分析复合材料层合板弯曲和振动的一种有效无网格方法  

An Effective Meshfree Method for Bending and Vibration Analyses of Laminated Composite Plates

作　　者：王伟[1,2] 伊士超[3] 姚林泉[2] 

机构地区：[1]苏州大学数学科学学院,江苏苏州215006 [2]苏州大学城市轨道交通学院,江苏苏州215131 [3]江苏科技大学数理学院,江苏镇江212003

出　　处：《应用数学和力学》2015年第12期1274-1284,共11页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11172192;11572210)~~

摘　　要：基于高阶剪切法向变形板理论(HOSNDPT)利用无网格方法对层合板弯曲和振动问题进行数值分析.在通常的径向点插值法(RPIM)中对每个Gauss(高斯)点或计算点需要求矩矩阵的逆,且受到影响域半径大小的限制.而在加权节点径向点插值法(WN-RPIM)近似中,求解系统矩阵的逆的数量等于问题域中的节点数量,它远远小于Gauss点的数目,可以大大减少矩矩阵求逆的计算量,且克服了RPIM中影响域半径大小的限制.首先,将三维板位移分解成厚度和面内位移的乘积,在厚度方向使用正交Legendre多项式作为基函数,在板的面内使用WN-RPIM来构造形函数.然后,通过对层合板的弯曲问题进行数值计算表明WN-RPIM的计算精度和稳定性.最后,将该方法推广到对不同边界条件、不同厚跨比、不同铺设方式的层合板振动问题的数值计算,数值结果表明了本文提供方法的适用性和有效性.Numerical analysis of laminated plates＇ bending and vibration problems was presen- ted based on the high order shear and normal deformation plate theory （HOSNDPT） with the meshless method. For the usual radial point interpolation method （ RPIM）, the inverses of the moment matrices are required for each Gauss point or calculation point, and are limited by the radius of the domain. For the weighted node radial point interpolation method （ WN-RPIM）, the number of the inverses of the system matrices is equal to the number of nodes in the problem domain, which is far less than the number of Gauss points, so the WN-RPIM can greatly reduce the computation complexity of the moment matrices and overcome the limitations on the RPIM. First, the 3D plate displacement was decomposed into the product of the thickness-direction and in-plane displacements, and the orthogonal Legendre polynomials were used as basis func- tions in the thickness direction, the WN-RPIM was employed in plane to construct the shape functions. Then, the numerical calculation of the bending problems of laminated plates verified the accuracy and stability of the WN-RPIM. At last, the proposed method was extended to the numerical calculation of the vibration problems of laminated plates with different boundary con- ditions, different thickness-to-span ratios and different laying patterns. The numerical results show the applicability and effectiveness of the proposed method.

关 键 词：复合材料层合板 振动 高阶剪切和法向变形板理论(HOSNDPT) 径向点插值法 加权节点的径向点插值无网格法(WN-RPIM) 

分 类 号：O343.8[理学—固体力学]