（1 香港理工大学土木与环境工程学系， 香港 999077；  2 广州宁达软件有限公司， 广州 510275）

［摘要］直接分析设计法，是一种通过在数值模型上更加精确地表征结构真实形态，采用非线性分析来获取结构的响应，不需要计算长度法进行构件受压稳定承载力验算的先进方法。该方法对数值计算提出了更高的要求，需要考虑几何非线性和材料非线性。因此，亟需针对直接分析设计法相关的基础理论展开研究。本文主要探讨适用于直接分析法的二阶弹塑性分析，介绍了一种基于柔度法的高性能梁柱单元(FBMI)。该单元采用力的平衡关系作为形函数，具有较高的精度。同时，该单元不仅能考虑轴力和弯矩的相互作用，且在单元推导过程中直接使用函数表征构件的几何初始缺陷，满足规范的相关要求。运用基于纤维截面技术的塑性区法，能够显式地考虑钢构件残余应力的影响，较为精细地模拟构件沿截面方向和沿构件方向的屈服过程。

［关键词］直接分析法； 几何非线性； 材料非线性； 力法单元

中图分类号：TU398-7文献标识码：A文章编号：1002-848X(2019)16-0072-06

Second-order elastic-plastic analysis for direct analysis method

Du Zuolei1, Liu Yaopeng1, Chen Wenfeng2, Chan Siulai1

(1 Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Hong Kong 999077, China; 2 NIDA (Guangzhou) R&D Co.， Ltd., Guangzhou 510275, China)

Abstract:Direct analysis design method is an advanced method which can more accurately represent the true shape of the structure from the numerical model and obtain the response of the structure by non-linear analysis. It does not need the calculation length method to check the bearing capacity of members under compression. This method puts forward higher requirements for numerical calculation, and needs to consider geometric nonlinearity and material nonlinearity. Therefore, it is urgent to study the basic theory of direct analysis design method. The second-order elastic-plastic analysis suitable for direct analysis method was discussed, and a flexibility-based beam-column element was introduced. The element uses the balance relation of forces as the shape function and has high accuracy. At the same time, the element not only considers the interaction of axial force and bending moment, but also directly uses functions to characterize the initial geometric defects of components in the process of element derivation, which meets the relevant requirements of the code. The plastic zone method based on fiber section technology can explicitly consider the effect of residual stress of steel members and simulate the yield process of members along the section direction and along the component direction.

Keywords:direct analysis method; geometric nonlinearity; material nonlinearity; force-based element

*香港特别行政区政府创新及科技基金（ITS/059/16FP）。

通讯作者：刘耀鹏，博士，研究员，Email: yaopeng.liu@connect.polyu.hk。