Structural Engineering and Mechanics

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On the receding contact plane problem for bi-FGM-layers indented by a flat indenter

  • Cong Wang (Intelligent Policing Key Laboratory of Sichuan Province, Sichuan Police College) ;
  • Jie Yan (Intelligent Policing Key Laboratory of Sichuan Province, Sichuan Police College) ;
  • Rui Cao (Jiangsu Key Laboratory of Engineering Mechanics, School of Civil Engineering, Southeast University)
  • Received : 2021.12.19
  • Accepted : 2023.01.30
  • Published : 2023.03.10
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Abstract

The major objective of this paper is to study the receding contact problem between two functional graded layers under a flat indenter. The gravity is assumed negligible, and the shear moduli of both layers are assumed to vary exponentially along the thickness direction. In the absence of body forces, the problem is reduced to a system of Fredholm singular integral equations with the contact pressure and contact size as unknowns via Fourier integral transform, which is transformed into an algebraic one by the Gauss-Chebyshev quadratures and polynomials of both the first and second kinds. Then, an iterative speediest descending algorithm is proposed to numerically solve the system of algebraic equations. Both semi-analytical and finite element method, FEM solutions for the presented problem validate each other. To improve the accuracy of the numerical result of FEM, a graded FEM solution is performed to simulate the FGM mechanical characteristics. The results reveal the potential links between the contact stress/size and the indenter size, the thickness, as well as some other material properties of FGM.

Keywords

Acknowledgement

The research described in this paper was financially supported by the Natural Science Foundation of China (No. 61602331), the Technical Research Program of the Ministry of Public Security of the People's Republic of China (No. 2022JSM04), and the Opening Project of Intelligent Policing Key Laboratory of Sichuan Province (No. ZNJW2022ZZMS002, ZNJW2022ZZMS004). The authors would also like to thank a lot to Dr. Lin Lin (Sichuan Police College) for the kindly help.

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