Stress calculations on multiply connected domains

Authors:
Johan Helsing;Anders Jonsson
Affiliations:
Numerical Analysis, Center for Mathematical Sciences, Lund University, Box 118, S-221 00 Lund, Sweden;Department of Solid Mechanics, Royal Institute of Technology, S-100 44 Stockholm, Sweden
Venue:
Journal of Computational Physics
Year:
2002

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Abstract

The outstanding problem of finding a simple Muskhelishvili-type integral equation for stress problems on multiply connected domains is solved. Complex potentials are represented in a way which allows for the incorporation of cracks and inclusions. Several numerical examples demonstrate the generality and extreme stability of the approach. The stress field is resolved with a relative error of less than 10-10 on a large, yet simply reproducible, setup with a loaded square plate containing 4096 holes and cracks. Comparison with previous results in the literature indicates that general-purpose finite-element software may perform better than many special-purpose codes.