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A new algorithm for shape parameter optimization in the multiquadric method for bending beam and elastic plane BVPs

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Abstract

In this study, an enhancement to the Multiquadric Radial Basis Function (MQ-RBF) method is presented for solving Elasticity Boundary Value Problems (E-BVPs). MQ-RBF is utilized to reproduce the system of governing partial differential equations and boundary conditions. Also the inefficacies of some existing methods in determining the Optimal Shape Parameter (OSP) when solving E-BVPs are shown. Afterward, a new algorithm is introduced based on Teaching–Learning-Based Optimization (TLBO). In addition, the lower and upper bounds of the shape parameter and a new objective function were introduced for the TLBO algorithm. Using the algorithm, one OSP is obtained for both MQ-RBF functions in 2D problems, resulting in reduced computational cost. Its efficiency is evidenced by solving several examples. Moreover, its accuracy is demonstrated by comparing its outcomes to those of analytical methods. Unlike the 1D problems, the OSP is found to be a function of loading and material properties as well as the geometry in 2D problems.

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Acknowledgements

This work was supported by the Iran National Science Foundation (Grant Number: 98001721). The authors gratefully acknowledge this financial support.

Funding

Funding was provided by Iran National Science Foundation (Grant Number: INSF-98001721).

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Authors and Affiliations

  1. Department of Civil Engineering, University of Qom, Qom, Iran

    Reza Babaee & Ehsan Jabbari

  2. School of Civil Engineering, College of Engineering, University of Tehran, Tehran, Iran

    Morteza Eskandari-Ghadi

  3. Civil and Environmental Engineering Program, Graduate School of Advanced Science and Engineering, Hiroshima University, 1-4-1, Kagamiyama, Higashi-Hiroshima, Hiroshima, 739-8527, Japan

    Naser Khaji

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  1. Reza Babaee
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  2. Ehsan Jabbari
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  3. Morteza Eskandari-Ghadi
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  4. Naser Khaji
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Contributions

All authors contributed to the study’s conception and design. Material preparation, data collection, and analyses were performed by [RB], [MEG], [EJ], and [NK]. The first draft of the manuscript was written by [RB], and all authors commented on previous versions of the manuscript. All authors read and approved the final draft of the manuscript.

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Correspondence to Ehsan Jabbari.

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Babaee, R., Jabbari, E., Eskandari-Ghadi, M. et al. A new algorithm for shape parameter optimization in the multiquadric method for bending beam and elastic plane BVPs. Arch Appl Mech 92, 3109–3125 (2022). https://doi.org/10.1007/s00419-022-02225-y

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