Frictional contact problem of an anisotropic laterally graded layer loaded by a sliding rigid stamp

Abstract

This study proposes analytical and computational methods for the solution of the sliding frictional contact problem of an anisotropic laterally graded layer loaded by an arbitrarily shaped rigid stamp. The plane-strain orthotropy prevails in the layer which is bonded to a rigid foundation. Each of four orthotropic stiffness coefficients is exponentially varied through the lateral direction of the elastic layer. The Fourier transformations of the field variables are employed in the formulation. The gradient of a displacement component on the surface is then converted to a singular integral equation of the second kind. The singular integral equation is solved by means of the Gauss–Jacobi quadrature integration techniques, a collocation method, and a recursive integration method for the Cauchy integral considering the flat and triangular stamp profiles. The finite element method solutions of the same contact problems are performed using the augmented Lagrange method which is implemented in virtue of ANSYS design parametric language. An iterative algorithm is additionally utilized for the (incomplete) triangular stamp problem to conveniently reach the solutions for predetermined contact lengths. The convergence and comparative analyses are carried out to elucidate the trustworthiness of the analytical and computational methods proposed. Moreover, the parametric analyses infer that the contact-induced damage risks can be effectively alleviated upon tuning the degree of orthotropy and the lateral heterogeneity of the elastic layer.

Dynamic frictional contact mechanics between a functionally graded orthotropic medium and a moving flat punch

“…The integral equation and equilibrium condition in normalized parameters are written as: In order to solve the singular integral equation, we adopt an expansion collocation technique which was previously developed by Erdogan and Gupta 55 and Erdogan et al 56 This technique has been frequently used in solving contact mechanics problems by several studies. 9–13,21–24,31,32 A series expansion solution is assumed for the unknown normal contact stress as follows 9–11 : Where W false( r false) = false( 1 − r ) α false( 1 + r ) β is the corresponding weight function, P n false( α , β false) false( r false) is the Jacobi polynomial of order n , A n is the unknown coefficients which will be determined. The singular behavior of the normal contact stress is found by function-theoretical analysis described in Erdogan.…”

“…3–14 The same elastostatic approximation was considered for the solutions of contact problems involving finite-thickness and semi-infinite models of orthotropic homogenous/graded media. 15–24…”

“…[3][4][5][6][7][8][9][10][11][12][13][14] The same elastostatic approximation was considered for the solutions of contact problems involving finite-thickness and semi-infinite models of orthotropic homogenous/graded media. [15][16][17][18][19][20][21][22][23][24] The punch speed, which is the prominent dynamic factor in sliding contact problems, should be considered as far as possible to increase the simulation capability of analytical solutions. Galin 25 examined whether it was necessary to take into account the dynamic character of the problem for contact problems involving moving punches.…”