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Smoothed FE-Meshfree method for solid mechanics problems

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Abstract

This paper presents a smoothed FE-Meshfree (SFE-Meshfree) method for solving solid mechanics problems. The system stiffness matrix is calculated via a strain-smoothing technique with the composite shape function, which is based on the partition of unity-based method, combing the classical isoparametric quadrilateral function and radial-polynomial basis function. The corresponding Gauss integration in the element is replaced by line integration along the edges of the smoothing cells, so no derivatives of the composite shape functions are needed during the field gradient estimation process. Several numerical examples including an automobile mechanical component are employed to examine the presented method. Calculation results indicate that SFE-Meshfree can obtain a high convergence rate and accuracy without introducing additional degrees of freedom to the system. In addition, it is also more tolerant with respect to mesh distortion. The volumetric locking problem is also explored in this paper under a selective smoothing integration scheme.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant No. 11472137.

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Authors and Affiliations

  1. School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, 210094, People’s Republic of China

    Guangsong Chen, Linfang Qian, Jia Ma & Yicheng Zhu

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  1. Guangsong Chen
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  2. Linfang Qian
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Correspondence to Guangsong Chen.

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Chen, G., Qian, L., Ma, J. et al. Smoothed FE-Meshfree method for solid mechanics problems. Acta Mech 229, 2597–2618 (2018). https://doi.org/10.1007/s00707-018-2124-4

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  • DOI: https://doi.org/10.1007/s00707-018-2124-4

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