Three-dimensional exact electric-elastic analysis of a multilayered two-dimensional decagonal quasicrystal plate subjected to patch loading

Yang, Lianzhi; Li, Yang; Gao, Yang; Pan, Ernian; Waksmanski, Natalie

doi:10.1016/j.compstruct.2017.02.036

Cited by 35 publications

(24 citation statements)

References 29 publications

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“…A 2D PQC with x 1 -x 2 plane being the quasi-periodic plane, x 3 being the periodic and poling directions referring to the Cartesian coordinates (x 1 , x 2 , x 3 ) is considered in this paper. The static equilibrium equations without body forces and electric charges are given by [28,29]:…”

Section: Fundamental Formulationsmentioning

confidence: 99%

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Bending Analysis of Laminated Two-Dimensional Piezoelectric Quasicrystal Plates with Functionally Graded Material Properties

Yang

Gao

2019

Acta Phys. Pol. A

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This paper presents an exact solution for a functionally graded multilayered two-dimensional piezoelectric quasicrystal plate with simply supported boundary conditions. The material properties of the functionally graded plate are assumed to be exponentially distributed along the thickness direction. Based on the pseudo-Stroh formalism, an exact solution for a functionally graded plate is derived, and the exact solution for the corresponding multilayered case is obtained in terms of the propagator matrix method. Numerical examples show the influences of functionally graded exponential factor, stacking sequence, and phonon-phason coupling coefficient on the plate. The obtained results should be useful for the analysis and design of the functionally graded two-dimensional piezoelectric quasicrystal plate.

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Section: Fundamental Formulationsmentioning

confidence: 99%

“…The linear constitutive equations for 2D decagonal PQC with point group10m2 in Laue 14 can be expressed by the following form [29]:…”

Section: Fundamental Formulationsmentioning

confidence: 99%

Bending Analysis of Laminated Two-Dimensional Piezoelectric Quasicrystal Plates with Functionally Graded Material Properties

Yang

Gao

2019

Acta Phys. Pol. A

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“…Also in equation (1), σ ij and ε ij are the phonon stress and phonon strain, respectively; H mj and w mj denote the stress and strain in the phason field, respectively; D j and E k represent the electric displacement and electric field, respectively; C ijkl , K mjkl , and R ijml are the elastic constants in the phonon field, phason field, and phonon–phason coupling field; κ jk is the permittivity constants; d ijk ( 1 ) and d mjk ( 2 ) denote the phonon piezoelectric and phason piezoelectric constants. The material constant matrices in equation (1) for 2D decagonal PQCs with the point groups 10 mm, 1022, and 10/ m mm can be obtained from Yang et al (2017). It is noted that the nonlocal constitution relations can be reduced to the local case (Yang et al, 2017) by setting the nonlocal parameter to be zero.…”

Section: The Nonlocal Theory For 2d Pqc Materialsmentioning

confidence: 99%

“…The material constant matrices in equation (1) for 2D decagonal PQCs with the point groups 10 mm, 1022, and 10/ m mm can be obtained from Yang et al (2017). It is noted that the nonlocal constitution relations can be reduced to the local case (Yang et al, 2017) by setting the nonlocal parameter to be zero.…”

Section: The Nonlocal Theory For 2d Pqc Materialsmentioning

confidence: 99%

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

Yang

Gao

et al. 2018

Journal of Intelligent Material Systems and Structures

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The piezoelectric effect is a significant property of quasicrystal. In this article, the exact solution is derived for a layered piezoelectric quasicrystal nanoplate with nonlocal effect in cylindrical bending. Based on the nonlocal theory and the pseudo-Stroh formalism, the exact solution for a homogeneous simply supported nanoplate is obtained. With the aid of the propagator matrix, the exact solution for a multilayered nanoplate is achieved. Numerical examples are carried out to reveal the influences of span-to-thickness ratio, nonlocal parameter, and stacking sequence on piezoelectric quasicrystal nanoplates with their top surface subjected to two loadings. One is a z-direction mechanical loading and the other is an electric potential loading. These results can be served as benchmarks for the design, numerical modeling, and simulation of layered two-dimensional piezoelectric quasicrystal nanoplates under cylindrical bending.

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“…Zhao [24] systematically analyzed the 1D hexagonal QCs with piezoelectric effect. Recently, Yang et al [25] analyzed the exact 3D mechanical behaviors of the plate by using the method of pseudo-Stroh formalism and propagator matrix, and investigated the plate response to three different patch surface loadings. Based on the 2D fundamental solutions, Hou [26] investigated the piezoelectric coated functional devices under external force and electrical loads, and proved that the method was accurate and efficient.…”

Section: Introductionmentioning

confidence: 99%

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

Cai-qi

Zhou

2019

Z Angew Math Mech

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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

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Three-dimensional exact electric-elastic analysis of a multilayered two-dimensional decagonal quasicrystal plate subjected to patch loading

Cited by 35 publications

References 29 publications

Bending Analysis of Laminated Two-Dimensional Piezoelectric Quasicrystal Plates with Functionally Graded Material Properties

Bending Analysis of Laminated Two-Dimensional Piezoelectric Quasicrystal Plates with Functionally Graded Material Properties

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

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

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