Complex variable method for an anti-plane elliptical cavity of one-dimensional hexagonal piezoelectric quasicrystals

Yu, Jing; Guo, Junhong; Xing, Yongming

doi:10.1016/j.cja.2015.04.013

Cited by 39 publications

(17 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The equilibrium equations which must be satisfied by the dislocation array to fulfil the imposed boundary conditions (17) are that σ III yz (ξ, 0) = −T (ξ),…”

Section: Moving Row Of Cracks Analysis Using the Extended Dislocationmentioning

confidence: 99%

“…For example, as a demonstration of the type of analyses needed, it follows from Eqs. (17), (27) and (26) that:…”

Section: Moving Row Of Cracks Analysis Using the Extended Dislocationmentioning

confidence: 99%

“…Further, Yu et al [16] adopted operator and complex variable techniques to give general solutions which were applied using a semi-inverse method to consider a stationary constantly-loaded crack in a one-dimensional hexagonal piezoelectric quasicrystal. Solutions for an antiplane uniformly-loaded elliptical cavity were obtained by Yu et al [17].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Non-Uniformly Loaded Row of Moving, Antiplane Shear Cracks in One-Dimensional Piezoelectric Quasicrystals

Tupholme

2018

Acta Phys. Pol. A

View full text Add to dashboard Cite

An antiplane shear deformation in one-dimensional piezoelectric quasicrystals created by a row of collinear cracks subject to non-uniform phonon, phason and electric displacement loads is analyzed using a generalized technique of dislocation layers. Closed-form expressions are derived for the components of the phonon and phason stress and electric displacement fields. Their variations with angle near a crack tip are demonstrated and the corresponding phonon and phason stress and electric displacement intensity factors are deduced. Previously constantly loaded rows of cracks in various media have been studied. But no explicit expressions for the field components at a general point nor their angular variations were presented for them; even in classical isotropic elastic solids. The material considered here is the currently most general that is amenable to such an investigation and some of the analogous results for non-quasicrystals or non-piezoelectric or purely elastic solids or stationary cracks that can be deduced as particular cases are outlined. Some illustrative numerical results are graphically presented.

show abstract

“…The equilibrium equations which must be satisfied by the dislocation array to fulfil the imposed boundary conditions (17) are that σ III yz (ξ, 0) = −T (ξ),…”

Section: Moving Row Of Cracks Analysis Using the Extended Dislocationmentioning

confidence: 99%

“…For example, as a demonstration of the type of analyses needed, it follows from Eqs. (17), (27) and (26) that:…”

Section: Moving Row Of Cracks Analysis Using the Extended Dislocationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Non-Uniformly Loaded Row of Moving, Antiplane Shear Cracks in One-Dimensional Piezoelectric Quasicrystals

Tupholme

2018

Acta Phys. Pol. A

View full text Add to dashboard Cite

show abstract

“…Piezoelectricity is an important physical property of QCs. The piezoelectric QCs [11][12][13][14] have been investigated to a certain degree. It is well known that the interaction among defects is of considerable importance in understanding the fracture mechanical behavior of materials.…”

Section: Introductionmentioning

confidence: 99%

Interaction of a Screw Dislocation with Interface and Wedge‐Shaped Cracks in One‐Dimensional Hexagonal Piezoelectric Quasicrystals Bimaterial

Zhao

2019

Mathematical Problems in Engineering

View full text Add to dashboard Cite

Interaction of a screw dislocation with wedge-shaped cracks in one-dimensional hexagonal piezoelectric quasicrystals bimaterial is considered. The general solutions of the elastic and electric fields are derived by complex variable method. Then the analytical expressions for the phonon stresses, phason stresses, and electric displacements are given. The stresses and electric displacement intensity factors of the cracks are also calculated, as well as the force on dislocation. The effects of the coupling constants, the geometrical parameters of cracks, and the dislocation location on stresses intensity factors and image force are shown graphically. The distribution characteristics with regard to the phonon stresses, phason stresses, and electric displacements are discussed in detail. The solutions of several special cases are obtained as the results of the present conclusion.

show abstract

“…To aid in providing general static solutions to threedimensional boundary value problems in hexagonal piezoelectric quasicrystals, Li et al [17] applied the rigorous operator theory. Yu et al [18] and Yu et al [19] used techniques of complex variable theory for studying a stationary uniformly loaded antiplane Griffith crack and an elliptical cavity, respectively, in a one-dimensional hexagonal piezoelectric quasicrystal.…”

Section: Introductionmentioning

confidence: 99%

Nonuniformly Loaded Stack of Antiplane Shear Cracks in One‐Dimensional Piezoelectric Quasicrystals

Tupholme

2018

Advances in Materials Science and Engineering

View full text Add to dashboard Cite

Representations in a closed form are derived, using an extension to the method of dislocation layers, for the phonon and phason stress and electric displacement components in the deformation of one-dimensional piezoelectric quasicrystals by a nonuniformly loaded stack of parallel antiplane shear cracks. Their dependence upon the polar angle in the region close to the tip of a crack is deduced, and the field intensity factors then follow. These exhibit that the phenomenon of crack shielding is dependent upon the relative spacing of the cracks. The analogous analyses, that have not been given previously, involving non-piezoelectric or non-quasicrystalline or simply elastic materials can be straightforwardly considered as special cases. Even when the loading is uniform and the crack is embedded in a purely elastic isotropic solid, no explicit representations have been available before for the components of the field at points other than directly ahead of a crack. Typical numerical results are graphically displayed.

show abstract

Complex variable method for an anti-plane elliptical cavity of one-dimensional hexagonal piezoelectric quasicrystals

Cited by 39 publications

References 35 publications

Non-Uniformly Loaded Row of Moving, Antiplane Shear Cracks in One-Dimensional Piezoelectric Quasicrystals

Non-Uniformly Loaded Row of Moving, Antiplane Shear Cracks in One-Dimensional Piezoelectric Quasicrystals

Interaction of a Screw Dislocation with Interface and Wedge‐Shaped Cracks in One‐Dimensional Hexagonal Piezoelectric Quasicrystals Bimaterial

Nonuniformly Loaded Stack of Antiplane Shear Cracks in One‐Dimensional Piezoelectric Quasicrystals

Contact Info

Product

Resources

About