有限元模型的整体刚度矩阵集成  

Assembling global stiffness matrix for finite element model

作　　者：罗帅 朱佳洋 梁超锋 刘伟[2] LUO Shuai;ZHU Jiayang;LIANG Chaofeng;LIU Wei(School of Civil Engineering,Shaoxing University,Shaoxing 312000,Zhejiang Province,P.R.China;Guangdong Communication Polytechnic,Guangzhou 510650,Guangdong Province,P.R.China)

机构地区：[1]绍兴文理学院土木工程学院,浙江绍兴312000 [2]广东交通职业技术学院,广东广州510650

出　　处：《深圳大学学报（理工版）》2018年第5期467-472,共6页Journal of Shenzhen University(Science and Engineering)

基　　金：国家自然科学基金资助项目(51308340);广东省自然科学基金资助项目(2015A030310168);绍兴文理学院自然科学基金资助项目(20155028)~~

摘　　要：在有限元分析过程中,定位单元刚度矩阵中的元素在整体刚度矩阵中的位置,对结构分析模型的正确建立起着重要作用.为了探究单元刚度矩阵向整体刚度矩阵的集成规律,推导了单元刚度矩阵和整体刚度矩阵之间的对应关系,得到单元刚度矩阵元素在整体刚度矩阵中的位置,依据单元结点号与结构整体坐标系下的结点编号的对应关系建立了统一的关联表,形成基于关联表的整体矩阵集成方法.与目前常用的结点平衡法相比,新建立的整体矩阵集成方法物理意义明确,建模过程简便快捷,且可靠稳定.算例分析结果表明该方法适合用有限元编程实现.Locating the positions of elements of the unit stiffness matrix in the global stiffness matrix plays an important part in establishment of structural analysis model by finite element method.In order to explore the integration law of the unit stiffness matrix to the global stiffness matrix,we derive the correspondence between the element stiffness matrix and the global stiffness matrix.We identify the positions of elements of the unit stiffness matrix in the global stiffness matrix,and generate the unified link table based on the correspondence between the element node number in the unit stiffness matrix and the node number in the global coordinate system.On the basis of the link table,we establish the integrated global stiffness matrix.We find that the new global matrix ensemble method has clear physical significance and rigorous logic reasoning,as well as with simple,fast,reliable and stable modeling process.The example analysis shows that the proposed method is suitable for finite element programming.

关 键 词：结构工程 有限元模型 整体刚度矩阵 单元刚度矩阵 关联表 过渡矩阵 

分 类 号：O302[理学—力学] TU12[建筑科学—建筑理论]