为提高空间梁单元在风力机叶片结构计算方面的精度,提出一种基于解析位移形函数的改进空间梁单元。首先考虑叶片截面偏心的影响,从空间Timoshenko梁的平衡方程出发,构建弯曲位移的解析解插值函数。根据弯曲位移与横向位移和剪切变形的关系,得到横向位移和剪切角的形函数。采用有限元理论,得到改进风力机叶片梁单元的刚度矩阵和质量矩阵。编制有限元程序,用3个算例验证改进叶片梁单元的正确性和精确性。最后对5 MW风力机叶片进行模态分析,准确获取叶片的固有频率和相应振型。
Abstract
An improved spatial Timoshenko beam element is presented to improve the calculation accuracy of wind turbine blades based on analytical displacement shape functions for bending deformation, Firstly, the eccentric effect of blade cross-section is considered, and analytical interpolation functions for bending deformation are constructed according to Timoshenko beam equilibrium equations. Shape functions for the translational deformation and transverse shear deformation are established on the basis of the relationships between total deflection, bending slope and transverse shear. Then the stiffness matrix and mass matrix of the improved blade beam element are derived by the finite element theory. Relevant finite element computation programs are compiled with the correctness and accuracy verified by three typical examples. Finally, modal analysis is conducted for the blades of a 5 MW wind turbine. Consequently, the natural frequencies and corresponding mode shapes of the blades are obtained accurately.
关键词
风力机 /
叶片 /
Timoshenko梁 /
空间梁单元 /
有限元法 /
刚度矩阵 /
模态分析
Key words
wind turbines /
blades /
Timoshenko beam /
spatial beam element /
finite element method /
stiffness matrix /
modal analysis
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基金
国家自然科学基金（51778103）; 广东省自然科学基金（2021A1515011770）; 汕头大学科研启动基金（NTF18012）
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