Complex variables BIE and BEM for a plane doubly periodic system of flaws

Abstract

New complex variable, singular and hypersingular, boundary integral equations (CV‐BIE) are derived for doubly periodic plane elasticity problems. They refer to systems of blocks (grains), inclusions, holes and cracks. Their forms, convenient when adjusting conventional programs for non‐periodic systems to periodic problems, are suggested. Simple formulae are presented to calculate effective compliances in complex variables.

Numerical implementation of the derived complex variable hypersingular (CVH) BIE in the mentioned forms is carried out by appropriately adjusting a program of CVH‐BEM, previously developed for non‐periodic problems. It is used to check accuracy and to obtain new results for doubly periodic systems of cracks. Stress intensity factors (SIFs) and effective compliances are calculated for straight cracks in square and triangular lattices to compare them with published results. They show agreement within the accuracy reached by other authors. New data on SIFs and effective compliances for doubly periodic systems of angular and curvilinear, strongly interacting cracks, illustrate abilities of the method.

Key words :

• complex variable boundary equations
• doubly periodic flaws
• elasticity.

Notes

Correspondence addressee