基于瞬态响应的一种功能梯度梁的材料参数反求方法
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摘要
随着功能梯度材料在实际工程中日益广泛的应用,需要一种有效的无损检测方法来获取功能梯度材料的材料特性参数。由于传统的检测方法在检测功能梯度材料时遇到的困难,以及一些先进的无损检测方法在实际工程应用中的局限,本文结合商业有限元软件,提出了一种基于瞬态响应的功能梯度梁的材料参数反求方法。
本文以功能梯度材料为研究对象,研究功能梯度材料的波动特性。研究应用商业有限元软件建立功能梯度梁波动响应模型的方法,仿真分析其瞬态响应,并对功能梯度梁材料参数的敏感性进行分析,为本文提出的基于瞬态响应反求功能梯度梁材料特性参数的方法提供依据。
在功能梯度梁波动特性分析的基础上,应用遗传算法建立功能梯度梁特性参数的反问题,提出一种基于瞬态响应的功能梯度梁材料特性参数的反求方法。其中,有限元软件获得的功能梯度梁的瞬态位移响应作为反求方法中的输入数据,功能梯度梁的体积参数作为输出数据。
引入了代理模型方法,应用响应面模型代替功能梯度梁波动响应模型作为本文反求方法中的正问题求解方法。建立不同的功能梯度梁波动响应模型的代理模型进行比较分析,证明所建立的响应面模型拟合度高,可以取代反求方法中的功能梯度梁波动响应模型,代理模型建立的过程中结合了试验设计方法。
最后,应用本文的反求方法反求两个实际SiC-C和SS-SN功能梯度梁的特性参数,验证所提出的功能梯度梁材料特性参数反求方法的有效性。
论文研究表明:对于功能梯度材料波动特性的研究为反求功能梯度材料的特性参数提供了一种有效的方法;功能梯度梁波动特性的分析可以借助于商业有限元软件;代理模型的引入提高了反求方法的计算效率;应用遗传算法建立的功能梯度梁材料特性参数反求方法获得的材料参数误差小、精度高。
With the gradually increasing applications of functionally graded materials, there is a need for an effective method to non-destructively measure the material property of functionally graded materials. Based on the difficulties in evaluating functionally graded materials by traditional techniques and the limitations of advanced non-destructive evaluation in engineering application, an inverse procedure built on the transient response analysis of functionally graded beam is presented for charactering the material property of functionally graded materials.
Focusing on the functionally graded material (FGM), the wave propagation in FGM was analyzed. The inverse procedure for charactering the material property of functionally graded beam is based on the analysis of transient response and material property sensitivity of the functionally graded beam built by the finite element software.
Based on the analysis of wave propagation behaviors in functionally graded beam, the inverse problem was established combined with genetic algorithm and an inverse procedure by using transient response analysis of functionally graded beam was developed for determining the material property. The dynamic displacement responses of functionally graded beam obtained by the finite element software were employed as the input data, and the volume fractions were output data.
A surrogate-based method was provided, and the dynamic response model of functionally graded beam was substituted by response surface model as forward calculation technique of the inverse procedure. The design of experiment technique was employed to establish different surrogate models for comparing analysis, and the response surface model was proved to be accurate to substitute the wave propagating model of functionally graded beam.
Finally, the inverse procedure presented in this thesis was validated by two applications for charactering material property of SiC-C and SS-SN functionally graded beams.
The study shows that the research on wave propagation behaviors in FGM provides an effective method for charactering material property of FGM, and is able to be conducted by the commercial finite element software. The efficiency of the inverse procedure is improved by employing surrogate model technique. The inverse procedure combined with genetic algorithm is accurate to determine material property of functionally graded beam.
本文以功能梯度材料为研究对象,研究功能梯度材料的波动特性。研究应用商业有限元软件建立功能梯度梁波动响应模型的方法,仿真分析其瞬态响应,并对功能梯度梁材料参数的敏感性进行分析,为本文提出的基于瞬态响应反求功能梯度梁材料特性参数的方法提供依据。
在功能梯度梁波动特性分析的基础上,应用遗传算法建立功能梯度梁特性参数的反问题,提出一种基于瞬态响应的功能梯度梁材料特性参数的反求方法。其中,有限元软件获得的功能梯度梁的瞬态位移响应作为反求方法中的输入数据,功能梯度梁的体积参数作为输出数据。
引入了代理模型方法,应用响应面模型代替功能梯度梁波动响应模型作为本文反求方法中的正问题求解方法。建立不同的功能梯度梁波动响应模型的代理模型进行比较分析,证明所建立的响应面模型拟合度高,可以取代反求方法中的功能梯度梁波动响应模型,代理模型建立的过程中结合了试验设计方法。
最后,应用本文的反求方法反求两个实际SiC-C和SS-SN功能梯度梁的特性参数,验证所提出的功能梯度梁材料特性参数反求方法的有效性。
论文研究表明:对于功能梯度材料波动特性的研究为反求功能梯度材料的特性参数提供了一种有效的方法;功能梯度梁波动特性的分析可以借助于商业有限元软件;代理模型的引入提高了反求方法的计算效率;应用遗传算法建立的功能梯度梁材料特性参数反求方法获得的材料参数误差小、精度高。
With the gradually increasing applications of functionally graded materials, there is a need for an effective method to non-destructively measure the material property of functionally graded materials. Based on the difficulties in evaluating functionally graded materials by traditional techniques and the limitations of advanced non-destructive evaluation in engineering application, an inverse procedure built on the transient response analysis of functionally graded beam is presented for charactering the material property of functionally graded materials.
Focusing on the functionally graded material (FGM), the wave propagation in FGM was analyzed. The inverse procedure for charactering the material property of functionally graded beam is based on the analysis of transient response and material property sensitivity of the functionally graded beam built by the finite element software.
Based on the analysis of wave propagation behaviors in functionally graded beam, the inverse problem was established combined with genetic algorithm and an inverse procedure by using transient response analysis of functionally graded beam was developed for determining the material property. The dynamic displacement responses of functionally graded beam obtained by the finite element software were employed as the input data, and the volume fractions were output data.
A surrogate-based method was provided, and the dynamic response model of functionally graded beam was substituted by response surface model as forward calculation technique of the inverse procedure. The design of experiment technique was employed to establish different surrogate models for comparing analysis, and the response surface model was proved to be accurate to substitute the wave propagating model of functionally graded beam.
Finally, the inverse procedure presented in this thesis was validated by two applications for charactering material property of SiC-C and SS-SN functionally graded beams.
The study shows that the research on wave propagation behaviors in FGM provides an effective method for charactering material property of FGM, and is able to be conducted by the commercial finite element software. The efficiency of the inverse procedure is improved by employing surrogate model technique. The inverse procedure combined with genetic algorithm is accurate to determine material property of functionally graded beam.
引文
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[33] Liu G R,Han X,Lam K Y.Material characterization of FGM plates using elastic waves and inverse procedure[J]. Journal of Composite Materials,2001,35(11): 954-971
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[35] Han X,Xu D,Liu G R.A computational inverse technique for material characterization of a functionally graded cylinder using a progressive neural network[J].Neurocomputing,2003,51:341-360
[36] Han X,Liu G R.Computational inverse technique for material characterization of functionally graded materials[J].AIAA Journal,2003,41(2):288-295
[37] 王礼立.应力波基础[M].国防工业出版社
[38] (美)J.L.罗斯著.何存富,吴斌,王秀彦译.固体中的超声波[M].北京:科学出版社,2004
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[42] Ohyoshi T.Stacking layer element for analyses of reflection and transmission of elastic waves to inhomogeneous layers[J].Mechanics Research Communication, 1993, 20(4):353-359
[43] Liu G R,Han X,Lam K Y.Stress waves in functionally gradient materials and its use for material characterization[J].Composite Part B,1999,30:383-394
[44] Liu G R,Han X,Lam K Y.A quadratic layer element for analyzing stress waves in FGMs and its application in material characterization[J].Journal of sound and vibration,2000,236(2):307-321
[45] Han X,Liu G R,Lam K Y.Transient waves in plates of functionally graded materials[J].INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING,2001,52:851-865
[46] Sasaki M,Wang Y,Hirano T.Design of SiC/C functionally gradient material and its propagation by chemical vapor deposition[J].Journal of Ceramic Society of Japan,1989,5:539-543
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[2] 新野正之,平井敏雄,渡边龙三.倾斜功能材料[J].日本复合材料学会志,1987,13: 257
[3] 朱信华,孟中岩. 梯度材料的研究现状与展望[J].功能材料,1998,29(2):121
[4] 李耀天,梯度功能材料研究与应用[J].金属功能材料,2000,7(4):15
[5] Yeo J G,Jung Y G,Choi S C.Design and microstructure of Zro2/SUS316 functionally graded materials by tape casting[J]. Materials letters, 1998, 37 : 304
[6] Miyamoto Y,Kaysser W A,Rabin B H.Functionally Graded Materials[M].Kluwer Academic Publishers,Boston Hardbound,1999
[7] Musil J, Fiala J.Plasma Spray Deposition of Graded Metal-ceramic Coatings[J]. Surface Coatings and Technology,1992,50:141-149
[8] Kajikama T,InShiota I,Miyamoto M Y.Functionally Graded Materials[M]. Elsevier Science,Tokyo,1996:475-482
[9] 解念锁.梯度功能材料的制造方法及应用[J].陕西工学院学报,2002,18(2):4-7
[10] Tsuda K,Ikegaya A.Development of functionally graded sintered hard material[J]. Powder Metallurgy,1996,39(4):296-300
[11] 程继贵,雷纯鹏,邓莉萍.梯度功能材料的制备及其应用研究的新进展[J].金属功能材料,2003,10(1):28-31
[12] Ma J,Tan G E.Fabrication and Characterization of Ti-TiB2 Functionally Graded Material System[J].Metallurgical and materials transactions,2002,33A:681-685
[13] 解念锁. SiCp/ Ni 梯度复合材料的制备及热震性能研究[J].陕西工学院学报, 2003,19 (1):41-43
[14] Pei Y T, J TH M DE hosson. Functionally Graded Materials Produced by Laser Cladding[J].Functionally Graded Mate2rials,2000,48:2617-2624
[15] Pei Y T, Zuo T C.Gradient microstructure in laser clad TiC-reinforced Ni- alloy composite coating[J].Materials Science and Engineering,1998,241A:259-263
[16] 李云凯,王勇,钟家湘.功能梯度材料[J].材料导报,2002,16(10):9-11
[17] 郭成,朱维斗.梯度功能材料的研究现状与展望[J].稀有金属材料工程,1993,24 (3):18-24
[18] SaSaki Keral.Strain-induced elastic anisotropy measured with ultrasonic waves[J].J Appl Mech,ASME,1990,57:930-936
[19] 余同希.弹塑性波的研究现状与趋势[J].力学进展,1992,22(3):347-357
[20] 杨桂通,张善元.弹性动力学[M].北京:中国铁道出版社,1988
[21] 廖振鹏.工程波动理论导论[M].2 版.北京:科学出版社,2002
[22] Pao Y H.The generalized ray theory and transient response of layered elastic solids[J].Physical Acoustics,1977,8(6):184-240
[23] Van der Hijden,JHMT.Propagation of Transient Elastic Waves in Stratified Anisotropic Media[M].North-Holland: Amsterdam,1987
[24] Booth D C,Grampin S.The anisotropic reflectivity technique: theory[J].Geophys, Journal of Royal Astrophysics Society,1983,72:755-766
[25] Scott RA,Miklowitz J.Transient elastic waves in anisotropic plates[J].ASME Journal of Applied Mechanics,1967,34:104-110
[26] Liu G R, Tani J, Ohyoshi T, et al.Transient waves in anisotropic laminated plates. Part 1: Theory; Part 2: Applications[J].Journal of Vibration and Acoustics,1991, 20(4):230-239
[27] Liu G R,Tani J,Ohyoshi T.Lamb waves in a functionally gradient material plates and its transient response.Part 1: theory[J].Transactions of the Japan Society of Mechanical Engineers,1991,57A(535):603-608
[28] Liu G R,Tani J,Ohyoshi T.Lamb waves in a functionally gradient material plates and its transient response. Part 2: calculation results[J].Transactions of the Japan Society of Mechanical Engineers,1991,57A(535):609-611
[29] Liu G R,Tani J.SH surface waves in functionally gradient piezoelectric material plates[J].Transactions of the Japan Society of Mechanical Engineers,1992,58A (547):504-507
[30] 杨建良,查开德,郭照南.复合材料内状态参数的实时无损检测系统[J].自动化仪表,1999, 20(12):5-13
[31] 刘怀喜,张恒,闫耀辰.人工神经网络在碳/ 环氧复合材料声发射检测中的应用[J].无损检测 NDT,2004,26(12):628-632
[32] Liu G R,Han X,Lam K Y.Stress waves in functionally gradient materials and its use for material characterization[J].Composites, Pt. B,1999,30(535):383-394
[33] Liu G R,Han X,Lam K Y.Material characterization of FGM plates using elastic waves and inverse procedure[J]. Journal of Composite Materials,2001,35(11): 954-971
[34] Liu G R,Han X,Xu Y G, et al.Material characterization of functionally graded material by means of elastic waves and a progressive-learning neural network[J]. Composites Science and Technology,2001,61:1401-1411
[35] Han X,Xu D,Liu G R.A computational inverse technique for material characterization of a functionally graded cylinder using a progressive neural network[J].Neurocomputing,2003,51:341-360
[36] Han X,Liu G R.Computational inverse technique for material characterization of functionally graded materials[J].AIAA Journal,2003,41(2):288-295
[37] 王礼立.应力波基础[M].国防工业出版社
[38] (美)J.L.罗斯著.何存富,吴斌,王秀彦译.固体中的超声波[M].北京:科学出版社,2004
[39] Doyle J F.Wave propagation in structures: spectral analysis using fast Fourier transforms[M],2nd edition,Springer,1997
[40] Tsai S W,Hahn T H.Introduction to composite materials[M].Techromic Publishing Company,Westport,1980
[41] Liu G R.A step-by-step method of rule-of-mixture of fiber-and particle- reinforced composite materials [J].Composite Struct,1998,40:313-322
[42] Ohyoshi T.Stacking layer element for analyses of reflection and transmission of elastic waves to inhomogeneous layers[J].Mechanics Research Communication, 1993, 20(4):353-359
[43] Liu G R,Han X,Lam K Y.Stress waves in functionally gradient materials and its use for material characterization[J].Composite Part B,1999,30:383-394
[44] Liu G R,Han X,Lam K Y.A quadratic layer element for analyzing stress waves in FGMs and its application in material characterization[J].Journal of sound and vibration,2000,236(2):307-321
[45] Han X,Liu G R,Lam K Y.Transient waves in plates of functionally graded materials[J].INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING,2001,52:851-865
[46] Sasaki M,Wang Y,Hirano T.Design of SiC/C functionally gradient material and its propagation by chemical vapor deposition[J].Journal of Ceramic Society of Japan,1989,5:539-543
[47] 美国 ABAQUS 公司编.庄茁主译.ABAQUS 有限元软件 6.4 版入门指南[M]. 北京:清华大学出版社,2004.9
[48] Goldberg D.Genetic Algorithms in Search Optimization and Machine Learning [M].Addison-Wesley,Reading,MA,1989
[49] Krishnakumar K.Micro-genetic Algorithms for Stationary and Non-Stationary Function Optimization[J].SPIE: Intelligent Control and Adaptive Systems, Philadelphia,PA,1196,1989,289
[50] Liu G R,Han X.Computational Inverse Techniques in Nondestructive Evaluation[M].NEW YORK:CRC PRESS,2003,107-121
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