Pseudospectral meshless radial point interpolation for generalized biharmonic equation subject to simply supported and clamped boundary conditions

Saeid Abbasbandy; Elyas Shivanian; Khalid Hammood AL-Jizani; Satya N. Atluri

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Pseudospectral meshless radial point interpolation for generalized biharmonic equation subject to simply supported and clamped boundary conditions

机译：广义双态方程的假谱无网径点插值，以至于简单地支持和夹紧边界条件

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摘要

In this study, we develop an approximate formulation for a generalized form of the biharmonic problem based on pseudospectral meshless radial point interpolation (PSMRPI). The boundary conditions are considered as simply supported or clamped, with application to the theory of static analysis of thin-plates. The rigorous steps to analyze such problem are defining the high order derivatives, implementing multiple boundary conditions especially when the geometry of the domain of the problem is complex. In PSMRPI method the nodal points do not need to be regularly distributed and can even be quite arbitrary. It is easy to have high order derivatives of unknowns in terms of the values at nodal points by constructing operational matrices. Furthermore, it is observed that the multiple boundary conditions can be imposed by applying PSMRPI on nodal points near the boundaries of the domain. The main results on the generalized biharmonic problem are demonstrated by some examples to show the validity and trustworthiness of PSMRPI technique. Also, a comparison with the previously standard studied method for the biharmonic problem is done.

机译：在这项研究中，我们基于伪谱网无径向点插值（PSMRPI）开发了对普通态问题的广义形式的近似配方。利用薄板静态分析理论，将边界条件视为简单地支持或夹紧。分析此类问题的严格步骤是定义高阶导数，特别是当问题的域的几何形状复杂时实现多个边界条件。在PSMRPI方法中，Nodal点不需要定期分发，甚至可以是非常任意的。通过构建操作矩阵，在节点点处的值方面很容易具有所未知的高阶衍生物。此外，观察到可以通过在域的边界附近的节点点上施加PSMRPI来施加多个边界条件。一些例子证明了普遍的比哈卡态问题的主要结果，以表明PSMRPI技术的有效性和可信度。此外，完成了与先前标准研究的比较问题的比较。

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来源
《Engineering analysis with boundary elements》 |2021年第4期|23-32|共10页
作者
Saeid Abbasbandy; Elyas Shivanian; Khalid Hammood AL-Jizani; Satya N. Atluri;
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作者单位

Department of Applied Mathematics Imam Khomeini International University Qazvin Iran;

Department of Applied Mathematics Imam Khomeini International University Qazvin Iran;

Department of Mathematics College of Science Mustansiriyah University Baghdad Iraq;

Department of Mechanical Engineering Center for Advance Research in Engineering Sciences Texas Tech University Lubbock TX 79415 USA;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Spectral method; Pseudospectral method; Meshless technique; Radial point interpolation (RPI); Radial basis function;

机译：光谱法;假谱法;无丝石技术;径向点插值（RPI）;径向基功能;

Pseudospectral meshless radial point interpolation for generalized biharmonic equation subject to simply supported and clamped boundary conditions

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