# An effective method for the sliding frictional contact of a conducting cylindrical punch on FGPMs

Jie Su, Liao Liang Ke, Sami El-Borgi, Yang Xiang, Yue Sheng Wang

Research output: Contribution to journalArticle

3 Citations (Scopus)

### Abstract

This paper presents an effective method to solve the sliding frictional contact between a rigid conducting cylindrical punch and a functionally graded piezoelectric coated half-plane. The electro-mechanical properties of the functionally graded piezoelectric materials (FGPMs) are position dependent along the thickness direction in the form of an exponential function against the thickness coordinate. A constant surface electric potential is assumed for the punch and the friction is of the Coulomb type. Using the superposition theorem and the Fourier integral transform, the present problem is reduced to a set of coupled Cauchy singular integral equations. These integral equations are then numerically discretized to form an overdetermined system which may lead to a non-unique solution for the conducting cylindrical punch problem. By using the least squares method together with an iterative procedure, the overdetermined algebraic equations are effectively solved to obtain the optimal solution. The effects of the friction coefficient and gradient index on the surface electro-mechanical fields are discussed.

Original language English International Journal of Solids and Structures https://doi.org/10.1016/j.ijsolstr.2018.02.017 Accepted/In press - 1 Jan 2018

### Fingerprint

sliding contact
Piezoelectric Material
Frictional Contact
punches
Piezoelectric materials
Integral equations
Friction
conduction
Overdetermined Systems
Fourier Integral
Cauchy Integral
Electric Potential
Exponential functions
Friction Coefficient
Singular Integral Equation
Integral Transform
Iterative Procedure
Half-plane
Least Square Method

### Keywords

• Conducting cylindrical punch
• FGPM coating
• Friction
• Least squares method

### ASJC Scopus subject areas

• Modelling and Simulation
• Materials Science(all)
• Condensed Matter Physics
• Mechanics of Materials
• Mechanical Engineering
• Applied Mathematics

### Cite this

An effective method for the sliding frictional contact of a conducting cylindrical punch on FGPMs. / Su, Jie; Ke, Liao Liang; El-Borgi, Sami; Xiang, Yang; Wang, Yue Sheng.

In: International Journal of Solids and Structures, 01.01.2018.

Research output: Contribution to journalArticle

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AU - Su, Jie

AU - Ke, Liao Liang

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AU - Wang, Yue Sheng

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N2 - This paper presents an effective method to solve the sliding frictional contact between a rigid conducting cylindrical punch and a functionally graded piezoelectric coated half-plane. The electro-mechanical properties of the functionally graded piezoelectric materials (FGPMs) are position dependent along the thickness direction in the form of an exponential function against the thickness coordinate. A constant surface electric potential is assumed for the punch and the friction is of the Coulomb type. Using the superposition theorem and the Fourier integral transform, the present problem is reduced to a set of coupled Cauchy singular integral equations. These integral equations are then numerically discretized to form an overdetermined system which may lead to a non-unique solution for the conducting cylindrical punch problem. By using the least squares method together with an iterative procedure, the overdetermined algebraic equations are effectively solved to obtain the optimal solution. The effects of the friction coefficient and gradient index on the surface electro-mechanical fields are discussed.

AB - This paper presents an effective method to solve the sliding frictional contact between a rigid conducting cylindrical punch and a functionally graded piezoelectric coated half-plane. The electro-mechanical properties of the functionally graded piezoelectric materials (FGPMs) are position dependent along the thickness direction in the form of an exponential function against the thickness coordinate. A constant surface electric potential is assumed for the punch and the friction is of the Coulomb type. Using the superposition theorem and the Fourier integral transform, the present problem is reduced to a set of coupled Cauchy singular integral equations. These integral equations are then numerically discretized to form an overdetermined system which may lead to a non-unique solution for the conducting cylindrical punch problem. By using the least squares method together with an iterative procedure, the overdetermined algebraic equations are effectively solved to obtain the optimal solution. The effects of the friction coefficient and gradient index on the surface electro-mechanical fields are discussed.

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KW - Least squares method

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