### 一种考虑截面任意变形模式梁的有限元模型

1. 1. 南京航空航天大学 机械结构力学及控制国家重点实验室, 南京 210016;
2. 南京航空航天大学 振动工程研究所, 南京 210016
• 收稿日期:2018-04-19 修回日期:2018-08-09 出版日期:2018-12-15 发布日期:2018-10-10
• 通讯作者: 何欢 E-mail:hehuan@nuaa.edu.cn
• 基金资助:
国家自然科学基金（11472132）；机械结构力学及控制国家重点实验室（南京航空航天大学）自主研究课题（MCMS-I-0118G01）；江苏高校优势学科建设工程

### Finite element model of beem considering arbitrary deformation mode of cross-section

HE Huan1,2, SONG Dapeng1, ZHANG Chenkai1,2, CHEN Guoping1,2

1. 1. State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;
2. Institute of Vibration Engineering Research, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
• Received:2018-04-19 Revised:2018-08-09 Online:2018-12-15 Published:2018-10-10
• Supported by:
National Natural Science Foundation of China (11472132); the Research Fund of State Key Laboratory of Mechanics and Control of Mechanical Structures (Nanjing University of Aeronautics and Astronautics) (MCMS-I-0118G01); the Priority Academic Program Development (PAPD) of Jiangsu Higher Education Institutions

Abstract: A cross-section interpolation beam model considering the complete deformation of the cross-section is proposed and used to model and analyze the wing structure. First, the Lagrange functions are introduced as the interpolation function to describe the shape of the beam cross-section, and the displacement vectors are used as unknown variables to describe the displacement of the cross-section. On this basis, the displacement field of the beam element is constructed according to the interpolation theory. While the displacements of the beam in the conventional beam element are determined by the deflection and rotation of the assumed neutral axis, the new beam element rejects the neutral axis hypothesis and flat section hypothesis, and the deformation of the beam cross-section is obtained by the interpolation functions. Then based on the finite element theory, the stiffness matrix and the mass matrix of the beam element are derived. Finally, the wing components are modeled by the cross-section interpolation beam element, and the static analysis and dynamic analysis under typical conditions are carried out. The validity of the beam model is verified by comparing the result with the results of Nastran solid model, showing that the model provides a one-dimensional beam simplified modeling method for the structural design and strength analysis of the wing.