Rapid Re-analysis In
BEM Elastostatic Calculations
Author(s)
J. Trevelyan & D. J. Scales
Abstract
The real time solution and updating of stress contours for small elasticity
problems allows the rapid and interactive evaluation of multiple design proposals
and the convergence on an optimum solution in a significantly reduced time.
The increased level of interactivity allows the user to see the potentially complex
interactions between multiple geometric features. A number of strategies are
proposed and compared with current techniques. Boundary element integrals are
accelerated by the use of Look-Up Tables (LUT’s) containing pre-computed
integrals. These can be employed in the matrix assembly and the internal point
calculations for both flat and arc elements. The effect of problem size on
propagated error has been investigated and the effect of interpolation has been
considered. An error analysis has been performed and a suitable scheme for
LUT refinement proposed. The approach has been benchmarked against regular
Gauss-Legendre quadrature. The large storage requirement of the LUT’s has
been considered and the use of a least squares surface fit to the LUT’s has been
investigated and the computational cost compared with Gauss-Legendre
quadrature. Iterative re-solution of the problem is accelerated by the use of an
approximate LU preconditioner that is updated as required by a secondary thread
of execution. The proposed preconditioner has been benchmarked against other
preconditioners and reduces solve times to typically less than 30% of the direct
solve time. The proposed techniques achieve the aim of providing a real-time
update of contours for small problems on a PC.
Keywords: rapid re-analysis, integrations, surface fitting.
1 Introduction
Accelerating the stress analysis of structures allows the rapid consideration of
multiple designs for a variety of criteria, and provides for efficient solution of
Keywords
rapid re-analysis, integrations, surface fitting.
Related Book
Other papers in this volume
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