使用无网格赫米特径向点插值法对功能分级夹层薄板进行屈曲分析

IF 8.7 2区 工程技术 Q1 Mathematics Engineering with Computers Pub Date : 2024-08-02 DOI:10.1007/s00366-024-02011-0
Sokayna baid, Youssef Hilali, Said Mesmoudi, Oussama Bourihane
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引用次数: 0

摘要

本文介绍了一种创新的无网格计算方法,用于模拟几何非线性问题,重点是薄板的屈曲分析。该研究以基尔霍夫板理论为基础,提出了控制偏微分方程,并使用 Galerkin 方法对其进行离散化处理,从而解决了重大变形问题。该问题要求形状函数具有高阶连续性,并同时满足迪里希勒和诺伊曼边界条件,为了解决这一复杂问题,研究扩展了赫米特型点插值法(HPIM)。尽管 HPIM 非常有效,但矩阵中偶尔出现的奇异点仍需要改进。本研究提出了一种由径向基函数(Hermite-RPIM)增强的改进型赫尔墨特型点插值法,以确保矩阵条件良好。通过详细的数值实例,包括在各种载荷、边界条件和材料类型下对夹层功能分级材料(FGM)板进行屈曲和屈曲后分析,验证了所提方法的有效性。这些实例凸显了增强型 Hermite-RPIM 的稳健性、可靠性和计算效率,使其有望成为分析几何非线性问题(尤其是薄板屈曲分析)的重要工具。
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Buckling analysis of functionally graded sandwich thin plates using a meshfree Hermite Radial Point Interpolation Method

This paper introduces an innovative mesh-free computational approach for simulating problems with geometric nonlinearity, focusing on the buckling analysis of thin plates. Addressing significant deformations, the study formulates governing partial differential equations based on Kirchhoff’s plate theory and discretizes them using the Galerkin method. To tackle the complexities of this problem, which demands higher-order continuity in shape functions and accommodates both Dirichlet and Neumann boundary conditions, the research extends the Hermite-type point interpolation method (HPIM). Despite HPIM’s effectiveness, occasional singularities in the moment matrix require enhancement. This work proposes an improved Hermite-type point interpolation method augmented by radial basis functions (Hermite-RPIM) to ensure a well-conditioned moment matrix. The efficacy of the proposed method is validated through detailed numerical examples, including buckling and post-buckling analysis of sandwich functionally graded material (FGM) plates under various loadings, boundary conditions, and material types. These examples highlight the robustness, reliability, and computational efficiency of the enhanced Hermite-RPIM, establishing its potential as a valuable tool for analyzing geometrically nonlinear problems, especially in thin plate buckling analysis.

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来源期刊
Engineering with Computers
Engineering with Computers 工程技术-工程:机械
CiteScore
16.50
自引率
2.30%
发文量
203
审稿时长
9 months
期刊介绍: Engineering with Computers is an international journal dedicated to simulation-based engineering. It features original papers and comprehensive reviews on technologies supporting simulation-based engineering, along with demonstrations of operational simulation-based engineering systems. The journal covers various technical areas such as adaptive simulation techniques, engineering databases, CAD geometry integration, mesh generation, parallel simulation methods, simulation frameworks, user interface technologies, and visualization techniques. It also encompasses a wide range of application areas where engineering technologies are applied, spanning from automotive industry applications to medical device design.
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