Static solution of two-dimensional decagonal piezoelectric quasicrystal laminates with mixed boundary conditions

Piezoelectric quasicrystals have attracted the tremendous attention of researchers for their unique properties. In this paper, the semi-analysis solutions of the functionally graded multilayered two-dimensional decagonal piezoelectric quasicrystal plates are investigated for mixed boundary-value problems. Based on the quasicrystal linear elastic theory, the state-space method is employed to derive the state equations composed of partial differential along the thickness direction. The differential quadrature method is utilized to discretize state variables to satisfy the mixed boundary conditions in the horizontal plane. Different from the conventional propagator matrix, a new propagator relationship is proposed to study numerical instability caused by extensive discrete points. Comprehensive numerical results are shown for the sandwich quasicrystal plate with four different stacking sequences. The numerical results reveal the effect of the functional gradient index factors, and boundary conditions on the electric potential, electric displacements, stresses, and displacements under the mechanical/electric loadings.