Thermoelastic analysis of a two-dimensional decagonal quasicrystal with a conductive elliptic hole

Guo, Junhong; Yu, Jing; Xing, Yongming; Pan, Ernian; Li, Lianhe

doi:10.1007/s00707-016-1657-7

Cited by 24 publications

(5 citation statements)

References 46 publications

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“…In the open literature, [1][2][3][4][5] a lot of work on dislocations and cracks in pure elastic materials, piezoelectric solids, and quasicrystals have been studied in order to build a fracture theory that describes plastic deformation of dislocations near the crack tip. Many methods and techniques, such as the Green function method, [6] integral transformation, [7] and the complex variable method [8][9][10][11][12][13][14] can be used to solve these problems. Head [15] first investigated the interaction between a screw dislocation and a bi-material interface.…”

Section: Introductionmentioning

confidence: 99%

The interaction between a screw dislocation and a wedge-shaped crack in one-dimensional hexagonal piezoelectric quasicrystals

Jiang

Liu

2017

Chinese Phys. B

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Based on the fundamental equations of piezoelasticity of quasicrystal material, we investigated the interaction between a screw dislocation and a wedge-shaped crack in the piezoelectricity of one-dimensional hexagonal quasicrystals. Explicit analytical solutions are obtained for stress and electric displacement intensity factors of the crack, as well as the force on dislocation. The derivation is based on the conformal mapping method and the perturbation technique. The influences of the wedge angle and dislocation location on the image force are also discussed. The results obtained in this paper can be fully reduced to some special cases already available or deriving new ones.

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Section: Introductionmentioning

confidence: 99%

The interaction between a screw dislocation and a wedge-shaped crack in one-dimensional hexagonal piezoelectric quasicrystals

Jiang

Liu

2017

Chinese Phys. B

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“…Based on the QC nonlocal theory, Yang et al (2018) obtained the thermo-elastic analysis solution for the two-dimensional (2D) QC simply supported nanoplates subjected to a temperature change. According to the pseudo-Stroh formalism, the deformation of a conductive elliptic hole embedded in the 2D decagonal QC plane (Guo et al, 2016) was derived under a remotely uniform heat flow. In TABLE 1 Material properties (C, K, and R in 10 9 N/m 2 , β in 10 6 N K/m 2 , k in W K/m, T 0 in K, C e in J kg/K, ρ in kg/m 3 ).…”

Section: Introductionmentioning

confidence: 99%

Forced vibration analysis of inhomogeneous quasicrystal coating in a thermal environment

et al. 2022

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The tremendous attention of researchers has been attracted to the unusual properties of quasicrystals in coatings. In this paper, the exact solutions of the functionally graded multilayered two-dimensional quasicrystal coating structures in a thermal environment are derived for advanced boundary-value problems with mixed boundary conditions. The state space method is formulated to the thermal coupling with quasicrystal linear elastic theory that derives the state equations for functionally graded quasicrystal coating structures along the thickness direction. The mixed supported boundary conditions in the x-direction and the simply supported boundary conditions in the y-direction are subjected to time-harmonic temperature loadings, which are represented by means of the differential quadrature technique and Fourier series expansions, respectively. Traction on both the bottom and top surfaces is free, and perfect thermal and mechanical contacts between constituents are incorporated at the internal interfaces. A global propagator matrix, which connects the field variables at the top interface to those at the bottom interface for the whole coating structure, is further completed by joint coupling matrices to overcome the numerical instabilities. Finally, three application examples are proposed to throw light on various effects of the power law index, frequency, and different boundary conditions on the field variables in three-layer coating structures. The present solution can serve as a benchmark for the modeling of functionally graded quasicrystal coating structures based on various numerical methods.

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“…For quasicrystal materials, the defects such as holes and inclusions have been studied by many scholars [7][8][9][10][11][12][13][14][15][16]. However, there are few studies on quasicrystal materials with rigid line inclusions.…”

Section: Introductionmentioning

confidence: 99%

Circular inclusion problem of two‐dimensional decagonal quasicrystals with interfacial rigid lines under concentrated force

Zhai

Ding

et al. 2021

Z Angew Math Mech

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The plane problem of two-dimensional decagonal quasicrystals with a rigid circular arc inclusion was investigated under infinite tension and concentrated force. Based on complex representations of stresses and displacements of two-dimensional decagonal quasicrystals, the above problem is transformed into Riemann boundary problem by using the analytic continuation principle of complex functions. The general solutions of two-dimensional decagonal quasicrystals under the action of plane concentrated force and infinite uniform tension are derived. The closed solutions of complex potential functions in several typical cases are obtained, and the formula of singular stress field at the tip of rigid line inclusions is given. The results show that the stress field at the tip of circular arc rigid line inclusions has singularity of oscillation under plane load. Numerical examples are given to analyze the effects of inclusion radius, different inclusions, the coupling coefficient and phason field parameter on stress singularity coefficients.

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Thermoelastic analysis of a two-dimensional decagonal quasicrystal with a conductive elliptic hole

Cited by 24 publications

References 46 publications

The interaction between a screw dislocation and a wedge-shaped crack in one-dimensional hexagonal piezoelectric quasicrystals

The interaction between a screw dislocation and a wedge-shaped crack in one-dimensional hexagonal piezoelectric quasicrystals

Forced vibration analysis of inhomogeneous quasicrystal coating in a thermal environment

Circular inclusion problem of two‐dimensional decagonal quasicrystals with interfacial rigid lines under concentrated force

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