基于CFRP等刚度设计的全模态等刚度验证
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摘要
等刚度验证是各种工程结构进行材料替换的重要依据,本文通过对钢制异型圆管进行碳纤维增强复合材料(CFRP)等刚度设计及验证,得到了一种高效可靠的等刚度验证方法。首先,通过理论计算得到异型圆管结构在不同受载工况下的变形结果,并分析了变形的影响因素及其影响程度;其次,选用CFRP和钢材作为等刚度设计对象,依据异型管的理论变形结果和等刚度设计原则,设计得到了满足等刚度要求的CFRP异型管和钢制异型管;最后,提出了一种高效可靠的等刚度验证方法——模态验证法,依据理论推导所得出的等刚度的验证条件,对已经满足等刚度要求的CFRP异型管和钢制异型管进行等刚度验证,结果表明CFRP异型管和钢制异型管能够满足该等刚度验证条件,进而验证了该方法的有效性。相较于以往的多工况加载验证方法,等刚度模态验证法主要的优势在于:①分析过程简单,只需对替代件和原件进行模态分析,就能够大幅度提高验证效率;②与结构本身的受载工况无关,能够适用于变载结构件的等刚度验证;③以结构的刚度矩阵相等为理论基础,验证结果更为可靠,能实现真正意义上的全方位等刚度验证。
Equal stiffness verification is an important basis for material replacement of various engineering structures. In this paper, an efficient and reliable equal stiffness verification method is obtained by designing and verifying the stiffness of carbon fiber-reinforced plastics(CFRP) replace steel shape tubes. Firstly, by the theoretical calculation, the deformation of the shape tube structure in different loading conditions is obtained, the influencing factors and degree of deformation are analyzed. Then, according to the theoretical deformation of the shape tube and the equal stiffness design principles, equal stiffness carbon fiber-reinforced plastics(CFRP) shape tube and steel shape tube are obtained. Finally, an efficient and reliable equal stiffness verification method, i.e., the modal verification method, is proposed. According to the theoretical derivation, the verification conditions of equal stiffness are used to verify the stiffness of CFRP shape tube and steel shape tube which have met the equal stiffness requirement. The results show that the CFRP shape tube and the steel shape tube satisfy the stiffness verification conditions, and the effectiveness of the method is verified. Compared with the previous multi-case loading verification method, main advantages of the equal stiffness mode verification method are as follows: ① The analysis process is simpler, which only includes the modal analysis of replacement parts and original parts, and this can greatly improve the verification efficiency; ② The validity of this method is not limited by the loaded condition of the structure, and it can be applied in the equal stiffness verification of variable-loading structure; ③ The verification results, which are based on the theory of the stiffness matrix, are more reliable, and the all-round equal stiffness verification can be obtained.
Equal stiffness verification is an important basis for material replacement of various engineering structures. In this paper, an efficient and reliable equal stiffness verification method is obtained by designing and verifying the stiffness of carbon fiber-reinforced plastics(CFRP) replace steel shape tubes. Firstly, by the theoretical calculation, the deformation of the shape tube structure in different loading conditions is obtained, the influencing factors and degree of deformation are analyzed. Then, according to the theoretical deformation of the shape tube and the equal stiffness design principles, equal stiffness carbon fiber-reinforced plastics(CFRP) shape tube and steel shape tube are obtained. Finally, an efficient and reliable equal stiffness verification method, i.e., the modal verification method, is proposed. According to the theoretical derivation, the verification conditions of equal stiffness are used to verify the stiffness of CFRP shape tube and steel shape tube which have met the equal stiffness requirement. The results show that the CFRP shape tube and the steel shape tube satisfy the stiffness verification conditions, and the effectiveness of the method is verified. Compared with the previous multi-case loading verification method, main advantages of the equal stiffness mode verification method are as follows: ① The analysis process is simpler, which only includes the modal analysis of replacement parts and original parts, and this can greatly improve the verification efficiency; ② The validity of this method is not limited by the loaded condition of the structure, and it can be applied in the equal stiffness verification of variable-loading structure; ③ The verification results, which are based on the theory of the stiffness matrix, are more reliable, and the all-round equal stiffness verification can be obtained.
引文
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[11] 杜平安,于亚婷,刘建涛.有限元法—原理建模及应用[M].北京:国防工业出版社,2009:57-64.
[12] 王耀先.复合材料力学与结构设计[M].上海:华东理工大学出版社,2012:312-326.
[13] 李丽,顾力强.碳纤维复合材料传动轴临界转速分析[J].汽车工程,2005,27(2):239-240.
[14] 赵娟.基于ANSYS的碳纤维复合材料传动轴的铺层设计[D].武汉:武汉理工大学,2011.
[15] 刘延柱,陈立群,陈文良.振动力学[M].北京:高等教育出版社,2011:103-144.
[16] Singiresu S R,李欣业,杨理诚.机械振动[M].北京:清华大学出版社,2016:412-468.
[2] Patton R,Li F,Edwards M.Causes of weight reduction effects of material substitution on constant stiffness components[J].Thin-Walled Structures,2004,42(1):613-637.
[3] 刘万双,魏毅,余木火.汽车轻量化用碳纤维复合材料国内外应用现状[J].纺织导报,2016(5):48-52.
[4] 冯琨程,高九州.某型系留无人机复合材料机体结构优化设计与分析[J].玻璃钢/复合材料,2018(10):56-61.
[5] LI FANG,Patton R,Moghal K.The relationship between weight reduction and force distribution for thin wall structures[J].Thin-Walled Structures,2005,43(1):591-616.
[6] Edwards C M.A method for determining weight reduction through material substitution in automotive structures of equivalent stiffness[D].MS,USA:Mississippi State University,2002.
[7] 吕毅宁,吕振华.基于等刚度条件的薄壁结构的一种材料替代轻量化设计分析方法[J].机械工程学报,2009,45(12):289-294.
[8] 陈文琳,吴洪亮,熊飞.基于等刚度原理的材料轻量化[J].塑性工程学报,2014,21(4):117-122.
[9] 郭永奇,黄小征,王帅,等.基于等刚度原理的碳纤维发动机罩开发[J].汽车实用技术,2017(19):100-103.
[10] 孙冬鸣,马其华,孙佳睿.基于等刚度原理的碳纤维汽车B柱抗撞性分析[J].玻璃钢/复合材料,2018(11):58-63.
[11] 杜平安,于亚婷,刘建涛.有限元法—原理建模及应用[M].北京:国防工业出版社,2009:57-64.
[12] 王耀先.复合材料力学与结构设计[M].上海:华东理工大学出版社,2012:312-326.
[13] 李丽,顾力强.碳纤维复合材料传动轴临界转速分析[J].汽车工程,2005,27(2):239-240.
[14] 赵娟.基于ANSYS的碳纤维复合材料传动轴的铺层设计[D].武汉:武汉理工大学,2011.
[15] 刘延柱,陈立群,陈文良.振动力学[M].北京:高等教育出版社,2011:103-144.
[16] Singiresu S R,李欣业,杨理诚.机械振动[M].北京:清华大学出版社,2016:412-468.
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