ON BENDING OF TRANSVERSELY INHOMOGENEOUS PLATE WITH PERIODIC SYSTEM OF COLLINEAR CONTACT CRACKS - Petrashchuk, V. M. (PRECARPATHIAN BULLETIN OF THE SHEVCHENKO SCIENTIFIC SOCIETY. Number, 2025)
The bending problem of functionally graded plate with periodic system of collinear through cracks with contact interaction of their faces, which arises due to non-uniform stress distribution through the plate thickness, is considered. Based on the classical Kirchhoff plate bending theory and special contact model along a line, which allows to eliminate the kinematic contradiction of mutual penetration of crack faces, the boundary value problem for a pair of biharmonic equations with interrelated conditions on cuts is formulated. Using the method of singular integral equations with periodic Hilbert kernel, an exact analytical solution of the problem in closed form is constructed. The influence of material inhomogeneity profile and mutual arrangement of cracks on stress and moment intensity factors, as well as on limit load value determined by energy fracture criterion, is studied in detail. Numerical analysis is performed for the specific case of inhomogeneity with quadratic distribution of elastic modulus through the plate thickness, described by the second-order Legendre polynomial, which models both plates with stiffer periphery and with rigid core.