Assumed stress quasi-conforming technique for static and free vibration analysis of Reissner-Mindlin plates
Assumed stress quasi-conforming technique for static and free vibration analysis of Reissner-Mindlin plates
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Reissner-Mindlin 板静态和自由振动分析的假设应力准一致技术
DOI：
10.1002/nme.5510
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发表时间：
2017
影响因子：
2.9
通讯作者：
Hu Ping
中科院分区：
文献类型：
--
作者：
Wang Changsheng;Wang Xuan;Zhang Xiangkui;Hu Ping
本文提出了一种基于 Hellinger-Reissner 变分原理的新公式，在准一致方法框架内用于 Reissner-Mindlin 板的静态和自由振动分析。该公式从应力的多项式近似开始，满足 Reissner-Mindlin 板理论的平衡方程。利用本构方程导出应变后，将应力矩阵作为加权函数来弱化应变-位移方程。最后，引入弦网函数来计算应变积分。作为示例，提出了两种新的板弯曲单元，即 4 节点四边形单元 QC-P4-11β 和 3 节点三角形单元 QC-P3-7β。演示了几个基准示例来显示元件的性能，并将获得的结果与其他可用的结果进行比较。数值结果证明这两种元件均具有优良的精度。特别是，即使当单元形状退化为三角形或凹四边形时，四边形单元也表现良好。版权所有 © 2017 约翰威利父子有限公司
This paper presents a novel formulation based on Hellinger–Reissner variational principle in the framework of quasi‐conforming method for static and free vibration analysis of Reissner–Mindlin plates. The formulation starts from polynomial approximation of stresses, which satisfy the equilibrium equations of Reissner–Mindlin plate theory. Then the stress matrix is treated as the weighted function to weaken the strain‐displacement equations after the strains are derived by using the constitutive equations. Finally, the string‐net functions are introduced to calculate strain integration. As examples, two new plate bending elements, a 4‐node quadrilateral element QC‐P4‐11βand a 3‐node triangular element QC‐P3‐7β, are proposed. Several benchmark examples are demonstrated to show the performance of the elements, and the results obtained are compared with other available ones. Numerical results have proved that both elements possess excellent precision. In particular, the quadrilateral element performs well even when the element shape degenerates into a triangle or concave quadrangle. Copyright © 2017 John Wiley & Sons, Ltd.