基于插值型无单元Galerkin法的复合材料层合板自由振动分析  

Free vibration analysis of laminated composite plates based on the interpolating element-free Galerkin method

作　　者：陈莘莘[1] 周文博 胡常福[1] Chen Shenshen;Zhou Wenbo;Hu Changfu(School of Civil Engineering and Architecture,East China Jiaotong University,330013,Nanchang,China)

机构地区：[1]华东交通大学土木建筑学院,南昌330013

出　　处：《应用力学学报》2021年第3期1280-1285,共6页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(11772129)。

摘　　要：为了更有效地求解复合材料层合板的自由振动问题,以一阶剪切变形理论为基础,对插值型无单元Galerkin法在此类问题中的应用进行了研究,并发展了相应的计算方法。该方法采用插值型移动最小二乘法建立试函数时可以只依赖于复合材料层合板中面上的一组离散节点,在继承无单元Galerkin法前处理简单、计算精度高等优点的同时,可直接施加本质边界条件,避免了使用Lagrange乘子法和罚函数法处理本质边界条件。采用本文提出的插值型无单元Galerkin法,对不同边界条件、不同厚跨比、不同材料参数的复合材料层合板的振动频率进行了计算,通过与文献结果对比验证了本文所提方法的有效性。In order to solve the free vibration problem of laminated composite plates more effectively,a novel numerical method based on the interpolating element-free Galerkin(IEFG)method is proposed in the present study.The first order shear deformation theory(FSDT)is employed to take into account the transverse shear strain and rotary inertia and the interpolating moving least-squares(IMLS)method is utilized to obtain the shape functions based on a set of distinct nodes are randomly distributed over the middle plane of the considered plate.Compared with the conventional EFG method,the essential boundary conditions can be directly applied in the IEFG method which makes the computing efficiency of the method higher.The natural frequencies computed by the proposed method for the laminated composite plates with different boundary conditions,side-to-thickness ratios and material parameters are all satisfactory,which demonstrates that the proposed method for free vibration analysis of laminated composite plates is efficient and highly accurate.

关 键 词：无网格法 移动最小二乘插值法 复合材料层合板 自由振动 

分 类 号：TU311.4[建筑科学—结构工程]