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        Crack-contact problem for an elastic layer with rigid stamps

        Ahmet Birinci 국제구조공학회 2011 Structural Engineering and Mechanics, An Int'l Jou Vol.37 No.3

        The plane crack-contact problem for an infinite elastic layer with two symmetric rectangular rigid stamps on its upper and lower surfaces is considered. The elastic layer having an internal crack parallel to its surfaces is subjected to two concentrated loads P on its upper and lower surfaces trough the rigid rectangular stamps and a pair of uniform compressive stress p0 along the crack surface. It is assumed that the contact between the elastic layer and the rigid stamps is frictionless and the effect of the gravity force is neglected. The problem is reduced to a system of singular integral equations in which the derivative of the crack surface displacement and the contact pressures are unknown functions. The system of singular integral equations is solved numerically by making use of an appropriate Gauss-Chebyshev integration formula. Numerical results for stress-intensity factor, critical load factor, Q_c, causing initial closure of the crack tip, the crack surface displacements and the contact stress distribution are presented and shown graphically for various dimensionless quantities.

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        Examination of analytical and finite element solutions regarding contact of a functionally graded layer

        Murat Yaylacı,Gökhan Adıyaman,Erdal Öner,AhmetBirinci 국제구조공학회 2020 Structural Engineering and Mechanics, An Int'l Jou Vol.76 No.3

        In this study, the continuous and discontinuous contact problems of functionally graded (FG) layer resting on a rigid foundation were considered. The top of the FG layer was loaded by a distributed load. It was assumed that the shear modulus and the density of the layer varied according to exponential functions along the depth whereas the the Poisson ratio remained constant. The problem first was solved analytically and the results were verified with the ones obtained from finite element (FE) solution. In analytical solution, the stress and displacement components for FG layer were obtained by the help of Fourier integral transform. Critical load expression and integral equation for continuous and discontinuous contact, respectively, using corresponding boundary conditions in each case. The finite element solution of the problem was carried out using ANSYS software program. In continuous contact case, initial separation distance and contact stresses along the contact surface between the FG layer and the rigid foundation were examined. Separation distances and contact stresses were obtained in case of discontinuous contact. The effect of material properties and loading were investigated using both analytical and FE solutions. It was shown that obtained results were compatible with each other.

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