Abstract
The frictionless contact problem for an elastic layer resting on an elastic half plane is considered. The problem is solved by using the theory of elasticity and integral transformation technique. The compressive loadsPandQ(per unit thickness in direction) are applied to the layer through three rigid flat punches. The elastic layer is also subjected to uniform vertical body force due to effect of gravity. The contact along the interface between elastic layer and half plane is continuous, if the value of the load factor,λ, is less than a critical value, . In this case, initial separation loads, and initial separation points, are determined. Also the required distance between the punches to avoid any separation between the punches and the elastic layer is studied and the limit distance between punches that ends interaction of punches is investigated for various dimensionless quantities. However, if tensile tractions are not allowed on the interface, for the layer separates from the interface along a certain finite region. Numerical results for distance determining the separation area, vertical displacement in the separation zone, contact stress distribution along the interface between elastic layer and half plane are given for this discontinuous contact case.
Highlights
Contact between deformable bodies abounds in industry and everyday life
The range of application in contact mechanics starts with problems like foundations in civil engineering, where the lift off the foundation from soil due to eccentric forces acting on a building, railway ballasts, foundation grillages, continuous foundation beams, runaways, liquid tanks resting on the ground, and grain silos is considered
Some of the calculated results obtained from the solution of the continuous and discontinuous contact problems for various dimensionless quantities such as μ2/μ1, a/h, (c−b)/h, Q/P, λ, and (b − a)/h are presented in Figures 2, 3, 4, 5, and 6 and Tables 1, 2, 3, 4, and 5
Summary
Contact between deformable bodies abounds in industry and everyday life. Because of the industrial importance of the physical processes that take place during contact, a considerable effort has been made in their modeling, analysis, and numerical simulations. The layer usually rests on a foundation which may be either elastic or rigid and the body force due to gravity may be neglected [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27] or effect of gravity may be taken into account [28,29,30,31,32,33,34,35]. When the magnitude of the compressive external load exceeds a certain value, a separation will take place between the layer and the foundation.
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