Analysis of Crack Problems in Multilayered Elastic Medium by a Consecutive Stiffness Method

Gongbo Long, Yingjie Liu, Wanrong Xu, Peng Zhou, Jiaqi Zhou, Guanshui Xu and Boqi Xiao ()
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Gongbo Long: School of Mechanical and Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, China
Yingjie Liu: School of Mechanical and Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, China
Wanrong Xu: School of Mechanical and Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, China
Peng Zhou: School of Mechanical and Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, China
Jiaqi Zhou: School of Mechanical and Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, China
Guanshui Xu: Department of Mechanical Engineering, The University of California, Riverside, CA 92521, USA
Boqi Xiao: School of Mechanical and Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, China

Mathematics, 2022, vol. 10, issue 23, 1-16

Abstract: We propose a boundary-element-based method for crack problems in multilayered elastic medium that consists of a set of individually homogeneous strata. The method divides the medium along the slit-like crack surface so that the effects of the elements placed along one crack surface become distinguishable from those placed along the other surface. As a result, the direct method that cannot be directly applied for crack problems turns out to be applicable. After that, we derive a recursive formula that obtains a “stiffness matrix” for each layer by exploiting the chain-like structure of the system, enabling a sequential computation to solve the displacements on the crack surface in each layer “consecutively” in a descending order from the very top layer to the very bottom one. In our method, the final system of equations only contains the unknown displacements on the crack surface, ensuring the efficiency of the method. The numerical examples demonstrate better accuracy and broader applicability of our method compared to the displacement discontinuity method and more-acceptable efficiency of our method compared to the conventional direct method.

Keywords: direct method; boundary element method; crack problems; multilayered elastic media (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (11)

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