大型风机叶片复合材料的三维拓扑优化设计

复合材料科学与工程 ›› 2015, Vol. 0 ›› Issue (6): 53-57.

大型风机叶片复合材料的三维拓扑优化设计

谢桂兰^*, 肖春芽, 贺礼财

湘潭大学机械工程学院,湖南湘潭 411105

收稿日期:2014-01-05 出版日期:2015-06-28 发布日期:2021-09-13
作者简介:谢桂兰(1966-),女,博士,教授,主要从事复合材料力学性能的预测,xieguilan@xtu.edu.cn。
基金资助:
国家自然科学基金资助项目(51475403,51375417)

THREE-DIMENSIONAL TOPOLOGY OPTIMIZATIONAL DESIGN OF COMPOSITES MICROSTRUCTURE OF LARGE-SCALE WIND TURBINE BLADE

XIE Gui-lan^*, XIAO Chun-ya, HE Li-cai

School of Mechanical Engineering, Xiangtan University, Xiangtan 411105, China

Received:2014-01-05 Online:2015-06-28 Published:2021-09-13

摘要/Abstract

摘要： 为实现大型风机叶片的轻量化,对纤维增强风机叶片复合材料进行三维拓扑优化设计。首先,基于均匀化理论,将碳纤维增强风机叶片复合材料等效为等效均质体,预测其宏观等效力学性能;然后,以单元相对密度为设计变量、实体材料总体积分数为约束条件、等效宏观弹性矩阵主对角线分量或分量的加权组合为目标函数建立优化模型。采用固体各向同性材料惩罚模型(SIMP)建立设计变量和宏观弹性模量之间的关系,采用灵敏度过滤技术和优化准则法控制材料的分布。在MATLAB平台上编写了相应程序,对大型风机叶片复合材料进行三维拓扑优化,计算得出不同优化目标下的三维最优结构。数值结果表明了该优化模型的正确性和有效性,为实现风机叶片结构轻质高强设计提供了一种参考。

关键词: 风机叶片, 轻量化, 复合材料, 均匀化, 拓扑优化

Abstract: Three-dimensional topological design of composites microstructure of large-scale wind turbine blade was conducted to achieve its lightweight properties in this paper. By homogenization theory, the effective elasticity of composite reinforced by carbon fiber was derived from the equivalent homogenized microstructure. Optimization model was established by using solid isotropic material with penalization (SIMP) model to build the relationship between the design variables and the macroscopic elastic modulus. In the model, the relative density of each element was defined as design variables, the volume fraction of overall solid material as optimization constraints,the weighted sum of main diagonal elements of the equivalent elasticity modulus matrix as objectives. Optimality criteria combined with sensitivity filter technique was applied to control the distribution of the material. The problem was solved under MATLAB platform. Numerical results of different objectives show correctness and efficiency of the proposed optimization model and have some influences on the lightweight design of wind turbine blade.

Key words: wind turbine blade, lightweight, composite, homogenization, topology optimization

中图分类号:

TB332

谢桂兰, 肖春芽, 贺礼财. 大型风机叶片复合材料的三维拓扑优化设计[J]. 复合材料科学与工程, 2015, 0(6): 53-57.

XIE Gui-lan, XIAO Chun-ya, HE Li-cai. THREE-DIMENSIONAL TOPOLOGY OPTIMIZATIONAL DESIGN OF COMPOSITES MICROSTRUCTURE OF LARGE-SCALE WIND TURBINE BLADE[J]. COMPOSITES SCIENCE AND ENGINEERING, 2015, 0(6): 53-57.

参考文献

[1] 罗永康, 李炜, 胡红, 等. 碳纤维复合材料在风力发电机叶片中的应用[J]. 电网与清洁能源, 2008, 24(11): 53-57.
[2] 谢桂兰, 郭锦, 曹尉南, 等. 碳纳米管增强风机叶片复合材料多尺度模型及性能预测[J]. 玻璃钢/复合材料, 2013, 8:I0021-I0025.
[3] Sigmund O. Material with prescribed constitutive parameters: an inverse homogenization problem[J]. International Journal of solid and Structures, 1994, 31(17): 2313-2329.
[4] Neves M, M, Rodrigues H, Guedes JM.Optimal design of periodic linear elastic microstructures[J]. Computers&Structures, 2000, 76(1-3):421-429.
[5] 李成良, 王继辉, 薛忠民. 大型风机叶片材料的应用和发展[J]. 玻璃钢/复合材料, 2008, 4: 49-52.
[6] 陈绍杰. 复合材料与风机叶片[J]. 高科技纤维与应用, 2007, 32(3): 8-12.
[7] 潘燕环, 嵇醒, 薛松涛. 复合材料中的渐近均匀化方法[J]. 上海力学, 1997, 04: 290-297.
[8] B.Hassani, E.Hinton. A review of homogenization and topology optimization I-homogenization theory for media with periodic structure[J]. Computer &Structure, 1998, 69:707-717.
[9] B.Hassani, E.Hinton. A review of homogenization and topology optimization II-analytical and numerical solution of homogenization equations[J]. Computer&Structure, 1998, 69: 719-738.
[10] Bendsoe M P, Sigmund O. Material interpolation schemes in topology optimization[J]. Archive of Mechanics,1999, 69(9/10): 635-654.
[11] Sigmund O. A 99 line topology optimization code written in Matlab[J]. Structural and Multidiscipline Optimization, 2001, 21(2): 120-127.
[12] 汤亚男, 谢桂兰, 曹尉南, 等. 基于均匀化的轻质高强件拓扑优化及方法研究[J]. 机械科学与技术, 2012, 31(7): 1184-1188.
[13] 蔡四维, 王健军. 复合材料三维等效弹性常数的计算[J]. 合肥工业大学学报(自然科学版),1986,(4): 1-12.
[14] 冯淼林, 吴长春. 基于三维均匀化方法的复合材料本构数值模拟[J]. 中国科学技术大学学报, 2000, 06: 64-70.
[15] 吴涛. 碳纳米管/碳纤维多尺度风机叶片复合材料力学性能预测[D]. 湘潭大学, 2014.
[16] Kepeng Qiu, Weihong Zhang, Shiping Sun, et al. Topological design of three-dimensional microstructure based on homogenization effective method[J]. Materials Science Forum, 2006, 532-533:705-708.
[17] 刘明昌. 碳纤维增强环氧树脂预浸料及其复合材料的制备与性能研究[D].华东理工大学,2012.