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（1 香港理工大學(xué)土木與環(huán)境工程學(xué)系， 香港 999077； 2 廣州寧達軟件有限公司， 廣州 510275）
［摘要］直接分析設(shè)計法，是一種通過在數(shù)值模型上更加精確地表征結(jié)構(gòu)真實形態(tài)，采用非線性分析來獲取結(jié)構(gòu)的響應(yīng)，不需要計算長度法進行構(gòu)件受壓穩(wěn)定承載力驗算的先進方法。該方法對數(shù)值計算提出了更高的要求，需要考慮幾何非線性和材料非線性。因此，亟需針對直接分析設(shè)計法相關(guān)的基礎(chǔ)理論展開研究。本文主要探討適用于直接分析法的二階彈塑性分析，介紹了一種基于柔度法的高性能梁柱單元(FBMI)。該單元采用力的平衡關(guān)系作為形函數(shù)，具有較高的精度。同時，該單元不僅能考慮軸力和彎矩的相互作用，且在單元推導(dǎo)過程中直接使用函數(shù)表征構(gòu)件的幾何初始缺陷，滿足規(guī)范的相關(guān)要求。運用基于纖維截面技術(shù)的塑性區(qū)法，能夠顯式地考慮鋼構(gòu)件殘余應(yīng)力的影響，較為精細地模擬構(gòu)件沿截面方向和沿構(gòu)件方向的屈服過程。
［關(guān)鍵詞］直接分析法； 幾何非線性； 材料非線性； 力法單元
中圖分類號：TU398-7文獻標(biāo)識碼：A文章編號：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
*香港特別行政區(qū)政府創(chuàng)新及科技基金（ITS/059/16FP）。
通訊作者：劉耀鵬，博士，研究員，Email: yaopeng.liu@connect.polyu.hk。
