The continuous contact problem for two elastic layers resting on an elastic
half-infinite plane and loaded by means of a rigid stamp is presented. The elastic
layers have different heights and elastic constants. An external load is applied to the
upper elastic layer by means of a rigid stamp. The problem is solved under the
assumptions that all surfaces are frictionless, body forces of elastic layers are taken
into account, and only compressive normal tractions can be transmitted
through the interfaces. General expressions of stresses and displacements are
obtained by using the fundamental equations of the theory of elasticity and the
integral transform technique. Substituting the stress and the displacement
expressions into the boundary conditions, the problem is reduced to a singular
integral equation, in which the function of contact stresses under the rigid
stamp is unknown. The integral equation is solved numerically by making use
of the appropriate Gauss–Chebyshev integration formula for circular and
rectangular stamp profiles. The contact stresses under the rigid stamp, contact
areas, initial separation loads, and initial separation distances between the
two elastic layers and the lower-layer elastic half-infinite plane are obtained
numerically for various dimensionless quantities and shown in graphics and
tables.
Keywords
continuous contact, elastic layer, integral equation, rigid
stamp, theory of elasticity
