Smooth Contact of a Rigid Indenter and a Beam of Two Orthotropic Layers

摘要

The contact problem of a frictionless rigid indenter acting on a beam of two orthotropic layers is solved. The two layers are assumed perfectly bonded thus requiring the continuity of stress and displacement across the interface. The support conditions studied are point loads, simple supports and clamped edges for the cases of plane stress and plane strain. The effects of contact length, beam length, layer thickness and lamina orientation are studied for graphite/epoxy and boron/aluminum composite materials. The mixed boundary value problems are solved using displacement potentials and integral transform techniques to define Fredholm integral equations of the second kind of the auxiliary functions with respect to the three support conditions. The equations are solved numerically using a Gaussian quadrature scheme. Stress under the indenter, indenter load, and centerline deflection are calculated numerically using the auxiliary function solutions. The stress field solution for the rigid indentation of two orthotropic layers supported by point loads is determined. The stress function kernels are asymptotically treated to extract the half plane solutions at the three surfaces of the beam. The Tsai-Hill yield criteria is applied to estimate the initial damage and failure.