IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v185y2021icp347-357.html
   My bibliography  Save this article

Bending analysis of simply supported and clamped thin elastic plates by using a modified version of the LMFS

Author

Listed:
  • Qu, Wenzhen
  • Sun, Linlin
  • Li, Po-Wei

Abstract

The localized method of fundamental solutions is a recent domain-type meshless collocation method with the fundamental solutions of governing equations as the radial basis functions. This approach forms a sparse system matrix and has a higher efficiency than the traditional method of fundamental solutions. In this paper, a modified version of the localized method of fundamental solutions is developed for bending analysis of simply supported and clamped thin elastic plates. Some auxiliary nodes on the boundary are firstly introduced to provide additional weight coefficients, which contribute to the construction of the determined system of equations and avoid the over-determined equation system of the localized method of fundamental solutions for bending analysis of thin elastic plates. Several numerical experiments with simply supported or clamped boundary conditions are provided, and numerical results are in good agreement with the analytical or COMSOL Multiphysics solutions.

Suggested Citation

  • Qu, Wenzhen & Sun, Linlin & Li, Po-Wei, 2021. "Bending analysis of simply supported and clamped thin elastic plates by using a modified version of the LMFS," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 347-357.
    • Handle: RePEc:eee:matcom:v:185:y:2021:i:c:p:347-357
    DOI: 10.1016/j.matcom.2020.12.031
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475420304997
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2020.12.031?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Li, Xiaolin & Chen, Hao & Wang, Yan, 2015. "Error analysis in Sobolev spaces for the improved moving least-square approximation and the improved element-free Galerkin method," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 56-78.
    2. 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).
    3. Xi, Qiang & Fu, Zhuojia & Wu, Wenjie & Wang, Hui & Wang, Yong, 2021. "A novel localized collocation solver based on Trefftz basis for potential-based inverse electromyography," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    4. Merta, M. & Zapletal, J., 2018. "A parallel library for boundary element discretization of engineering problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 145(C), pages 106-113.
    5. Malatip, A. & Prasomsuk, N. & Siriparu, C. & Paoprasert, N. & Otarawanna, S., 2020. "An efficient matrix tridiagonalization method for 3D finite element analysis of free vibration," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 172(C), pages 90-110.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Jianliang Chen & Qinghai Zhao & Liang Zhang, 2022. "Multi-Material Topology Optimization of Thermo-Elastic Structures with Stress Constraint," Mathematics, MDPI, vol. 10(8), pages 1-18, April.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. 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).
    3. Sun, Linlin & Fu, Zhuojia & Chen, Zhikang, 2023. "A localized collocation solver based on fundamental solutions for 3D time harmonic elastic wave propagation analysis," Applied Mathematics and Computation, Elsevier, vol. 439(C).
    4. Shirzadi, Mohammad & Rostami, Mohammadreza & Dehghan, Mehdi & Li, Xiaolin, 2023. "American options pricing under regime-switching jump-diffusion models with meshfree finite point method," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    5. Wang, Fajie & Zhao, Qinghai & Chen, Zengtao & Fan, Chia-Ming, 2021. "Localized Chebyshev collocation method for solving elliptic partial differential equations in arbitrary 2D domains," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    6. Zhijuan Meng & Xiaofei Chi & Lidong Ma, 2022. "A Hybrid Interpolating Meshless Method for 3D Advection–Diffusion Problems," Mathematics, MDPI, vol. 10(13), pages 1-21, June.
    7. Li, Yang & Liu, Dejun & Yin, Zhexu & Chen, Yun & Meng, Jin, 2023. "Adaptive selection strategy of shape parameters for LRBF for solving partial differential equations," Applied Mathematics and Computation, Elsevier, vol. 440(C).
    8. Jue Qu & Hongjun Xue & Yancheng Li & Yingbin Chai, 2022. "An Enriched Finite Element Method with Appropriate Interpolation Cover Functions for Transient Wave Propagation Dynamic Problems," Mathematics, MDPI, vol. 10(9), pages 1-12, April.
    9. Sina Dang & Gang Wang & Yingbin Chai, 2023. "A Novel “Finite Element-Meshfree” Triangular Element Based on Partition of Unity for Acoustic Propagation Problems," Mathematics, MDPI, vol. 11(11), pages 1-21, May.
    10. 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.
    11. Sun, FengXin & Wang, JuFeng, 2017. "Interpolating element-free Galerkin method for the regularized long wave equation and its error analysis," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 54-69.
    12. 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).
    13. Xunbai Du & Sina Dang & Yuzheng Yang & Yingbin Chai, 2022. "The Finite Element Method with High-Order Enrichment Functions for Elastodynamic Analysis," Mathematics, MDPI, vol. 10(23), pages 1-27, December.
    14. 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.
    15. 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.
    16. Tingting Sun & Peng Wang & Guanjun Zhang & Yingbin Chai, 2022. "A Modified Radial Point Interpolation Method (M-RPIM) for Free Vibration Analysis of Two-Dimensional Solids," Mathematics, MDPI, vol. 10(16), pages 1-20, August.
    17. Nikan, O. & Avazzadeh, Z., 2021. "A localisation technique based on radial basis function partition of unity for solving Sobolev equation arising in fluid dynamics," Applied Mathematics and Computation, Elsevier, vol. 401(C).
    18. Zhang, Tao & Li, Xiaolin, 2020. "Analysis of the element-free Galerkin method with penalty for general second-order elliptic problems," Applied Mathematics and Computation, Elsevier, vol. 380(C).
    19. Xi, Qiang & Fu, Zhuojia & Wu, Wenjie & Wang, Hui & Wang, Yong, 2021. "A novel localized collocation solver based on Trefftz basis for potential-based inverse electromyography," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    20. Wang, Qiao & Zhou, Wei & Feng, Y.T. & Ma, Gang & Cheng, Yonggang & Chang, Xiaolin, 2019. "An adaptive orthogonal improved interpolating moving least-square method and a new boundary element-free method," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 347-370.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:185:y:2021:i:c:p:347-357. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.