The interaction between a circular elastic plate and a transversely isotropic elastic half-space

The axisymmetric problem of flexure of a centrally loaded or uniformly loaded thin-elastic plate resting on or buried in a transversely isotropic elastic half-space is solved using a constraint variational scheme. A fundamental solution corresponding to a unit vertical pressure acting over an annular region in the interior of the half-space which is derived through the application of Hankel integral transforms is used to evaluate the strain energy of the elastic half-space. The deflected shape of the plate is represented by a power series of radial coordinate together with a term corresponding to a concentrated load derived from classical plate theory. The coefficients of the power series representation, which could be considered as generalized coordinates corresponding to the interaction problem, are determined through the minimization of a constraint energy functional. The energy functional consists of the strain energies of the plate and half-space, the potential of the applied loads and a term corresponding to plate edge boundary conditions incorporated with a penalty number. The entire formulation is developed as a convenient and flexible matrix solution scheme. The numerical stability and convergence of the solution scheme are established, and the response of the plate is investigated over a range of relative rigidities of practical interest.