Vasil’ev, Kirill; Pasternak, Yaroslav; Sulim, Georgyij Antiplane deformation of a solid with rectangular base containing a thin internal heterogeneity. (Ukrainian. English summary) Zbl 1249.74001 Visn. L’viv. Univ., Ser. Mekh.-Mat. 73, 165-176 (2010). Summary: This paper presents two methods for studying the antiplane deformation of finite solids containing thin ribbon-like inclusions. The first one is an analytic-numerical method, which consists of modelling bounded domains through the space with the system of the contacting heterogeneities at their contact points which are unknown concentrated forces and dislocations. For the verification of this method, a second numerical approach is proposed based on the boundary element method. Numerical examples are presented for a square domain with an arbitrarily located crack. The difference between the results of the two methods is less than \(1\%\) which shows the efficiency of the proposed approaches. MSC: 74A05 Kinematics of deformation 74S30 Other numerical methods in solid mechanics (MSC2010) Keywords:antiplane deformation; method of direct complete cutting; BEM rectangular solid; crack PDFBibTeX XMLCite \textit{K. Vasil'ev} et al., Visn. L'viv. Univ., Ser. Mekh.-Mat. 73, 165--176 (2010; Zbl 1249.74001)