An advanced direct time domain BEM formulation for general 3-D elastodynamic problems

A new advanced time domain BEM formulation is presented for the study of general 3-D elastodynamic problems. The proposed method is based on the infinite space Stokes fundamental solutions, which, for the first time, are written in terms of body forces in the form of higher order B-spline time distributions. Higher order spatial and temporal discretization schemes are applied to the boundary integral equations of the elastodynamic system yielding a time marching solution for the characteristic response of the system due to an excitation with a B-spline distribution in time. This characteristic response due to a B-spline excitation forms the basis, within the framework of a general B-spline superposition scheme, for the calculation of the responses of the same elastodynamic system due to any transient forcing function.

[1]  Horace Lamb,et al.  On the propagation of tremors over the surface of an elastic solid , 1904, Proceedings of the Royal Society of London.

[2]  Dimitris L. Karabalis,et al.  Dynamic response of 3-D embedded foundations by the boundary element method , 1986 .

[3]  A. Love.  The Propagation of Wave‐Motion in an Isotropic Elastic Solid Medium , 1904 .

[4]  Dimitris L. Karabalis.  Recent Applications in Computational Mechanics , 1986 .

[5]  C. Brebbia,et al.  Boundary Element Techniques , 1984 .

[6]  Anestis S. Veletsos,et al.  LATERAL AND ROCKING VIBRATION OF FOOTINGS , 1971 .

[7]  Paul G. Richards,et al.  Quantitative Seismology: Theory and Methods , 1980 .

[8]  J. Wolf.  Dynamic soil-structure interaction , 1985 .

[9]  Herbert A. Mang,et al.  A new method for evaluating singular integrals in stress analysis of solids by the direct boundary element method , 1985 .

[10]  Prasanta K. Banerjee,et al.  Time‐domain transient elastodynamic analysis of 3‐D solids by BEM , 1988 .

[11]  P. K. Banerjee,et al.  Boundary element methods in engineering science , 1981 .

[12]  S. Timoshenko,et al.  Theory of Elasticity (3rd ed.) , 1970 .

[13]  J. Penzien,et al.  Two-dimensional hybrid modelling of soil-structure interaction , 1981 .

[14]  A. Love.  A treatise on the mathematical theory of elasticity , 1892 .

[15]  L. Wheeler,et al.  Some theorems in classical elastodynamics , 1968 .

[16]  S. Timoshenko,et al.  Theory of elasticity , 1975 .

[17]  G. Nürnberger.  Approximation by Spline Functions , 1989 .

[18]  J. Z. Zhu,et al.  The finite element method , 1977 .

[19]  K. Graff.  Wave Motion in Elastic Solids , 1975 .

[20]  Dimitri E. Beskos.  Boundary Element Methods in Structural Analysis , 1989 .

[21]  J. Achenbach.  Wave propagation in elastic solids , 1962 .

[22]  Carl de Boor,et al.  A Practical Guide to Splines , 1978, Applied Mathematical Sciences.

[23]  Ivar Fredholm.  Sur une classe d’équations fonctionnelles , 1903 .

[24]  Eduardo Kausel,et al.  Dynamic Analysis of Footings on Layered Media , 1975 .

[25]  I. J. Schoenberg.  Contributions to the problem of approximation of equidistant data by analytic functions. Part B. On the problem of osculatory interpolation. A second class of analytic approximation formulae , 1946 .

[26]  Dimitri E. Beskos,et al.  Boundary Element Methods in Mechanics , 1988 .

[27]  Shad M. Sargand,et al.  Hybrid FE Procedure for Soil‐Structure Interaction , 1984 .

[28]  Dimitris L. Karabalis,et al.  Dynamic response of 3‐D rigid surface foundations by time domain boundary element method , 1984 .

[29]  I. J. Schoenberg.  Contributions to the problem of approximation of equidistant data by analytic functions. Part A. On the problem of smoothing or graduation. A first class of analytic approximation formulae , 1946 .

[30]  Dimitrios E. Beskos,et al.  Dynamic response of 3-D flexible foundations by time domain BEM and FEM , 1985 .

[31]  Yih-Hsing Pao,et al.  Diffraction of elastic waves and dynamic stress concentrations , 1973 .

[32]  D. Beskos,et al.  Boundary Element Methods in Elastodynamics , 1988 .

[33]  A. Eringen,et al.  Elastodynamics, Vol. II, Linear Theory , 1978 .

[34]  Prasanta K. Banerjee,et al.  Transient elastodynamic analysis of three‐dimensional problems by boundary element method , 1986 .