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A 3D pyramid spline element

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Abstract

In this paper, a 13-node pyramid spline element is derived by using the tetrahedron volume coordinates and the B-net method, which achieves the second order completeness in Cartesian coordinates. Some appropriate examples were employed to evaluate the performance of the proposed element. The numerical results show that the spline element has much better performance compared with the isoparametric serendipity element Q20 and its degenerate pyramid element P13 especially when mesh is distorted, and it is comparable to the Lagrange element Q27. It has been demonstrated that the spline finite element method is an efficient tool for developing high accuracy elements.

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Authors and Affiliations

  1. School of Mathematics and Quantitative Economics, Dongbei University of Finance and Economics, 116025, Dalian, China

    Juan Chen

  2. School of Mathematical Sciences, Dalian University of Technology, 116024, Dalian, China

    Chong-Jun Li

  3. Key Laboratory of Liaoning Province for Composite Structural Analysis of Aerocraft and Simulation, Shenyang Aerospace University, 110136, Shenyang, China

    Wan-Ji Chen

  4. State Key Laboratory for Structural Analysis of Industrial Equipment, Dalian University of Technology, 116024, Dalian, China

    Wan-Ji Chen

Authors
  1. Juan Chen
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  2. Chong-Jun Li
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  3. Wan-Ji Chen
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Corresponding author

Correspondence to Chong-Jun Li.

Additional information

The project was supported by the National Natural Science Foundation of China (11001037, 11102037, 11072156) and the Fundamental Research Funds for the Central Universities of China (DUT10ZD112, DUT10JS02).

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Chen, J., Li, CJ. & Chen, WJ. A 3D pyramid spline element. Acta Mech Sin 27, 986–993 (2011). https://doi.org/10.1007/s10409-011-0513-1

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  • DOI: https://doi.org/10.1007/s10409-011-0513-1

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