General Solutions for Three-Dimensional Thermoelasticity of Two-Dimensional Hexagonal Quasicrystals and an Application

Self Cite

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.

“…According to Refs. [], the linear constitutive relations of 2D thermoelastic decagonal QCs with point groups 10 mm , 1022,

\bar{10} m 2

and 10/ mmm can be written as follows:

\begin{matrix} left σ_{11} = C_{11} ε_{11} + C_{12} ε_{22} + C_{13} ε_{33} + R_{1} ((), w_{11} + w_{22}) - β_{1} T, \\ left σ_{22} = C_{12} ε_{11} + C_{11} ε_{22} + C_{13} ε_{33} - R_{1} ((), w_{11} + w_{22}) - β_{1} T, \\ left σ_{33} = C_{13} ε_{11} + C_{13} ε_{22} + C_{33} ε_{33} - β_{3} T, \\ left σ_{23} = σ_{32} = 2 C_{44} ε_{23}, \\ left σ_{31} = σ_{13} = 2 C_{44} ε_{13}, \\ left σ_{12} = σ_{21} = 2 C_{66} ε_{12} - R_{1} w_{12} + R_{1} w_{21}, \\ left H_{11} = R_{1} ((), ε_{11} - ε_{22}) + K_{1} w_{11} + K_{2} w_{22}, \\ left H_{22} = R_{1} ((), ε_{11} - ε_{22}) + K_{1} w_{22} + K_{2} w_{11}, \\ left H_{23} = K_{4} w_{23}, \\ left H_{12} = - 2 R_{1} ε_{12} + K_{1} w_{12} - K_{2} w_{21}, \\ left H \end{matrix}

…”

Section: Problem Description and Basic Formulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…According to Refs. [15,31], the linear constitutive relations of 2D thermoelastic decagonal QCs with point groups 10mm, 1022, 10 2 and 10/mmm can be written as follows: 11…”

mentioning

confidence: 99%

See 2 more Smart Citations

Thermo‐elastic analysis of functionally graded multilayered two‐dimensional decagonal quasicrystal plates

Yang

Gao

2018

Self Cite

“…Subsequently, some researchers obtained the 3D fundamental solutions of 1D hexagonal QCs in the thermo-elastic field, [12] in the piezoelectric field, [13] and in the thermo-electro-elastic field, [14] and the 3D fundamental solutions of 2D hexagonal QCs in the elastic field [15] and in the thermo-elastic field. [16] Because of the brittleness of the QCs, [5] the mechanical behavior of QCs with defects, such as crack, dislocation, void, inclusion, etc., has aroused the attention of many researchers'. The crack and dislocation problems of QCs have been got a lot of researches.…”

Section: Introductionmentioning

confidence: 99%

Fundamental solutions and frictionless contact problem in a semi‐infinite space of 2D hexagonal piezoelectric QCs

Cai-qi

Zhou

2019

General solutions for the semi-infinite space of two-dimensional (2D) piezoelectric quasicrystals (QCs) are acquired by means of the potential theory method and the generalized Almansi's theorem. Then based on the fundamental solutions of the concentrated loadings case, the frictionless contact problem in a semi-infinite of 2D hexagonal piezoelectric QCs is addressed by using the superposition principle and potential theory. Analytic solutions of fields quantities in terms of elementary functions for the phonon field, phason field and electric field are obtained under three different rigid indenters (flat-ended cylindrical, conical and spherical), which are convenient for numerical analysis. Numerical examples are given to display the relationship between the contact stiffness and the penetration depth through the change of the curves, and to demonstrate the distribution of the field components under the action of the flat-ended cylindrical. K E Y W O R D Scontact problem, fundamental solutions, potential theory, two-dimensional piezoelectric quasicrystals

Guided wave characteristics in the functionally graded two‐dimensional hexagonal quasi‐crystal plate

Zhang

et al. 2019

Due to the limit of preparation technology, defects, such as cracks and inclusions, are inevitable in the functionally graded quasi‐crystal material. For the purpose of the guided wave non‐destructive testing on the functionally graded (FG) two‐dimensional(2‐D) hexagonal quasi‐crystal(QC) plates, Lamb and SH wave characteristics in the context of the Bak's model are investigated by means of the Legendre polynomial method. The convergence of the polynomial method applied on the FG 2‐D hexagonal QC plate is analyzed. Some new wave characteristics resulted from the phonon‐phason coupling effect are revealed. There are three Lamb‐like modes without cut‐off frequencies for the x‐y and y‐z QC plates, but four Lamb‐like modes without cut‐off frequencies for the x‐z QC plate. For phonon modes, phonon displacements and stresses are bigger than phason displacements and stresses. However, they are just opposite for phason modes. It can be utilized to distinguish phonon modes and phason modes.