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The extrinsic enriched finite element method based on RBFs for linear elastic solid dynamic analysis

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  • Liu, Qingliang
  • Zou, Zhihong
  • Chu, Wei

Abstract

A novel extrinsic enriched finite element method (EFEM) based on radial basis functions (RBFs) is proposed for dynamic analysis of linear elastic solids to obtain accurate numerical solutions and avoid the potential linear dependence (LD) problem. In the proposed method, the RBFs are used in conjunction with the linear polynomial functions from the conventional finite element method (FEM) to construct the nodal interpolation functions. Moreover, the approximation space formed by the RBFs is enriched using enrichment functions based on the partition of unity (PU) concept without requiring any extra nodes. The LD issue commonly encountered in PU-based methods is effectively avoided by the present RBF formulation. In this paper, free and forced vibrations of a series of classical numerical models are simulated using both the proposed method and the conventional FEM. The results demonstrate that the proposed method achieves better computational accuracy and efficiency. Additionally, sufficiently accurate numerical solutions are obtained even when distorted meshes are used. With the proposed approach, essential and natural boundary conditions can be directly imposed as in the conventional FEM. Therefore, the proposed method may offer a promising alternative to the conventional FEM for dynamic analysis of linear elastic solids.

Suggested Citation

  • Liu, Qingliang & Zou, Zhihong & Chu, Wei, 2026. "The extrinsic enriched finite element method based on RBFs for linear elastic solid dynamic analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 247(C), pages 244-265.
    • Handle: RePEc:eee:matcom:v:247:y:2026:i:c:p:244-265
    DOI: 10.1016/j.matcom.2026.03.019
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    References listed on IDEAS

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    1. Chai, Yingbin & Li, Wei & Liu, Zuyuan, 2022. "Analysis of transient wave propagation dynamics using the enriched finite element method with interpolation cover functions," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    2. Gui, Qiang & Li, Wei & Chai, Yingbin, 2023. "The enriched quadrilateral overlapping finite elements for time-harmonic acoustics," Applied Mathematics and Computation, Elsevier, vol. 451(C).
    3. Yancheng Li & Sina Dang & Wei Li & Yingbin Chai, 2022. "Free and Forced Vibration Analysis of Two-Dimensional Linear Elastic Solids Using the Finite Element Methods Enriched by Interpolation Cover Functions," Mathematics, MDPI, vol. 10(3), pages 1-21, January.
    4. Liu, Qingliang & Zou, Zhihong & Chu, Wei, 2026. "The extrinsic enriched finite element method based on RBFs for linear elastic solid dynamic analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 247(C), pages 244-265.
    5. Dell’Accio, Francesco & Di Tommaso, Filomena & Guessab, Allal & Nudo, Federico, 2023. "A general class of enriched methods for the simplicial linear finite elements," Applied Mathematics and Computation, Elsevier, vol. 456(C).
    6. Dell’Accio, Francesco & Guessab, Allal & Nudo, Federico, 2025. "Improved methods for the enrichment and analysis of the simplicial vector-valued linear finite elements," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 230(C), pages 370-385.
    7. Dell’Accio, Francesco & Di Tommaso, Filomena & Guessab, Allal & Nudo, Federico, 2023. "Enrichment strategies for the simplicial linear finite elements," Applied Mathematics and Computation, Elsevier, vol. 451(C).
    8. Li, Yancheng & Liu, Cong & Li, Wei & Chai, Yingbin, 2023. "Numerical investigation of the element-free Galerkin method (EFGM) with appropriate temporal discretization techniques for transient wave propagation problems," Applied Mathematics and Computation, Elsevier, vol. 442(C).
    9. You, Xiangyu & Li, Wei & Chai, Yingbin, 2020. "A truly meshfree method for solving acoustic problems using local weak form and radial basis functions," Applied Mathematics and Computation, Elsevier, vol. 365(C).
    10. Yingbin Chai & Kangye Huang & Shangpan Wang & Zhichao Xiang & Guanjun Zhang, 2023. "The Extrinsic Enriched Finite Element Method with Appropriate Enrichment Functions for the Helmholtz Equation," Mathematics, MDPI, vol. 11(7), pages 1-25, March.
    11. Cong Liu & Shaosong Min & Yandong Pang & Yingbin Chai, 2023. "The Meshfree Radial Point Interpolation Method (RPIM) for Wave Propagation Dynamics in Non-Homogeneous Media," Mathematics, MDPI, vol. 11(3), pages 1-27, January.
    12. Qingliang Liu & Zhihong Zou & Yingbin Chai & Wei Li & Wei Chu, 2026. "An Extrinsic Enriched Finite Element Method Based on RBFs for the Helmholtz Equation," Mathematics, MDPI, vol. 14(1), pages 1-35, January.
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    1. Liu, Qingliang & Zou, Zhihong & Chu, Wei, 2026. "The extrinsic enriched finite element method based on RBFs for linear elastic solid dynamic analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 247(C), pages 244-265.

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