主从约束在有限元计算中的实现方式和过程  

Realization Method and Process of Master-Slave Constraint in Finite Element Method

作　　者：张军锋[1] 温珺博 张金鹏 李杰[1] 叶雨山 ZHANG Junfeng;WEN Junbo;ZHANG Jinpeng;LI Jie;YE Yushan(School of Hydraulic and Civil Engineering,Zhengzhou University,Zhengzhou,He’nan 450001,China;He’nan Puze Expressway Co.,Ltd.,Puyang,He’nan 457000,China;China Construction Seventh Engineering Division Co.,Ltd.,Zhengzhou,He’nan 450004,China)

机构地区：[1]郑州大学水利与土木工程学院,河南郑州450001 [2]河南濮泽高速公路有限公司,河南濮阳457000 [3]中国建筑第七工程局有限公司,河南郑州450004

出　　处：《水利与建筑工程学报》2023年第2期195-200,共6页Journal of Water Resources and Architectural Engineering

基　　金：国家自然科学基金(51508523);河南省交通运输厅科技项目(2021J2)。

摘　　要：为明确主从约束这一自由度耦合关系在有限元计算过程中的实现方式和具体过程,从主从约束的基本概念入手,基于直接消除法的思想,采用宏单元的概念,在剔除从节点自由度的同时保留其结构荷载和刚度的贡献,根据有限元分析的基本原理推导得到了宏单元在整体和局部坐标系下的刚度矩阵,从而使其可以与普通单元一起整合到结构整体刚度矩阵中参与计算。另外,对主从约束自身的单元方向、主从约束的组合和联合应用等亦给出了分析和刚度矩阵表达式。最后,采用多个算例根据本文推导方式进行编程计算,并通过midas、ANSYS和ABAQUS进行了对比计算验证,为深入理解主从约束在有限元计算中的实现方式和过程以及实际工程应用提供了参考和帮助。This work focuses on realization method and process of master-slave constraint in Finite Element(FE)method,which is a concept of freedom coupling.The derivation was based on the basic concept of master-slave constraint and direct elimination method.A concept of macro-element is introduced which contains the master-slave constraint and normal elements.According to the macro-element,the freedoms of slave node could be eliminated but the load and coupling effects could be reserved.The stiffness matrixes of macro-element in global and local coordinator system were obtained according to the matrix analysis of structures,and could be incorporated into the FE analysis of structures as the stiffness matrixes of normal elements.Moreover,the local axis direction of the master-slave constraint,the combined and united application of master-slave constraint were also discussed,and their stiffness matrixes were also given.Several examples were provided and the results were obtained by virtue of self-programmed calculation codes.FE software such as midas,ANSYS and ABAQUS were also used for validation calculation.The work is helpful for the theoretical interpretation and engineering application of the master-slave constraint.

关 键 词：主从约束 自由度耦合关系 直接消除法 宏单元 刚度矩阵 

分 类 号：TU311[建筑科学—结构工程]