Ðàññìàòðèâàåòñÿ ñòàòè÷åñêàÿ çàäà÷à òåîðèè óïðóãîñòè î êîíöåíòðàöèè íàïðÿaeåíèé â îêðåñòíîñòè âåðøèí âíóòðåííåé òðåùèíû êîíå÷íîé äëèíû â ïîëîñå, óñèëåííîé òîíêèì ãèáêèì ïîêðûòèåì. Òðåùèíà ðàñïîëîaeåíà ïàðàëëåëüíî ãðàíèöàì ïîëîñû, áåðåãà åå íå âçàèìîäåéñòâóþò. Çàäà÷à ñèììåòðè÷íà îòíîñèòåëüíî ëèíèè òðåùèíû. Èññëåäîâàíèå îñíîâàíî íà ìåòîäå èíòåãðàëüíûõ ïðåîáðàçîâàíèé, êîòîðûé ïîçâîëèë ñâåñòè çàäà÷ó ê ðåøåíèþ ñèíãóëÿðíîãî èíòåãðàëüíîãî óðàâíåíèÿ ïåðâîãî ðîäà ñ ÿäðîì Êîøè.  êà÷åñòâå ìîäåëè ïîêðûòèÿ èñïîëüçîâàíû ñïåöèàëüíûå ãðàíè÷íûå óñëîâèÿ, ñôîðìóëèðîâàííûå íà îñíîâå àñèìïòîòè÷åñêîãî àíàëèçà ðåøåíèÿ çàäà÷è äëÿ òîíêîé óïðóãîé ïîëîñû, èçãèáíîé aeåñòêîñòüþ êîòîðîé ìîaeíî ïðåíåáðå÷ü. Ïðîâåäåíî èññëåäîâàíèå ðåãóëÿðíîé ÷àñòè ÿäðà â çàâèñèìîñòè îò ñîîòíîøåíèé ôèçè÷åñêèõ õàðàêòåðèñòèê ìàòåðèàëîâ ïîëîñû è ïîêðûòèÿ, à òàêaeå òàêèõ ãåîìåòðè÷åñêèõ ïàðàìåòðîâ, êàê ðàçìåð òðåùèíû è òîëùèíû ïîëîñû è ïîêðûòèÿ. Ðåøåíèå èíòåãðàëüíîãî óðàâíåíèÿ ïîñòðîåíî ìåòîäîì êîëëîêàöèé â âèäå ðàçëîaeåíèÿ ïî ïîëèíîìàì ×åáûøåâà ñ çàðàíåå âûäåëåííîé îñîáåííîñòüþ. Ïðîâåäåí àíàëèç ñõîäèìîñòè ìåòîäà â çàâèñèìîñòè îò ñîîòíîøåíèÿ çíà÷åíèé ïàðàìåòðîâ çàäà÷è. Ïîëó÷åíû çíà÷åíèÿ ôàêòîðà âëèÿíèÿ, ïðèâåäåííîãî êîýôôèöèåíòà èíòåíñèâíîñòè íîðìàëüíûõ íàïðÿaeåíèé â îêðåñòíîñòè âåðøèí òðåùèíû äëÿ ðàçëè÷íûõ êîìáèíàöèé ãåîìåòðè÷åñêèõ è ôèçè÷åñêèõ ïàðàìåòðîâ çàäà÷è.  ÷àñòíîñòè, óñòàíîâëåíî, ÷òî óâåëè÷åíèå òîëùèíû è aeåñòêîñòè ïîêðûòèÿ âåäåò ê ñíèaeåíèþ âåëè÷èíû ôàêòîðà âëèÿíèÿ. Óâåëè÷åíèå äëèíû òðåùèíû èëè óìåíüøåíèå øèðèíû ïîëîñû ïðèâîäèò ê óâåëè÷åíèþ âåëè÷èíû ôàêòîðà âëèÿíèÿ. Ðàññìîòðåíû èçâåñòíûå ÷àñòíûå ñëó÷àè óêàçàííîé çàäà÷è.  ÷àñòíîñòè, â ñëó÷àå îòñóòñòâèÿ ïîêðûòèÿ ðåçóëüòàòû ñîïîñòàâëåíû ñ èìåþùèìèñÿ â ëèòåðàòóðå äàííûìè. Êëþ÷åâûå ñëîâà: òðåùèíà, òîíêîå ãèáêîå ïîêðûòèå, êîýôôèöèåíò èíòåíñèâíîñòè íàïðÿaeåíèé, ôàêòîð âëèÿíèÿ, ìåòîä èíòåãðàëüíûõ ïðåîáðàçîâàíèé, ìåòîä êîëëîêàöèé, ñèíãóëÿðíîå èíòåãðàëüíîå óðàâíåíèå, ÿäðî Êîøè. Ââåäåíèå Ýêñïëóàòàöèÿ äåòàëåé ìàøèí è êîíñòðóêöèé ïðîèñõîäèò â óñëîâèÿõ âîçíèêíîâåíèÿ êîððîçèè, áîëüøèõ íàãðóçîê, ïîâûøåííîãî èçíàøèâàíèÿ, êîãäà êîíöåíòðà
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