基于有限元及修正梯度法的材料二维缺陷弹性波识别
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摘要
文章研究了一种利用弹性波识别二维缺陷形状的方法。采用有限元方法直接由入射场计算散射场,反演计算中采用二元三角基函数将扰动函数展开,并取残差模量的梯度作为迭代收敛的方向,同时引入梯度因子与梯度相乘以对其进行修正从而加快收敛,通过对扰动函数的反演识别出缺陷的形状。从算例可以看出,此方法能够有效地识别材料的二维缺陷。
The method of2-D flawidentification using elastic wave is studied in this paper.The fringe field is obtained directˉlyfromthe incidentfield throughFEM.The disturbed functionis expanded accordingtothe bivariate circular function in the inverˉsion calculation.The gradientfactor is introduced and modified to accelerate the convergence along the gradient of residual moduˉlus,and the shape of the flaws is identified through the inversion of disturbed function.From the examples,the2-D flaws of materials are identified effectively based on this method.
The method of2-D flawidentification using elastic wave is studied in this paper.The fringe field is obtained directˉlyfromthe incidentfield throughFEM.The disturbed functionis expanded accordingtothe bivariate circular function in the inverˉsion calculation.The gradientfactor is introduced and modified to accelerate the convergence along the gradient of residual moduˉlus,and the shape of the flaws is identified through the inversion of disturbed function.From the examples,the2-D flaws of materials are identified effectively based on this method.
引文
[1]马兴瑞,陶良,牛玉清,等.弹性动力学反问题[A].《走向21世纪的中国力学》中国科协第9次“青年科学家论坛”[C].北京:清华大学出版社,1996.164-178.
[2]杨慧珠,张远高,鲁小蓉.动力学的反问题[A].固体力学发展趋势[C].北京:北京理工大学出版社,1995.55-73.
[3]杨慧珠.弹性动力学反问题[A].《走向21世纪的中国力学》中国科协第9次“青年科学家论坛”[C].北京:清华大学出版社,1996.264-273.
[4]金星.利用地震记录反演震源特征的一些问题[J].地震工程与工程振动,1997,(3):15-23.
[5]邵秀民,蓝志凌.各向异性弹性介质中波动方程的吸收边界条件[J].地球物理学报,1995,38(增1):56-73.
[6]方静,张玉胜,肖衍明.边元有限元法与矢量吸收边界条件相结合计算三维散射问题[J].西安交通大学学报,1996,30(2):28-34.
[7]Gan H,Levin P L,Ludwig R.Finite element formulation ofacoustic scattering phenomena with absorbing boundary condi-tion in the frequency domain[J].J Acoust Soc Am,1993,(94):1651-1662.
[8]Engquist B,Majda A.Radiation boundary conditions for a-coustic and elastic wave caculations[J].Commun Pure ApplMath,1979,(32):313-357.
[9]Flanery B P,Teukolsky S A,Vetterling W T.Numerical Re-ciples,The Art of Scientific Computing[M].Cambridge NewYork:Unir Press,1986.275-307.
[2]杨慧珠,张远高,鲁小蓉.动力学的反问题[A].固体力学发展趋势[C].北京:北京理工大学出版社,1995.55-73.
[3]杨慧珠.弹性动力学反问题[A].《走向21世纪的中国力学》中国科协第9次“青年科学家论坛”[C].北京:清华大学出版社,1996.264-273.
[4]金星.利用地震记录反演震源特征的一些问题[J].地震工程与工程振动,1997,(3):15-23.
[5]邵秀民,蓝志凌.各向异性弹性介质中波动方程的吸收边界条件[J].地球物理学报,1995,38(增1):56-73.
[6]方静,张玉胜,肖衍明.边元有限元法与矢量吸收边界条件相结合计算三维散射问题[J].西安交通大学学报,1996,30(2):28-34.
[7]Gan H,Levin P L,Ludwig R.Finite element formulation ofacoustic scattering phenomena with absorbing boundary condi-tion in the frequency domain[J].J Acoust Soc Am,1993,(94):1651-1662.
[8]Engquist B,Majda A.Radiation boundary conditions for a-coustic and elastic wave caculations[J].Commun Pure ApplMath,1979,(32):313-357.
[9]Flanery B P,Teukolsky S A,Vetterling W T.Numerical Re-ciples,The Art of Scientific Computing[M].Cambridge NewYork:Unir Press,1986.275-307.
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