A modified Laurent series for hole/inclusion problems in plane elasticity.

We propose a modified Laurent series for investigating the elastic field around holes/inclusions under plane deformation by dividing the classical Laurent series over the first derivative of the conformal mapping, which is justified from a mathematical point of view. Through a group of numerical examples concerning the stress concentration around holes of common shapes, the accuracy of the modified Laurent series is verified. It is also demonstrated that the use of the modified Laurent series as compared with the classical one generally leads to significantly more accurate results with even much fewer terms of the series. Utilizing the modified Laurent series, we revisit the stress field around an irregularly shaped elastic inclusion embedded in an infinite matrix and effectively eliminate the severe interfacial stress fluctuation reported earlier in the literature. More importantly, the modified Laurent series may be very useful for a highly accurate prediction of the physical field in particulate composites with densely packed inclusions. [ABSTRACT FROM AUTHOR]