تحليل تنش در باريكه ارتوتروپيك غير همگن حاوي چندين ترك محدود شده توسط دو لايه پيزوالكتريك

Stress analysis in an orthotropic non-homogeneous strip sandwiched between two piezoelectric layers weakened by multiple cracks

در اين مقاله، تحليل تنش در باريكه ارتوتروپيك با رفتار تابعي محدود شده توسط دو لايه پيزوالكتريك انجام شده است. يكي از روش‌هاي كارا در حل مسائل محيط‌هاي تضعيف شده توسط تركها، استفاده از حل نابجايي است. ابتدا حل نابجايي در باريكه با حل معادله حاكم، اعمال شرايط مرزي و شرايط پيوستگي مربوط به نابجايي بكمك تبديل فوريه انجام مي‌گردد و ميدان تنش ارائه مي‌گردد. سپس معادلات انتگرالي براي تحليل مساله چندين ترك در باريكه بدست مي‌آيد. اين معادلات با استفاده از روش عددي مناسب حل مي‌گردند تا ضريب شدت تنش در نوك ترك بدست آيد.

In the present paper, the problem of multiple cracks in a non-homogeneous orthotropic layer bonded between two piezoelectric layers is considered. The shear modulus of the middle layer is considered for a class of functional forms for which the equilibrium equation has an analytical solution. The elastic shear modulus of the functionally graded orthotropic layer is considered to vary exponentially. The analysis is based on the stress fields caused by Volterra-type screw dislocation in the functionally graded orthotropic strip. The solution for dislocation is obtained by means of the complex Fourier transform. The dislocation solution is then employed as strain nuclei to derive singular integral equations for a medium weakened by multiple smooth cracks. The integral equations are of Cauchy singular type at the location of dislocation which are solved numerically for dislocation density functions. Several examples are solved and the stress intensity factors for multiple cracks with different configuration are obtained.