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A gradient continuous smoothed GFEM for heat transfer and thermoelasticity analyses

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Abstract

A gradient continuous smoothed GFEM (SGFEM) is proposed to solve the heat transfer and thermoelasticity problem. The SGFEM is based on the idea of the PU method, whose composite shape function is composed of an element shape function and a local nodal shape function. The higher-order finite-element shape function is employed to ensure the continuity of the gradient between the elements. The local nodal shape function is obtained by introducing the gradient smoothed meshfree shape function in the Taylor expansion of the nodal function. The composite shape function satisfies many valuable properties such as the Kronecker-delta property, gradient continuity; unit decomposition and linear independence. More importantly, the SGFEM retains the Kronecker-delta property and is independent of the meshfree approximation. All these properties guarantee the excellent performance of the proposed method in practical examples. Four typical numerical examples including steady, transient heat transfer and thermoelasticity are calculated by SGFEM together with three other common numerical methods including the finite-element method with triangular element (FEM-T3), the finite-element method with quadrilateral element (FEM-Q4), and the node-based finite-element method with triangular element (NSFEM-T3). All examples demonstrate significant advantages of the SGFEM in accuracy, error convergence rate, stability and efficiency.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 11472137) and the Fundamental Research Funds for the Central Universities (Grant Nos. 309181A8801 and 30919011204). We would also like to appreciate Ms. Cui Zhenqi from Nanjing University of Science and Technology, who checked the writing of our manuscript and put forward valuable suggestions during our revision process.

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  1. School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, 210094, China

    Jinsong Tang, Linfang Qian & Guangsong Chen

  2. Nanjing University of Science and Technology, Changshu Research Institute Co., Ltd., Suzhou, 215500, China

    Guangsong Chen

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

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Tang, J., Qian, L. & Chen, G. A gradient continuous smoothed GFEM for heat transfer and thermoelasticity analyses. Acta Mech 232, 3737–3765 (2021). https://doi.org/10.1007/s00707-021-03018-0

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