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Transient elastodynamic analysis by time domain bem in cylindrical coordinates
Author(s) -
Lei Z. X.,
Tham L. G.,
Cheung Y. K.
Publication year - 1992
Publication title -
earthquake engineering and structural dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.218
H-Index - 127
eISSN - 1096-9845
pISSN - 0098-8847
DOI - 10.1002/eqe.4290211204
Subject(s) - mathematical analysis , boundary element method , mathematics , singular integral , cylindrical coordinate system , fourier transform , field (mathematics) , time domain , boundary (topology) , domain (mathematical analysis) , integral equation , geometry , physics , finite element method , computer science , pure mathematics , computer vision , thermodynamics
Abstract A time domain boundary element in a cylindrical coordinate system is developed for the analysis of wave propagation in a half space. The integral formulation is based on Graffi's dynamic reciprocal theorem and Stokes' fundamental solutions. The field quantities (displacements and tractions) are expressed as products of Fourier series in the tangential direction and linear polynomials in the other spatial directions. Gaussian integration is used to integrate the non‐singular parts of the integral equations, whereas the integration of the singular components, which are either of order 1/ r or 1/ r 2 , is handled by special numerical schemes. In the time marching aspect, the field quantities are assumed to vary linearly in the temporal direction as well. Examples for wave propagation due to various forms of surface excitations are reported to demonstrate the accuracy of the method.