Continuous and discontinuous contact problem of layered composite resting on two rigid flat supports

SUMMARY Continuous and Discontinuous Contact Problem of Layered Composite Resting on Two Rigid Flat Supports In this study, the continuous and discontinuous contact problem of a layered composite which consists of two materials with different elastic constants and heights hj and h2 resting on two rigid flat supports with sharp edges is considered according to the theory of elasticity. Layered composite is subjected to a uniform clamping pressure over a finite portion of width 2a on its top surface. It is assumed that there is no friction between the supports and the layered composite. In the first chapter, the historical development of contact problems are mentioned and some studies which are done on contact problems are summarised. Also stress and displacement integral expressions are obtained using the integral transforms technique from the fundamental equations of elasticity. In the second chapter, continuous contact is examined first. Stress and displacement expressions are substituted into the continuous contact boundary conditions and the problem is reduced to a singular integral equation, where the contact pressure is the unknown function. The solution of singular integral equation is done using the Gauss- Chebyshev integration formulas. Then the first separation load and the first separation distance at the interface of two elastic layers are investigated. Discontinuous contact problem is divided into two parts. Separation between layered composite and rigid flat supports is examined first. Afterwards stress and displacement expressions are substituted into the boundary conditions which are written for the separation between the two elastic layers and the problem is reduced to solution of two singular integral equations where the contact pressure and the slope of separation at the interface of two elastic layers are the unknown functions. Singular integral equation system is also solved using Gauss-Chebyshev integration formulas. In the continuous contact problem and discontinuous contact problem between layered composite and rigid flat supports mentioned above are considered with and without friction at the interface of elastic layers separately. With solving the integral equations, contact pressure, separation between two elastic layers and ox, o*y and x^ stress components at every point of layered composite can be determined. In the third chapter, the stress and displacement results which are obtained for different values of various dimensionless quantities such as support width, load width and material properties are presented in graphical forms. When there is no separation between two elastic layers, the effect of friction between two elastic layers on stresses are shown in graphics and the graphics are discussed. In the fourth chapter, the conclusions obtained from this study is given. Key Words: Theory of Elasticity, Continuous Contact, Discontinuous Contact, Contact Pressure, Initial Separation Load, Initial Separation Distance, Separation, Integral Transforms Technique, Integral Equation. VII ? J^mmms^