Tensionless contact of a flexible plate and annulus with a smooth half-space under axisymmetric loads by integral equations

In this paper, a new hybrid method of analysis is presented for the problem of a frictionless circular plate or annulus in tensionless contact with a half-space. By virtue of a set of analytically explicit Green's functions for the two interacting continua, an exact but compact integral equation formulation with closed-form kernels is derived. With the incorporation of a newly developed adaptive-gradient (AG) element capable of capturing regular-to-singular solution transitions smoothly, an accurate numerical procedure is developed and validated in a number of benchmark cases of nonlinear plate–annulus–half-space interaction. From the simplicity and rate of convergence demonstrated, the hybrid method is apt to be an attractive analytical–numerical platform that can be extended to a large class of contact problems.