An exact closed-form solution for a multilayered one-dimensional orthorhombic quasicrystal plate

Abstract

By extending the pseudo-Stroh formalism to multilayered one-dimensional orthorhombic quasicrystal plates, we derive an exact closed-form solution for simply supported plates under surface loadings. The propagator matrix method is introduced to efficiently and accurately treat the multilayered cases. As a numerical example, a sandwich plate made of quasicrystals and crystals with two different stacking sequences is investigated. The displacement and stress fields for these two stacking sequences are presented, which clearly demonstrate the importance of the stacking sequences on the induced physical quantities. Our exact closed-form solution should be of particular interest to the design of one-dimensional quasicrystal laminated plates. The numerical results can be further used as benchmarks to various numerical methods, such as the finite element and finite difference methods, on the analysis of laminated composites made of one-dimensional quasicrystals.

Cylindrical bending analysis of a layered two-dimensional piezoelectric quasicrystal nanoplate

“…The 12 eigenvalues s α ( α = 1, 2, …, 12) and vector a corresponding to the eigenvalues are obtained by solving the eigenrelation in equation (16). Because no model parameter p exists in matrix N , the eigenvalues are only related to material properties for the cylindrical bending case which is different from the rectangular plate case (Yang et al, 2015). Unlike the local case (Yang et al, 2015), the vector b needs to be solved by equation (9).…”

“…Because no model parameter p exists in matrix N , the eigenvalues are only related to material properties for the cylindrical bending case which is different from the rectangular plate case (Yang et al, 2015). Unlike the local case (Yang et al, 2015), the vector b needs to be solved by equation (9). Then, the general solution for the extended displacement vector and traction vector can be obtained as…”

Analytic solution of angle-ply laminated plates under extension, bending, and torsion

“…Yang et al. 9 used pseudo-Stroh formalism to derive an exact solution for simply supported plates under surface loadings.…”

Elastodynamic Analysis of a Hollow Cylinder with Decagonal Quasicrystal Properties: Meshless Implementation of Local Integral Equations

“…Some exact solutions have been presented for one-dimensional cases in beams and plates made of quasicrystals [4,5]. Yang et al [5] proposed an exact solution for analysis of plates subjected to surface loading and made of one-dimensional orthorhombic quasicrystal.…”

“…Some exact solutions have been presented for one-dimensional cases in beams and plates made of quasicrystals [4,5]. Yang et al [5] proposed an exact solution for analysis of plates subjected to surface loading and made of one-dimensional orthorhombic quasicrystal. They obtained the displacement and stress fields in a sandwich plate with simply supported boundary conditions, which was assumed to be made of quasicrystals and crystals with two different stacking sequences.…”