Three-dimensional transient half-space dynamics using the dual reciprocity boundary element method

Abstract

The dual reciprocity boundary element method (DRBEM) is studied thoroughly in the present paper. To the best knowledge of the authors, the DRBEM has never been applied to 3D half-space dynamics previously. In the present paper, the mathematical derivation of the method is presented, with stress placed on peculiarities of the method when applied to transient half-space dynamics. It has been found that semi-infinite domains (half-space) are more difficult to simulate, since the truncation of the discretization of the half-space surface by boundary elements results in excessive spurious wave reflection on the border of the discretized region. Mathematical derivation of the method is followed by its numerical implementation. Wave propagation due to various kinds of loading in the time-domain is studied afterward, aimed at the validation of the method. The main advantage of the DRBEM over its counterparts, used to model infinite and semi-infinite domains (such as classical BEM formulation, integral transformations, thin layer method), is that it produces time- and frequency-independent matrices (mass and stiffness matrix), by preserving a boundary-only discretization (no internal nodes necessary). This makes the method very attractive, since this feature is very close to the common engineering understanding and the final equation of motion has a similar form like the one known from the finite element method. Moreover, the formulation allows for seamless incorporation of non-homogeneous initial conditions, i.e. non-zero initial displacements and velocities and surface tractions can be prescribed.