地震波激励下土与结构的动力边界单元法分析
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摘要
以连续介质力学和弹性波动理论为基础，在Ｌａｐｌａｃｅ积分变换域内推导了地震波激励下土与结构的多子域边界积分－边界单元方程，采用了一系列特殊的数值积分处理技术；根据随机过程原理以及基于基岩面运动的地震力理论建立了随机地震波数学模型；提出了一种新的Ｌａｐｌａｃｅ数值反演变换方法，并引入了最小标准误差原理，实现了Ｌａｐｌａｃｅ 反演变换中各控制参数的最优化关联取值，使计算精度与计算速度均有较大的改进和提高；编制了相应的计算机程序，并通过几个土－结构的地震响应算例分析，证实了方法和程序的可行性与有效性
It is suitable to analyse the dynamic problems of soil--structure system under seismic wave excitation by dynamic boundary element method, if a mathematical model is established for inputting seismic motion loading-an unsteady stochastic dynamic process. The multi-subregion boundary integral equation of soil-structure system under seismic wave excitation on tile basis of elastic wave theory has been derived by Laplace transformation. A series of special techniques have been adopted for numerical integration and a mathematical model of seismic motion is proposed based on the stochastic process theory and motion of bedrock surface. The history process curve showing different characteristics close to the recorded one can be simulated, when the positive real number a_j, b_j,w_j and stochastic variable _j in Eq.(8) are selected according to the features of recorded curve of seismic acceleration. An unsteady stochastic seismic wave history process simulative curve is shown in Fig.l. The real values in time domain can be obtained by Laplace inversion. A new numerical inversion method is proposed by expanding the solved function into the Fourier sine and cosine series. In computation, the evaluation by modified recursive procedure only requires (n + 1) multiplications if the sin and cos in Eq.(11) are computed. Then the sum of series in Eq.(11) is obtained. It is found that the results are obtained fairly accurately with relatively little work. The least standard error principle for Laplace numerical inversion transformation is put forward in order to optimize the selection of all control parameters or, N, T, etc. in Eq.(15). The precision and stability of numerical inversion, especially at later sample points, has improved greatly. The corresponding code of the program is compiled. A few numerical examples illustrating seismic response of soil-structure system are presented to confirm feasibility and effectiveness of the proposed method.
It is suitable to analyse the dynamic problems of soil--structure system under seismic wave excitation by dynamic boundary element method, if a mathematical model is established for inputting seismic motion loading-an unsteady stochastic dynamic process. The multi-subregion boundary integral equation of soil-structure system under seismic wave excitation on tile basis of elastic wave theory has been derived by Laplace transformation. A series of special techniques have been adopted for numerical integration and a mathematical model of seismic motion is proposed based on the stochastic process theory and motion of bedrock surface. The history process curve showing different characteristics close to the recorded one can be simulated, when the positive real number a_j, b_j,w_j and stochastic variable _j in Eq.(8) are selected according to the features of recorded curve of seismic acceleration. An unsteady stochastic seismic wave history process simulative curve is shown in Fig.l. The real values in time domain can be obtained by Laplace inversion. A new numerical inversion method is proposed by expanding the solved function into the Fourier sine and cosine series. In computation, the evaluation by modified recursive procedure only requires (n + 1) multiplications if the sin and cos in Eq.(11) are computed. Then the sum of series in Eq.(11) is obtained. It is found that the results are obtained fairly accurately with relatively little work. The least standard error principle for Laplace numerical inversion transformation is put forward in order to optimize the selection of all control parameters or, N, T, etc. in Eq.(15). The precision and stability of numerical inversion, especially at later sample points, has improved greatly. The corresponding code of the program is compiled. A few numerical examples illustrating seismic response of soil-structure system are presented to confirm feasibility and effectiveness of the proposed method.
引文
1 Zhou XR, Wiberg NR. Boundary Element Analysis for Dynamic Response of Vibration Foundation. ActaMechanica Solida Sinica, 1988, 9(2): 113-120
2周锡礽,吴小杰 三维瞬态动力场的基本解及积分方程.应用数学学报, 1991, 14(2): 213～219(Zhou XR, Wu XJThe fundamental solution and boundary integral equation on three dimensions transient elastodynamic problem.Acta Methematicae Applicatae Sinia, 1991, 14(2): 213-219 (in Chinese))
3 Liu JL, Wallg H, Zhou XR. The boundary element analysis program for 3-D transient dynamic field. Transactions of Tianjin University, 1997, 3(2). 144~149
4 Manolis GD, Beskos DE著、周锡礽,陈火坤译.弹性动力的边界单元法,天津科技出版社. 1991 (Manoli GD, Beskos DE. Boundary Element Methods in Elastodynamics. London: UnWin Hyman Ltd 1988)
5周锡礽,伍志国.成层土体与结构组合体系的动力数值模型.岩土工程学报, 1989, 11(1): 1～12(Zhou XR, Wu ZG. A dynamic numerical model for the combined system of loyered soil-structure.Journal of Geotechnical Engineering,1989,11(1):1～2(in Chinese))
6 Zhou XR, Feng HB, Chen HK. The least criteria error principle on laplace numerical inversion transformation.In: Proc of 4th China-Japan Symposium on BEM. 1991. 129-134
7 Katsikadelis JT, Nerantzaki MS. The boundary element method applied to dynamic problems. BoundaryElement XIV, 2: 1992,
8 Manolis CD, Ahmad S, Banerjee PK. BEM Implementation for 3-D Transient Elastodynamics. Development in BEM 4, 1986
2周锡礽,吴小杰 三维瞬态动力场的基本解及积分方程.应用数学学报, 1991, 14(2): 213～219(Zhou XR, Wu XJThe fundamental solution and boundary integral equation on three dimensions transient elastodynamic problem.Acta Methematicae Applicatae Sinia, 1991, 14(2): 213-219 (in Chinese))
3 Liu JL, Wallg H, Zhou XR. The boundary element analysis program for 3-D transient dynamic field. Transactions of Tianjin University, 1997, 3(2). 144~149
4 Manolis GD, Beskos DE著、周锡礽,陈火坤译.弹性动力的边界单元法,天津科技出版社. 1991 (Manoli GD, Beskos DE. Boundary Element Methods in Elastodynamics. London: UnWin Hyman Ltd 1988)
5周锡礽,伍志国.成层土体与结构组合体系的动力数值模型.岩土工程学报, 1989, 11(1): 1～12(Zhou XR, Wu ZG. A dynamic numerical model for the combined system of loyered soil-structure.Journal of Geotechnical Engineering,1989,11(1):1～2(in Chinese))
6 Zhou XR, Feng HB, Chen HK. The least criteria error principle on laplace numerical inversion transformation.In: Proc of 4th China-Japan Symposium on BEM. 1991. 129-134
7 Katsikadelis JT, Nerantzaki MS. The boundary element method applied to dynamic problems. BoundaryElement XIV, 2: 1992,
8 Manolis CD, Ahmad S, Banerjee PK. BEM Implementation for 3-D Transient Elastodynamics. Development in BEM 4, 1986
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