Uncovering the finite difference model equivalent to Hencky bar-net model for axisymmetric bending of circular and annular plates

H. Zhang; C.M. Wang; N. Challamel; Y.P. Zhang

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Uncovering the finite difference model equivalent to Hencky bar-net model for axisymmetric bending of circular and annular plates

机译：揭示等效于Hencky杆网模型的圆形和环形板轴对称弯曲的有限差分模型

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As there are a few finite difference models in the literature for axisymmetric bending of plates, only one of these models is equivalent to the Hencky bar-net model (HBM) that comprises a finite number of rigid circular arcs and straight radial segments joined by frictionless hinges with elastic rotational springs. This paper is concerned with uncovering the one finite difference model (FDM) that is equivalent to the HBM. Based on the energy formulation, the governing equation for HBM is derived and it will be used to identify the FDM that has the same discrete set of equations. By using this equivalency between the HBM and the identified FDM, the expressions of edge spring stiffnesses of HBM are derived for various boundary conditions. As illustrative examples, the HBM is used to solve the bending problems of circular plates under uniformly and linearly increasing distributed loads. The analytical solutions of HBM avoids the singularity problem faced in FDM at the plate center. This paper also presents some benchmark bending solutions for annular plates with and without an internal ring support for different boundary restraints by using the HBM.

机译：由于文献中存在一些关于板轴对称弯曲的有限差分模型，因此这些模型中只有一个等效于Hencky钢筋网模型（HBM），该模型包括有限数量的刚性圆弧和通过无摩擦连接的直径向段带有弹性旋转弹簧的铰链。本文涉及发现与HBM等效的一个有限差分模型（FDM）。基于能量公式，可导出HBM的控制方程，并将其用于识别具有相同离散方程组的FDM。通过在HBM和已识别的FDM之间使用这种等效性，可以得出针对各种边界条件的HBM边缘弹簧刚度的表达式。作为说明性示例，HBM用于解决圆形板在均匀且线性增加的分布载荷下的弯曲问题。 HBM的解析解决方案避免了FDM板中心面临的奇异性问题。本文还通过使用HBM，针对带有和不带有内部环支撑的环形板，针对不同的边界约束，提出了一些基准弯曲解决方案。

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来源
《Applied Mathematical Modelling》 |2018年第9期|300-315|共16页
作者
H. Zhang; C.M. Wang; N. Challamel; Y.P. Zhang;
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作者单位

School of Civil Engineering, The University of Queensland;

School of Civil Engineering, The University of Queensland;

Centre de Recherche, Rue de Saint Maudé, Université de Bretagne Sud, IRDL−UBS−Lorient, Institut de Recherche Dupuy de Lôme;

School of Mechanical and Mining Engineering, The University of Queensland;

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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
Finite difference; Hencky bar-net; Distributed load; Axisymmetric bending; Circular plate; Annular plate;

机译：有限差分;弯曲钢筋网;分布载荷;轴对称弯曲;圆形板;环形板;

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5. EQUIVALENT CONTINUUM FINITE ELEMENT MODELLING OF PLATE-LIKE SPACE LATTICE STRUCTURES (OPTIMAL, VIBRATIONS, CONTROL). [D] . LAMBERSON, STEVEN EDWARD. 1985

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7. Uncovering the finite difference model equivalent to Hencky bar-net model for axisymmetric bending of circular and annular plates [O] . H. Zhang, C.M. Wang, N. Challamel, 2018

机译：揭示圆形和环形板轴对称弯曲的Hencky Bar-Net模型等效的有限差分模型
8. Equivalent Continuum Finite Element Modelling of Plate-Like Space Lattice Structures [R] . Lamberson, S. E. 1985

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Uncovering the finite difference model equivalent to Hencky bar-net model for axisymmetric bending of circular and annular plates

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