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Accurate evaluation of mixed-mode intensity factors of cracked shear-deformable plates by an enriched meshfree Galerkin formulation

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Abstract

A novel meshfree discretization technique in terms of the reproducing kernel particle method is presented for accurately evaluating mixed-mode intensity factors of cracked shear-deformable plates. Mindlin–Reissner plate theory is adopted to solve the cracked plates problem in the Galerkin formulation, considering transverse shear deformation. The diffraction method, visibility criterion and enriched basis are included in the generation of meshfree interpolants for the modeling of fracture. In this work, numerical integration is treated using the stabilized conforming nodal integration (SCNI) and subdomain stabilized conforming integration (SSCI). The J-integral (contour integral) is employed to analyze the fracture mechanics parameters. SCNI/SSCI is thus adopted to evaluate the contour integral and to split the original J-integral into symmetric and asymmetric J-integral values. They are calculated by decomposing the smoothed displacement, moment and shear force quantities into symmetric/asymmetric parts. In addition, a displacement ratio method is introduced to divide the asymmetric J-integral value into corresponding moment and shear force intensity factors. The accuracy of the intensity factors and the path-independent properties in mixed-mode fracture problems are critically examined through several numerical examples.

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Acknowledgments

This research was partially supported by the JSPS Grants-in-Aid for Young Scientists (B)(16K18323) and for Scientific Research (A)(15H02328), (B)(15H04212), (B)(16H04603), (C)(15K06632). This work was performed as part of the Cooperative Research Program of the Joining and Welding Research Institute, Osaka University. Tinh Quoc Bui gratefully acknowledges support from Grant-in-Aid for Scientific Research - JSPS. TT Yu gratefully acknowledges support from the National Natural Science Foundation of China (51179063) and the National Sci-Tech Support Plan of China (2015BAB07B10).

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Authors and Affiliations

  1. Graduate School of Engineering, Hiroshima University, 4-1, Kagamiyama 1-chome, Higashi-Hiroshima, 739-8527, Japan

    S. Tanaka, H. Suzuki & S. Sadamoto

  2. Division of Mechanical Engineering, Faculty of Engineering, University of Yamanashi, Kofu, Japan

    S. Okazawa

  3. Department of Engineering Mechanics, Hohai University, Nanjing, China

    T. T. Yu

  4. Department of Civil and Environmental Engineering, Tokyo Institute of Technology, Meguro, Japan

    T. Q. Bui

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  1. S. Tanaka
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  2. H. Suzuki
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  4. S. Okazawa
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  5. T. T. Yu
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  6. T. Q. Bui
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Correspondence to S. Tanaka.

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Tanaka, S., Suzuki, H., Sadamoto, S. et al. Accurate evaluation of mixed-mode intensity factors of cracked shear-deformable plates by an enriched meshfree Galerkin formulation. Arch Appl Mech 87, 279–298 (2017). https://doi.org/10.1007/s00419-016-1193-x

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