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

基于一阶剪切变形理论,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。计算时在复合材料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复合材料层合板自由振动分析的离散化控制方程,并且这些子域可由Delaunay三角形方便创建。自然邻接点插值形函数具有Kronecker delta函数性质,因而无需经过特别处理就能准确地施加本质边界条件。对不同边界条件、不同跨厚比、不同材料参数和不同铺设角度的复合材料层合板,由本文提出的无网格自然邻接点Petrov-Galerkin法进行自由振动分析时均可得到满意的结果。数值算例结果表明,本文方法求解复合材料层合板的自由振动问题是行之有效的。

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 on 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 accurately without any special techniques.The natural frequencies computed by the present meshless natural neighbour Petrov-Galerkin method for the laminated composite plates with various boundary conditions,side-to-thickness ratios,material parameters and laying angles are all satisfactory,which demonstrates that the proposed method for free vibration analysis of laminated composite plates is effective.