The influence of layers with low transverse stiffness on the contact response of composite half planes

A previously developed local-global stiffness matrix methodology for the re sponse of a composite half plane, arbitrarily layered with isotropic, ortho tropic or monoclinic plies, to indentation by a rigid parabolic punch is fu rther extended to accommodate the presence of layers with complex eigenvalu es (e.g., honeycomb or piezoelectric layers). First, a generalized plane de formation solution for the displacement held in an orthotropic layer or hal f plane characterized by complex eigenvalues is obtained by using Fourier t ransforms. A local stiffness matrix in the transform domain is subsequently constructed for this class of layers and half planes, which is then assemb led into a global stiffness matrix for the entire multi-layered half plane by enforcing continuity conditions along the interfaces. Application of the mixed boundary condition on the top surface of the half plane indented by a rigid punch results in an integral equation for the unknown pressure in t he contact region. The integral possesses a divergent kernel which is decom posed into Cauchy-type and regular parts by the use of the asymptotic prope rties of the local stiffness matrix and a relationship between Fourier and finite Hilbert transforms of the contact pressure. The solution of the resu lting singular integral equation is obtained by using a collocation techniq ue based on the properties of orthogonal polynomials developed by Erdogan a nd Gupta. Examples are presented that illustrate the important influence of low transverse properties of layers with complex eigenvalues, such as thos e exhibited by honeycombs, on the load versus contact length response and c ontact pressure distributions for half planes containing typical composite materials. (C) 1999 Elsevier Science Ltd. All rights reserved.