层合板分析的无网格局部Petrov-Galerkin方法  

A MESHLESS LOCAL PETROV-GALERKIN METHOD FOR THE LAMINATED PLATES

作　　者：熊渊博[1] 龙述尧[1] 李光耀[2] 

机构地区：[1]湖南大学工程力学系 [2]湖南大学现代车身技术教育部重点实验室,长沙410082

出　　处：《复合材料学报》2005年第6期165-171,共7页Acta Materiae Compositae Sinica

基　　金：国家973项目(2004CB719402);国家自然科学基金(10372030)

摘　　要：基于Kirchhoff均匀各向异性板控制方程的等效积分弱形式和对挠度函数采用移动最小二乘近似函数进行插值,进一步研究无网格局部Petrov-Galerkin方法在纤维增强对称层合板弯曲问题中的应用。该方法不需要任何形式的网格划分,所有的积分都在规则形状的子域及其边界上进行,其问题的本质边界条件采用罚因子法来施加。通过数值算例和与其他方法的结果比较,表明无网格局部Petrov-Galerkin法求解层合薄板弯曲问题具有解的精度高、收敛性好等一系列优点。The meshless local Petrov-Galerkin （MLPG） method is extended to solve the symmetric laminates of fiber-reinforced composite materials using the moving least-square approximation to interpolate solution variables, and the equivalent integral weak form to the governing equation of Kirchhoff＇s anisotropic plates. The present method is an effective truly meshless one as it doesn＇t need any meshgrids, and all integrals can be easily evaluated over regularly shaped domains and their boundaries. In the analysis, the essential boundary conditions are enforced by a penalty method. Several examples are given and compared with other methods. The result shows that the meshless local Petrov-Galerkin method has a number of advantages such as the quite good accuracy and the high rate of convergence in solving the problems of composite laminated plates.

关 键 词：层合板 无网格方法 局部Petrov—Galerkin法 等效积分弱形式 移动最小二乘近似 

分 类 号：TB330.1[一般工业技术—材料科学与工程] V214.8[航空宇航科学与技术—航空宇航推进理论与工程]