基面力单元法在空间几何非线性问题中的应用  

Application of the Base Force Element Method to Spacial Geometrically Nonlinear Problems

作　　者：龚琳琦 陈曦昀 郭庆 彭一江[1] GONG Linqi;CHEN Xiyun;GUO Qing;PENG Yijiang(Key Laboratory of Urban Security and Disaster Engineering Ministry of Technology,Beijing University of Technology,Beijing 100124,P.R.China;Hongkong Huayi Design Consultants(Shenzhen)Ltd.,Shenzhen,Guangdong 518000,P.R.China)

机构地区：[1]北京工业大学城市与工程安全减灾教育部重点实验室,北京100124 [2]香港华艺设计顾问(深圳)有限公司,广东深圳518000

出　　处：《应用数学和力学》2021年第8期785-793,共9页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(10972015)。

摘　　要：基于基面力的概念,并结合Euler角的位移描述方法,提出了适用于几何非线性计算的空间6结点余能基面力单元.使用MATLAB语言编程并对典型梁、板结构进行弹性大变形数值模拟.由计算结果可以看出,基于余能原理的基面力元法(BFEM)在计算构件的空间大变形时有较好的计算精度,对比传统有限元计算方法具有网格尺寸影响小和抗畸变能力强的特点,有良好的计算性能.Based on the base force element method(BFEM)and the principle of complementary energy,a 6⁃node spatial solid unit was proposed for spacial geometrically nonlinear calculation,and the Euler angles were used to describe the displacement.MATLAB was used to program and simulate the elastic large deformation problem of typical beam and plate structures.The calculation results show that,the finite element model based on the BFEM and the complementary energy principle has good calculation accuracy for the spatial geometrical⁃ly nonlinear components.Compared with the traditional finite element method,the model has the characteris⁃tics of smaller mesh size effects and stronger anti⁃distortion ability.

关 键 词：基面力元法 余能原理 空间几何非线性 有限元 

分 类 号：O343.2[理学—固体力学] O242.21[理学—力学]