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

Author

Listed:
  • 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
    Institute of Textiles and Clothing, Hong Kong Polytechnic University, Hong Kong, China)

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.

Suggested Citation

  • Gongbo Long & Yingjie Liu & Wanrong Xu & Peng Zhou & Jiaqi Zhou & Guanshui Xu & Boqi Xiao, 2022. "Analysis of Crack Problems in Multilayered Elastic Medium by a Consecutive Stiffness Method," Mathematics, MDPI, vol. 10(23), pages 1-16, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4403-:d:980587
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    References listed on IDEAS

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    1. Boqi Xiao & Jing Fang & Gongbo Long & Yuanzhang Tao & Zijun Huang, 2022. "Analysis Of Thermal Conductivity Of Damaged Tree-Like Bifurcation Network With Fractal Roughened Surfaces," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(06), pages 1-13, September.
    2. Wan Cheng & Chunhua Lu & Bo Xiao, 2021. "Perforation Optimization of Intensive-Stage Fracturing in a Horizontal Well Using a Coupled 3D-DDM Fracture Model," Energies, MDPI, vol. 14(9), pages 1-18, April.
    3. Alessandra Cantini & Leonardo Leoni & Filippo De Carlo & Marcello Salvio & Chiara Martini & Fabrizio Martini, 2021. "Technological Energy Efficiency Improvements in Cement Industries," Sustainability, MDPI, vol. 13(7), pages 1-28, March.
    4. Boqi Xiao & Qiwen Huang & Hanxin Chen & Xubing Chen & Gongbo Long, 2021. "A Fractal Model For Capillary Flow Through A Single Tortuous Capillary With Roughened Surfaces In Fibrous Porous Media," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(01), pages 1-10, February.
    5. Farshad BahooToroody & Saeed Khalaj & Leonardo Leoni & Filippo De Carlo & Gianpaolo Di Bona & Antonio Forcina, 2021. "Reliability Estimation of Reinforced Slopes to Prioritize Maintenance Actions," IJERPH, MDPI, vol. 18(2), pages 1-12, January.
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