基于SABRE软件的大规模RBE3单元快速求解方法及程序开发  

A Fast Solution Method and Program Development for Large-Scale RBE 3 Elements Based on the SABRE Software

作　　者：张长兴 王立凯[1] 常亮[1] 聂小华[1] ZHANG Changxing;WANG Likai;CHANG Liang;NIE Xiaohua(National Key Laboratory of Strength and Structural Integrity,Aircraft Strength Research Institute of China,Xi’an 710065,P.R.China)

机构地区：[1]中国飞机强度研究所强度与结构完整性全国重点实验室,西安710065

出　　处：《应用数学和力学》2025年第4期483-494,共12页Applied Mathematics and Mechanics

基　　金：国家重点研发计划(2021YFB3302301);陕西省重点研发计划(2022ZDLGY02-08)。

摘　　要：随着复杂结构仿真建模的精细化程度越来越高,应用到零部件连接和载荷分配的RBE3单元数量急剧增加,由此引起了自主结构分析软件的数值求解困难.该文首先建立了RBE3单元主、从节点之间的位移约束关系,剖析了线性消去理论引起求解困难的原因.然后,采用增广Lagrange理论将位移约束关系引入到有限元问题的泛函中,并利用泛函的变分推导出了RBE3单元的刚度矩阵显式表达形式,从而将约束处理问题转化为单元求解问题.最后,在上述理论基础上,结合自主结构分析软件SABRE进行了相关功能模块的设计与开发,并通过工程算例验证.结果表明,该文改进后的SABRE软件在求解含大规模RBE3单元的分析模型时求解精度与NASTRAN基本一致,求解效率提升明显.With the increasing sophistication of complex structural simulation modeling,the number of RBE3 elements applied to component connections and load distribution increases dramatically,which brings difficulties in the numerical solution with autonomous structural analysis software.First the displacement constraint relationship between the master and slave nodes of the RBE3 element was established,the reasons for the linear elimination theory bringing the difficulty in solving the problem was analyzed,and then the augmented Lagrange theory was used to introduce the displacement constraint relationship into the functional for the finite element problem,and derive the explicit expression of the stiffness matrix for the RBE3 element by means of the variation of the functional.Thereby,the constraint processing problem was converted into an element solution problem.Finally,based on the above theory,the design and development of relevant functional modules were combined with autonomous structural analysis software SABRE.The engineering example verification shows that,the developed program is basically consistent with NASTRAN in solving the analysis model containing large-scale RBE3 elements,with significantly improved solution efficiency.

关 键 词：有限元法 增广Lagrange理论 RBE3单元快速求解方法 SABRE软件 

分 类 号：V215.2[航空宇航科学与技术—航空宇航推进理论与工程]