Stress Calculations on Multiply Connected Domains

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.