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By introducing four displacement functions, the governing equations of the threedimensional thermoelasticity of two-dimensional hexagonal quasicrystals are decoupled into two uncorrelated problems. Two higher-order displacement functions are introduced to represent the general solutions, which are eighth-order and fourth-order, respectively, for the two problems. By taking a decomposition and superposition procedure, the general solutions are further simplified in seven cases in terms of six quasi-harmonic displacement functions. To show the application of the general solutions obtained, a closed form solution is obtained for an infinite space containing a penny-shaped crack, subjected to a uniformly distributed temperature at the crack surface.

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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.

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Functionally graded materials have been extensively used as thermal barrier materials and composite laminates to resist high temperatures and reduce the thermal stresses. In this paper, an analytical solution is presented to investigate the response of functionally graded multilayered two‐dimensional thermoelastic decagonal quasicrystal plates. The general solution for a functionally graded simply supported plate with the material properties being assumed to be exponentially distributed along the thickness direction is derived by using the pseudo‐Stroh formalism, and the solution for the corresponding multilayered case is obtained in terms of the propagator matrix method. Numerical results show the influences of functionally graded exponential factor, phonon‐phason coupling coefficient and the thickness of functionally graded quasicrystal layer on the phonon, phason and thermal fields of the plates under the steady‐state thermal load. The obtained results should be useful for future analysis and design of functionally graded layered thermoelastic quasicrystal plates.