复合材料层合板应力分析的小波有限元法  

Stress Analysis of Laminated Composite Plates with Wavelet Finite Element Method

作　　者：彭惠芬[1,2] 孟广伟[1] 范森[3] 周立明[1] 

机构地区：[1]吉林大学机械科学与工程学院,吉林长春130022 [2]东北石油大学机械科学与工程学院,黑龙江大庆163318 [3]东北石油大学石油工程学院,黑龙江大庆163318

出　　处：《华南理工大学学报（自然科学版）》2012年第7期117-122,共6页Journal of South China University of Technology(Natural Science Edition)

基　　金：高等学校博士学科专项科研基金资助项目(20060183063);吉林省科学技术厅基金资助项目(20090540)

摘　　要：为提高层合板数值计算精度和效率,基于复合材料层合板理论,采用同尺度不同阶数区间B样条小波(BSWI)尺度函数的张量积插值,构造满足节点位移、挠度及其导数连续性和兼容性的BSWI层合板单元转换矩阵,并从虚功原理出发,推导了层合板单元BSWI单元刚度方程,计算并分析了层合板承受轴向拉伸时对角线OA上各点挠度与板心O距离变化关系及应力、应变沿板厚分布规律.数值结果表明:BSWI有限元法在复合材料层合板应力分析方面,可用较少单元和自由度数获得较高计算精度.In order to improve the accuracy and efficiency of numerical calculation of laminated composite plates, based on laminated composite plate theories, the element transformation matrixes of BSWI （ B-spline Wavelet on the Interval） for laminated composite plates are constructed. The tensor product of scaling functions of BSWI with the same scale but different orders is used as interpolation function; the matrixes have the characteristics of continuity and compatibility for node displacement, deflection and its derivatives. Based on the principle of virtual work, the BSWI element stiffness equation of laminated composite plates is derived. The relationship between deflections of nodes on diagonal OA and their distances to the center of the laminated composite plate is analyzed. The distributions of stress and strain of laminated composite plates under axial loads are also analyzed. Numerical experiments show that BSWI finite element method for stress analysis of laminated composite plates can achieve higher numerical accuracy with fewer elements and freedoms.

关 键 词：区间B样条小波 复合材料层合板 转换矩阵 刚度方程 

分 类 号：O242[理学—计算数学] TB115[理学—数学]