考虑场地介质随机特性的无限域波动分析
|
摘要
针对场地介质具有随机特性的无限域地震波动分析问题,在概率空间中将随机反应向量按随机介质场离散所得主导随机变量的正交多项式级数形式展开,使随机微分方程变换为确定性的扩阶线性方程组;并在波动有限元模拟技术的基础上,构造了扩阶透射人工边界公式,两者结合形成了求解无限域随机介质中波动传播问题的有限元分析方法.该方法不仅不受基于摄动思想各类方法的久期项的干扰,而且避免了采用模拟方法时人工边界区单元参数样本不均匀所引起的数值计算不稳定问题.
The random parameter field is discretized into random variables which are expanded in the form of orthogonal polynomials in probability space, and the random differential wave equation is transformed into deterministic linear order-expanded equations. An order-expanded multi-transmitting artificial boundary formula is also derived based on the finite element simulation of wave motion. The combination of the deterministic order-expanded equations and the order-expanded multi-transmitting artificial boundary formula can provide a method to analyze the problem of wave motion analysis in infinite domain with uncertainty in site. Not only is this method free from the secular problem of the corresponding methods which are based on perturbation idea, but also it avoid the numerical instability resulted from the heterogeneity of the ABC elements samples when the Monte Carlo simulation method is used.
The random parameter field is discretized into random variables which are expanded in the form of orthogonal polynomials in probability space, and the random differential wave equation is transformed into deterministic linear order-expanded equations. An order-expanded multi-transmitting artificial boundary formula is also derived based on the finite element simulation of wave motion. The combination of the deterministic order-expanded equations and the order-expanded multi-transmitting artificial boundary formula can provide a method to analyze the problem of wave motion analysis in infinite domain with uncertainty in site. Not only is this method free from the secular problem of the corresponding methods which are based on perturbation idea, but also it avoid the numerical instability resulted from the heterogeneity of the ABC elements samples when the Monte Carlo simulation method is used.
引文
1 Sobczyk K. Stochastic Wave Propagation. Warsaw: PWN-Polish Scientific Publishers, 1985． 248
2 Uscinski BJ. The Elements of Wave Propagation in Random Media. New York: McGraw-Hill, 1977． 153
3 Faccioli E, Tagliani A. Attenuation analysis of high frequency SH waves in random media by finite differences, Proceedings of Ninth World Conference on Earthquake Engineering, Vol. VIII, Paper SA-2． Tokyo, 1989． 25-30
4 Manolis GD, Shaw RP. Harmonic wave propagation through visco-elastic heterogeneous media exhibiting mild stochasticity-II. Applications. Soil Dynamics and Earthquake Engineering, 1996, 15 (2) : 129-139
5 Burczynski T, Skrzypczyk J. Theoretical and computational aspects of the stochastic boundary element method. Computer Methods in Applied Mechanics and Engineering, 1999, 168(1-4) : 321-344
6 向家琳,姚振汉,杜庆华.弹性半平面中SH波动问题的随机边界元法及其应用.清华大学学报(自然科学版),1996,36(10) :56-61 (Xiang Jialin, Yao Zhenhan, Du Qinghua. Stochastic boundary element method and its applications to SH wave propagation in half plane. Journal of Tsinghua University (Sci & Tech), 1996, 36(10) : 56-61 (in Chinese))
7 Smith WD. The application of finite element analysis to body wave propagation problems. Geophys J R Astr Soc, 1975, 42(9) : 747-768
8 廖振鹏.工程波动理论导引.北京:科学出版社, 1996． 322(Liao Zhenpeng.An Introduction to Wave Theory in En-gineering.Beijing:Science Press,1996． 322(in Chinese))
9 李杰.随机结构系统--分析与建模.北京:科学出版社,1996． 297 (Li Jie. Stochastic Structural System-Analysis and Modeling. Beijing: Science Press, 1996． 297 (in Chinese))
2 Uscinski BJ. The Elements of Wave Propagation in Random Media. New York: McGraw-Hill, 1977． 153
3 Faccioli E, Tagliani A. Attenuation analysis of high frequency SH waves in random media by finite differences, Proceedings of Ninth World Conference on Earthquake Engineering, Vol. VIII, Paper SA-2． Tokyo, 1989． 25-30
4 Manolis GD, Shaw RP. Harmonic wave propagation through visco-elastic heterogeneous media exhibiting mild stochasticity-II. Applications. Soil Dynamics and Earthquake Engineering, 1996, 15 (2) : 129-139
5 Burczynski T, Skrzypczyk J. Theoretical and computational aspects of the stochastic boundary element method. Computer Methods in Applied Mechanics and Engineering, 1999, 168(1-4) : 321-344
6 向家琳,姚振汉,杜庆华.弹性半平面中SH波动问题的随机边界元法及其应用.清华大学学报(自然科学版),1996,36(10) :56-61 (Xiang Jialin, Yao Zhenhan, Du Qinghua. Stochastic boundary element method and its applications to SH wave propagation in half plane. Journal of Tsinghua University (Sci & Tech), 1996, 36(10) : 56-61 (in Chinese))
7 Smith WD. The application of finite element analysis to body wave propagation problems. Geophys J R Astr Soc, 1975, 42(9) : 747-768
8 廖振鹏.工程波动理论导引.北京:科学出版社, 1996． 322(Liao Zhenpeng.An Introduction to Wave Theory in En-gineering.Beijing:Science Press,1996． 322(in Chinese))
9 李杰.随机结构系统--分析与建模.北京:科学出版社,1996． 297 (Li Jie. Stochastic Structural System-Analysis and Modeling. Beijing: Science Press, 1996． 297 (in Chinese))
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心