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A meshfree Hermite point interpolation method for buckling and post-buckling analysis of thin plates
Engineering with Computers ( IF 8.7 ) Pub Date : 2021-06-25 , DOI: 10.1007/s00366-021-01457-w
Youssef Hilali , Oussama Bourihane

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.



中文翻译:

一种用于薄板屈曲和后屈曲分析的无网格Hermite点插值方法

本文旨在开发一种基于 Hermite 型点插值法 (HPIM) 和高阶延续 (HOC) 求解器耦合的无网格方法,用于对需要高阶连续性形状函数的几何非线性问题进行数值模拟,例如薄板的屈曲。详细介绍了点插值法(PIM)和Hermite型点插值法(HPIM)的形状函数构造过程。第一种用于近似平面内位移,而第二种用于横向分量及其导数。采用标准伽辽金方法离散控制偏微分方程,这些方程是使用基尔霍夫板理论推导出来的。由于求解器将泰勒级数展开与延续过程相结合,因此可以解决所考虑的问题。给出了具有不同几何形状、各种边界条件和载荷的数值例子,以验证所提出方法的效率、准确性和鲁棒性。

更新日期:2021-06-25
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