混合元分裂因子的取值与层合板静力学问题分析

doi:10.19936/j.cnki.2096-8000.20250428.006

复合材料科学与工程 ›› 2025, Vol. 0 ›› Issue (4): 47-56.DOI: 10.19936/j.cnki.2096-8000.20250428.006

混合元分裂因子的取值与层合板静力学问题分析

黄选红¹, 王永钢^2*

1.中国民用航空飞行学院工程技术训练中心,广汉 618307;
2.中国民航大学航空工程学院,天津 300300

收稿日期:2024-01-15 出版日期:2025-04-28 发布日期:2025-06-03
通讯作者: 王永钢(1996—),男,硕士研究生,主要研究方向为广义混合元理论与方法,yonggangw@foxmail.com。
作者简介:黄选红(1976—),男,硕士,高级实验师,主要研究方向为复合材料力学。
基金资助:
通航维修人员实作培训规范研究(GAMRC2023ZC03)

The value of mixed elements splitting factor and analysis of static problems in laminated plates

HUANG Xuanhong¹, WANG Yonggang^2*

1. Engineering Techniques Training Center, Civil Aviation Flight University of China, Guanghan 618307, China;
2. College of Aeronautical Engineering, Civil Aviation University of China, Tianjin 300300, China

Received:2024-01-15 Online:2025-04-28 Published:2025-06-03

摘要/Abstract

摘要： 相对于传统的混合变分原理,带有分裂因子的广义混合变分原理的优越性非常明显。目前,广义混合元模型中分裂因子值的选取是一个开放性问题。基于线弹性问题的应变能等于余能且应变能和余能分别等于混合能量的一半的理论,提出了一种选择分裂因子的误差分析方法。该方法为获取协调广义混合元的适当分裂因子提供了新的途径。数值实例分析表明,通过本文方法获得的协调混合元的分裂因子值,同样适用于3D复合材料层合板问题的求解,且在网格模型相同的情下,可获得更精确的数值结果。

关键词: 广义混合元, 分裂因子, 应变能, 余能, 复合材料

Abstract: Compared to the traditional mixed variational principles, the superiority of generalized mixed variational principles with splitting factors is very obvious. At present, the selection of splitting factor values in generalized mixed models is an open problem. Based on the theory of strain energy equal to complementary energy and strain energy and complementary energy equal to half of the mixed energy in the linear elastic problem, an error analysis method for selecting splitting factors is proposed. This method provides a new approach for obtaining appropriate splitting factors for the compatible generalized mixed elements. Numerical example analyses show that the splitting factor value of the compatible mixed element obtained by the method in this paper can adapt to the 3D composite laminated plate problem, and more accurate numerical results can be obtained under the same mesh model.

Key words: generalized mixed elements, splitting factor, strain energy, complementary energy, composites

中图分类号:

TB332

黄选红, 王永钢. 混合元分裂因子的取值与层合板静力学问题分析[J]. 复合材料科学与工程, 2025, 0(4): 47-56.

HUANG Xuanhong, WANG Yonggang. The value of mixed elements splitting factor and analysis of static problems in laminated plates[J]. COMPOSITES SCIENCE AND ENGINEERING, 2025, 0(4): 47-56.

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混合元分裂因子的取值与层合板静力学问题分析

The value of mixed elements splitting factor and analysis of static problems in laminated plates

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