基于超级混合单元的复合材料层合板应力分析

中国民航大学学报

基于超级混合单元的复合材料层合板应力分析

刘艳红，张莹

（中国民航大学航空工程学院，天津300300）

收稿日期:2017-12-25 修回日期:2018-03-04 出版日期:2018-08-25 发布日期:2018-10-25
作者简介:刘艳红（1970—），女，河南驻马店人，博士，教授，研究方向为复合材料结构力学.
基金资助:
国家自然科学基金青年科学基金项目（11502286）

Stress analysis of laminated composite plate based on super mixed element

LIU Yanhong, ZHANG Ying

(College of Aeronautical Engineering, CAUC, Tianjin 300300, China)

Received:2017-12-25 Revised:2018-03-04 Online:2018-08-25 Published:2018-10-25

摘要/Abstract

摘要： 就有限元法而言，单元数值积分运算的时间所占比例较大。根据复合材料层结构的特点，基于三维的线弹性问题的非协调辛元，建立了超级混合单元。由于超级混合单元的组装是简单的加法运算，消耗时间较少，因此按层的形式划分超级单元，最明显的优点是可节省因相同单元重复积分运算而消耗的时间。实例分析证明了混合单元的可靠性。

关键词: 复合材料层合板, 应力分析, 广义部分混合元, 超级混合单元

Abstract: For finite element methods, calculating time of element numerical integration operation takes a large proportion.According to the characteristics of laminated composite plate structure, a super mixed element is constructed based on incompatible symplectic element of 3D linear elasticity problems. Since the assembly of super mixed element is a simple addition operation which consumes less time, the most obvious advantage of super element in the form of layers is saving the time consumed by repetitive integral operation of the same elements. The reliability of super mixed element is proven by example analysis.

Key words: laminated composite plate, stress analysis, generalized partial mixed element, super mixed element

中图分类号:

O342
O343

刘艳红，张莹. 基于超级混合单元的复合材料层合板应力分析[J]. 中国民航大学学报.

LIU Yanhong, ZHANG Ying. Stress analysis of laminated composite plate based on super mixed element[J]. .

参考文献

[1] HERRMANN L. Finite element bending analysis for plates[J]. J Eng Mech Div, 1967, ASCE 98: 13-26.
[2] ATLURI S N, GALLAGHER R H, ZIENKIEWICZ O C. Hybrid and Mixed Finite Element Methods[M]. New York: John Wiley & Sons, 1983.
[3] BREZZI F, FORTIN M. Mixed and Hybrid Finite Element Methods[M].New York: Springer Science & Business Media, 2012.
[4] ARNOLD D, FALK R, WINTHER R. Mixed finite element methods for linear elasticity with weakly imposed symmetry[J]. Mathematics of Computation,2007, 76: 1699-1723.
[5] ADAMS S, COCKBURN B. A mixed finite element method for elasticity in three dimensions[J]. Journal of Scientific Computing, 2005, 25: 515-521.
[6] QING GUANGHUI, MAOJUNHUI, LIU YANHONG. Generalized mixed finite element method for 3D elasticity problems[J]. Acta Mechanica Sinica, 2018, 34(2): 371-380
[7] QING GUANGHUI, MAO JUNHUI, LIU YANHONG. Highly accurate noncompaltible generalized mixed finite element method for 3D elasticity problems[J]. Journal of Mechanical of Material and Structures，2017,12(4): 505-519.
[8] QING GUANGHUI, TIAN JIA. Highly accurate symplectic element based on two variational principles[J]. Acta Mechanica Sinica, 2018, 34(1): 151-161.
[9] 钟万勰. 应用力学的辛数学方法[M]. 北京: 高等教育出版社, 2006.
[10] 唐立民, 褚致中, 邹贵平, 等. 混合状态Hamiltonian 元的半解析解和叠层板的计算[J]. 计算力学学报, 1992, 9(4): 347-360.
[11] QING GUANGHUI, QIU JIAJUN, LIU YANHONG. Modified mixed variational principle for magnetoelectroelastic solids and state-vector equation[J].AppliedMathematicsand Mechanics,2005,26(6):722-728.
[12] QING GUANGHUI, QIU JIAJUN, LIU YANHONG. A semi-analytical solution for static and dynamic analysis of plates with piezoelectric patches[J]. International Journal of Solids and Structures, 2006, 43(6):1388-1403.
[13] 田宗漱, 卞学鐄. 多变量变分原理与多变量有限元方法[M]. 北京:科学出版社, 2011.
[14] 陈万吉. 一个高精度八结点六面体单元[J]. 力学学报, 1982, 18(3):262-271.
[15] 范家让. 强厚叠层板壳的精确理论[M]. 北京: 科学出版社, 1996.