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

Cai-qi, LI; Zhou, Yueting

doi:10.1002/zamm.201800132

Cited by 6 publications

(3 citation statements)

References 28 publications

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“…Using the trial and error method, Hou et al [20,21] studied the 3D fundamental solution of 1D hexagonal QCs layer. Li and Zhou [22] studied the fundamental solutions and frictionless contact problem in a semi-infinite space of 2D hexagonal PEQCs.…”

Section: Introductionmentioning

confidence: 99%

Frictional contact problem of one-dimensional hexagonal piezoelectric quasicrystals layer

et al. 2021

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Based on three-dimensional (3D) general solutions for one-dimensional (1D) hexagonal piezoelectric quasicrystals (PEQCs), this paper studied the frictional contact problem of 1D-hexagonal PEQCs layer. The frequency response functions (FRFs) for 1D-hexagonal PEQCs layer are analytically derived by applying double Fourier integral transforms to the general solutions and boundary conditions, which are consequently converted to the corresponding influence coefficients (ICs). The conjugate gradient method (CGM) is used to obtain the unknown pressure distribution, while the discrete convolution-fast Fourier transform technique (DC-FFT) is applied to calculate the displacements and stresses of phonon and phason, electric potentials and electric displacements.Numerical results are given to reveal the influences of material parameters and loading conditions on the contact behavior. The obtained 3D contact solutions are not only helpful further analysis and understanding of the coupling characteristics of phonon, phason and electric field, but also provide a reference basis for experimental analysis and material development.

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Section: Introductionmentioning

confidence: 99%

Frictional contact problem of one-dimensional hexagonal piezoelectric quasicrystals layer

et al. 2021

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“…The frictional and frictionless contact problems for electro-elastic materials are studied in [16,24,25,34]. Analysis and numerical simulation of contact with or without friction for piezoelectric materials, coupled with other effects, can be found in [1,7,17,18,27,33,35] and references therein. The coupling between the mechanical and electrical properties leads to a non symmetric and non coercive mathematical problem.…”

Section: Introductionmentioning

confidence: 99%

J‐ADMM for a multi‐contact problem in electro‐elastostatics

Essoufi

Zafrar

2021

Z Angew Math Mech

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In this work we apply a regularized alternating direction method of multiplier of Jacobi type (J-ADMM) to a frictional multi-contact (both unilateral and bilateral) problem between an electro-elastic material and a rigid non conductive foundations. The frictional contact is modelled by the Coulomb friction law. The resulted problem is non symmetric and non coercive. By dissociating the electric potential from the mechanical field, we obtain a symmetric and coercive problem which can be reformulated as a convex minimization problem. We then apply a J-ADMM for the numerical approximation to the resulting perturbed elastic problem. The resolution of obtained sub-problems is based on convex dualities. Numerical experiments are proposed to illustrate the efficiency of the proposed approach.

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“…It is the purpose of this paper to develop our previous work [30], and devote to general solutions of the three‐dimensional thermo‐electro‐elastic problems of 2D hexagonal QC with piezoelectric effect under various loadings by using the strict operator theory and the generalized Almansi theorem. First, we derive the general solutions.…”

Section: Introductionmentioning

confidence: 99%

Thermo‐electric response in 2D hexagonal QC exhibiting piezoelectric effect

2020

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Based on the theory of quasicrystal (QC) with piezoelectric effect, the general solutions of a two‐dimensional hexagonal QC under the thermo‐electric loadings are derived by using the strict operator theory and the generalized Almansi theorem. Based on the general solutions, two potential functions are introduced, and the basic solutions of QC are obtained according to the boundary conditions of the point source acting on the infinite body and the semi‐infinite body. Numerical examples are given to analyze the variations of temperature, displacement and stress of phonon field, electric field potential, and electric displacement.

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

Cited by 6 publications

References 28 publications

Frictional contact problem of one-dimensional hexagonal piezoelectric quasicrystals layer

Frictional contact problem of one-dimensional hexagonal piezoelectric quasicrystals layer

J‐ADMM for a multi‐contact problem in electro‐elastostatics

Thermo‐electric response in 2D hexagonal QC exhibiting piezoelectric effect

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