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复合材料层合板自由振动分析的无网格自然 邻接点Petrov-Galerkin法
Free vibration analysis of laminated composite plates by the meshless natural neighbour Petrov-Galerkin method
投稿时间:2017-10-05  修订日期:2017-11-07
DOI:
中文关键词:  无网格法  自然邻接点插值  层合板  自由振动
英文关键词:meshless method  laminated composite plates  natural neighbour interpolation  free vibration
基金项目:国家自然科学基金项目(面上项目,重点项目,重大项目)
作者单位E-mail
陈莘莘 华东交通大学土木建筑学院 chenshenshen@tsinghua.org.cn 
摘要点击次数: 39
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中文摘要:
      基于一阶剪切变形理论,本文提出了复合材料层合板自由振动分析的无网格自然邻接点Petrov-Galerkin法。计算时在层合板中面上仅需要布置一系列的离散节点,并利用这些节点构建插值函数。在板中面上的局部多边形子域上采用加权余量法建立层合板自由振动的离散化控制方程,并且这些子域可由Delaunay三角形方便地创建。自然邻接点插值构造的试函数具有Kronecker delta函数性质,可以直接准确地施加本质边界条件。采用本文给出的方法,对不同边界条件、不同跨厚比、不同材料参数和铺设角度的层合板进行自由振动分析,均得到满意的结果。数值算例结果表明,所提出的方法求解层合板的自由振动问题是行之有效的。
英文摘要:
      Based on the first-order shear deformation theory, a meshless natural neighbour Petrov-Galerkin method has been developed for free vibration analysis of laminated composite plates in this paper. In the computation, only a set of randomly distributed nodes over the middle plane of the considered plate are required and the interpolation functions are constructed through these nodes. The discretized governing equations for free vibration analysis of laminated composite plates are derived by using the weighted residual method over local polygonal sub-domains in the mean surface of the plate. These polygonal sub-domains can be conveniently constructed with Delaunay tessellations. Because the constructed shape functions from the natural neighbour interpolation possess the Kronecker delta function property, the essential boundary conditions can be imposed directly and accurately. The natural frequencies computed by the present method for the laminated composite plates with various boundary conditions, side-to-thickness ratios, material parameters and laying angles are all well, which demonstrate that the proposed method for free vibration analysis of laminated composite plates is effective.
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