体外预应力筋非线性有限元模型及其迭代算法  

Nonlinear FEM and Iterative Algorithm on External Prestressed Tendon

作　　者：邓继华 杨倩[1] 谭平 田仲初[1] DENG Ji-hua;YANG Qian;TAN Ping;TIAN Zhong-chu(School of Civil Engineering,Changsha University of Science and Technology,Changsha Hunan 410076,China;Key Laboratory of Ministry of Education for Bridge Engineering Safety Control,Changsha University of Science and Technology,Changsha Hunan 410114,China;Earthquake Engineering Research and Test Center,Guangzhou University,Guangzhou Guangdong 510405,China)

机构地区：[1]长沙理工大学土木工程学院,湖南长沙410114 [2]长沙理工大学桥梁工程安全控制教育部重点实验室,湖南长沙410114 [3]广州大学工程抗震研究中心,广东广州510405

出　　处：《公路交通科技》2023年第12期82-88,共7页Journal of Highway and Transportation Research and Development

基　　金：国家自然科学基金项目(52278142);湖南省自然科学基金项目(2023JJ30019);湖南省教育厅项目(21A0187);桥梁结构健康与安全国家重点实验室开放基金项目(BHSKL21-06-GF)。

摘　　要：为了准确模拟体外预应力筋的非线性受力行为,采用理论推导和程序研制开展了体外预应力筋非线性有限元模型及其算法的研究。首先,基于体外预应力筋与转向块之间可自由滑动而导致体外预应力筋在全长范围内为常应变构件的受力特点,建立了非线性体外预应力单元研究方法。其次,以锚固块之间设置2个转向块的三段四节点平面体外筋为例,基于变分法得到应变微分与平面梁单元节点位移矩阵微分的表达式,再运用虚功原理推导出该类型体外预应力筋在结构坐标系下具体的非线性切线刚度矩阵。然后,结合常规的平面线弹性梁单元,提出了适用于结构分析的体外预应力梁非线性分析方法和计算程序。最后,对2个简支体外预应力梁算例进行了数值分析,其中算例1进行了本研究方法、Abaqus软件计算以及静载试验实测值的对比分析,算例2进行了线性与非线性的对比分析。结果表明:在算例1中,2种方法得到的计算值均与实测值吻合良好,相对而言,前一种方法建立有限元模型更简单,且更能准确体现体外预应力筋的受力特点;在算例2中,体外预应力梁的受力行为很容易表现出非线性特征,且非线性对体外筋轴力比对节点位移的影响较大,体外预应力结构受力分析时考虑非线性是很有必要的。In order to simulate the nonlinear behavior of external prestressed tendons accurately,the nonlinear FEM and its algorithm of external prestressed tendons are studied by theoretical deduction and program development.Firstly,the nonlinear external prestressing element research method is established based on the characteristic that the external prestressing tendon is a constant strain member in the whole length due to the free sliding between the external prestressing tendon and the steering block.Secondly,the expression of strain differential and displacement matrix differential of plane beam element is obtained based on the variational method,and the concrete nonlinear tangential stiffness matrix of this type of external prestressed reinforcement is derived by using the principle of virtual work in the structural coordinate system.Then,a nonlinear analysis method and calculation program for external prestressed beams are proposed based on the conventional planar linear elastic beam elements.Finally,2 examples of simply supported external prestressed beams are numerically analyzed.Example 1 is compared with the proposed method,ABAQUS software and static load test,and example 2 is compared with linear and nonlinear.The result shows that(1)in example 1,the calculated values obtained with the 2 methods are in good agreement with the measured values,and comparatively speaking,the FEM established with the former method is simpler and can reflect the stress characteristics of external prestressed tendons more accurately;(2)in example 2,the stress behavior of the external prestressed beam is easy to show nonlinear characteristics,and the nonlinear has a greater impact on the axial force ratio of the external reinforcement to the displacement of the joint,so it is necessary to consider nonlinear characteristics in the stress analysis of the external prestressed structure.

关 键 词：桥梁工程 非线性有限元模型 迭代算法 体外预应力筋 多段多节点 

分 类 号：TU378.2[建筑科学—结构工程]