Three-dimensional exact electric-elastic analysis of a multilayered two-dimensional decagonal quasicrystal plate subjected to patch loading

An exact electric-elastic analysis of a multilayered two-dimensional decagonal quasicrystal plate subjected to patch loading with simply supported boundary conditions is presented. The pseudo-Stroh formalism and propagator matrix method are used to obtain the exact three-dimensional mechanical behaviors of the plate. By expressing the patch loading in the form of a double Fourier series expansion an exact closed-form solution with a concise and elegant expression is deduced. Three different kinds of patch surface loadings are applied to the surface of the plate and the response of the plate is investigated. Comprehensive numerical results are shown for a sandwich plate subjected to the three patch loadings with two different stacking sequences. The results show that the stacking sequences, patch loading areas, and patch loading types have a great influence on the stress, displacement and electric components of the plate. Also, different coupling constants between the phonon and phason fields will influence the physical quantities. The useful features observed from numerical results can be used in the design of composite laminates made of two-dimensional piezoelectric quasicrystals. The numerical results can also serve as a reference in convergence studies of other numerical methods and for verification of existing or future plate theories.