梁的挠度和转角分布与完整梁的挠度和转角分布差异较大，在刚度变化位置处损伤梁转角斜率存在突变．这些结果可为轴力作用下Euler-Bernoulli梁损伤识别提供理论支撑．

Perturbation Solution of Bending of Damage Beam with Second-Order Effect of Axial Compressive Load

Regarding the damage beam as a stepped varying-stiffness Euler-Bernoulli beam, the unified expression of bending stiffness of the stepped varying-stiffness beam was presented using the generalized Heaviside function. On this basis, considering second-order effect of the axial compressive load, the first-order or second-order perturbation analytical solutions of bending deflection of a simply-supported damage beam subjected to a uniform transverse load were obtained with damage as the perturbation parameters, and the precisions of these perturbation solutions and the bending deformations of the damage beam were examined numerically.  It is shown that the errors of the first-order or second-order perturbation analytical solutions of deflection increase with increase of the axial compressive load and the stiffness damage of the beam, and the error of the second-order perturbation analytical solution of deflection is generally less than that of the first-order perturbation analytical solution of deflection. The error of the second-order perturbation analytical solution is rather small and is acceptable for engineering applications. Furthermore, there exist major differences of deflections and rotational angles between the damage beam and the intact beam, and there exists a jump of slope for the rotational angle of the damage beam. All these results provide the theoretical support for damage identification of Euler-Bernoulli beam subjected to axial load.