We construct a system of singular integral equations for the first fundamental problem of the plane elasticity theory for a quasiorthotropic body containing holes and cracks. For this purpose, we use the wellknown integral equations obtained for a system of curvilinear cracks (cuts) in a quasiorthotropic plane. The integral equations for a multiply connected region with holes are constructed with the help of the limit transition from open cuts in an infinite elastic plane to closed cuts. These singular integral equations of the first kind on closed contours (boundary of the body) are supplemented with the corresponding regularizing functionals guaranteeing the unique solvability of the integral equations for arbitrary right-hand sides.
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Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 52, No. 4, pp. 30–39, July–August 2016.
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Savruk, M.P., Kazberuk, A. & Chornenkyi, A.B. Integral Equations of a Plane Problem of the Elasticity Theory for a Multiply Connected Quasiorthotropic Body. Mater Sci 52, 472–484 (2017). https://doi.org/10.1007/s11003-017-9979-8
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DOI: https://doi.org/10.1007/s11003-017-9979-8