钢截面弹塑性分析的迭代法

An Iteration Method for Elastic-Plastic Analysis of Steel Section

对钢截面的弹塑性分析应用非线性方程组求解的牛顿-拉夫逊法,给出荷载-变形计算的一种正算算法,即任意给定一组轴力-弯矩,由迭代得到截面形心应变-曲率。基于截面纤维模型,采用平衡法推导截面刚度矩阵和计算截面承载力,为边缘屈服判断提供了方便,适用于各种形状和双向受力的截面。参考有限元程序设计方法,给出模块化的迭代流程,具有良好的通用性。给出手算算例,分别采用解析法和迭代法计算,结果吻合。

For the elastic-plastic analysis of steel section,the Newton-Raphson Procedure is applied to solve the nonlinear equations.One direct method is proposed to calculate the load and the deformation that is for any given axial forcemoment of a cross section,the corresponding centroid strain-curvature is obtained using an iterative method.Based on the fiber model and by equilibrium conditions,the section stiffness matrix is derived and the bearing capacity is calculated.This method provides convenience for yielding judgment and is suitable for all kinds of shape and biaxial load condition.By referring to the design procedure of finite element method,the iterative process of modular design is presented.One design example is then given,in which the analytical method and the iterative method are used respectively,and their results match well.