Analytical Investigation of Interaction Between Flexible Circular Plate with Transversely Isotropic Half-space

A transversely isotropic half-space with axis of material symmetry perpendicular to the free surface supports a flexible circular plate. The contact area of the plate and the half-space is considered to be both frictionless and unbonded (tensionless). The foundation is affected by a vertical static axisymmetric load. Detailed analysis of the interaction of these two systems is the target of this paper. With the use of ring load Green’s functions for both the plate and the continuum half-space, dual integral equations accompanied with some inequalities are obtained to model the complex boundary value problem. With the incorporation of the ring-shape finite element method, where its size gradually varies, we are capable of capturing both regular and singular solution smoothly. The validity of the combination of the analytical and numerical method is proved with comparing the results of this paper with a number of benchmark cases of both linear and nonlinear interaction of circular plate and half-space. Some new illustrations are presented to portray the aspect of the anisotropy of the half-space.