A Space-time Boundary Element Method For
3D Elastodynamic Analysis
Author(s)
J. X. Zhou & T. G. Davies
Abstract
The classical BEMapproach for elastodynamics,which employs a finite difference methodology in time (with piece-wise analytic integration in the time domain) and
boundary element discretisation in space, can produce poor results for elastodynamic
problems where high gradients occur, such as wave fronts. High gradient
areas evolve over time and their locations are unknown a priori. Such high gradients
can neither be captured by mesh refinement in advance, nor can they be
properly approximated by ordinary lower order polynomial shape functions. In
this paper,we propose a novel method which interpolates both spatial and temporal
domains. A posteriori error estimation formula in space-time is developed to
locate the moving wave front. An h- hierarchical adaptive scheme is used to capture
the wave fronts accurately and to forestall generation of spurious oscillations
there. An numerical examples is given to demonstrate the power and scope of the
method.
Keywords: time domain BEM, Elastodynamics, error estimation, adaptive mesh
refinement.
1 Introduction
Since the time domain Boundary Element formulation for elastodynamics and
scalar wave propagation was firstly developed (Mansur and Brebbia [1]. Banerjee
and Kobayashi [2]), algorithmic has been the major numerical difficulty. To
address this problem, various spatial and temporal interpolation schemes have
been implemented to improve accuracy and stability, such as combinations of constant,
linear and quadratic functions (Dominguez [3], Mansur and Carrer [4]), Bsplines
interpolation schemes (Rizos and Karabalis [5]), quadratic time interpolation
schemes (Wang and Wang [6]). Other strategies to improve stability include
Keywords
time domain BEM, Elastodynamics, error estimation, adaptive mesh
refinement.
Related Book
Other papers in this volume
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