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A meshfree Hermite point interpolation method for buckling and post-buckling analysis of thin plates

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Abstract

This paper aims to develop a meshfree approach based on the coupling of the Hermite-type point interpolation method (HPIM) and a high order continuation (HOC) Solver for numerical simulation of the geometrically nonlinear problems that require higher order continuity shape functions such as the buckling of a thin plate. The point interpolation method (PIM) and Hermite-type point interpolation method (HPIM) shape functions construction procedure is presented in detail. The first type is used to approximate the in-plane displacements, while the second one is used for the transverse component and its derivatives. The standard Galerkin method is adopted to discretize the governing partial differential equations which were derived from using the Kirchhoff’s plate theory. The resolution of the considered problem is performed thanks to a solver that combines a Taylor series expansion with a continuation procedure. Numerical examples with different geometric shapes, various boundary conditions and loadings are given to verify the efficiency, accuracy, and robustness of the proposed approach.

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Authors and Affiliations

  1. Laboratory of Mechanical Engineering, Faculty of Sciences and Technologies Fez, Sidi Mohamed Ben Abdellah University, Imouzzer Road, BP 2202, Fez, Morocco

    Youssef Hilali & Oussama Bourihane

  2. Laboratory of Engineering and Materials, Faculty of Sciences Ben M’sik, Hassan II University of Casablanca, Av Driss El Harti, Sidi Othmane, BP 7955, Casablanca, Morocco

    Youssef Hilali

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  1. Youssef Hilali
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  2. Oussama Bourihane
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Correspondence to Oussama Bourihane.

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Hilali, Y., Bourihane, O. A meshfree Hermite point interpolation method for buckling and post-buckling analysis of thin plates. Engineering with Computers 38 (Suppl 4), 3171–3190 (2022). https://doi.org/10.1007/s00366-021-01457-w

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  • DOI: https://doi.org/10.1007/s00366-021-01457-w

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