On Deformation of a Poroelastic Plate with Variable Properties

This article examines the deformation of a circular, isotropic, poroelastic plate with fluid-filled pores and elastic bonds at the edge. The simulation is based on a Timoshenko-type model using Biot’s constitutive relations. The effect of plate porosity on its deflection and rotation angle under a constant load is analyzed. The application of the studied model to the investigation of the deformation of the lamina cribrosa of the eye is presented. A potential energy functional is constructed for the plates using the Lagrange variational principle. An approximate numerical solution for minimizing the functional is constructed using the Ritz method. The influence of the number of coordinate functions on the solution accuracy is analyzed. Graphs of the deflection and rotation angle are plotted for parameters corresponding to a healthy eye and for various stages of primary open-angle glaucoma (POAG). Inflection points of the deflection function are found for various cases.