复合材料层合板应力分析的小波有限元法

华南理工大学学报(自然科学版) ›› 2012, Vol. 40 ›› Issue (7): 117-122.

复合材料层合板应力分析的小波有限元法

彭惠芬^1,2 孟广伟¹ 范森³周立明¹

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

收稿日期:2011-06-09 修回日期:2012-03-07 出版日期:2012-07-25 发布日期:2012-06-01
通信作者: 彭惠芬(1969-) ，女，副教授，主要从事疲劳、断裂数值计算研究． E-mail:phfdaqing@163.com
作者简介:彭惠芬(1969-) ，女，副教授，主要从事疲劳、断裂数值计算研究．
基金资助:
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)

Stress Analysis of Laminated Composite Plates with Wavelet Finite Element Method

Peng Hui-fen^1,2Meng Guang-wei¹ Fan Sen³ Zhou Li-ming¹

1. College of Mechanical Science and Engineering,Jilin University,Changchun 130022,Jilin,China; 2. College of Mechanical Science and Engineering,Northeast Petroleum University,Daqing 163318,Heilongjiang,China; 3. College of Petroleum Engineering,Northeast Petroleum University,Daqing 163318,Heilongjiang,China

Received:2011-06-09 Revised:2012-03-07 Online:2012-07-25 Published:2012-06-01
Contact: 彭惠芬(1969-) ，女，副教授，主要从事疲劳、断裂数值计算研究． E-mail:phfdaqing@163.com
About author:彭惠芬(1969-) ，女，副教授，主要从事疲劳、断裂数值计算研究．
Supported by:
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/Abstract

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．

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

Abstract:

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.

Key words: BSWI, laminated composite plates, transformation matrix, stiffness equation

中图分类号:

O242
TB115

彭惠芬孟广伟范森周立明. 复合材料层合板应力分析的小波有限元法[J]. 华南理工大学学报(自然科学版), 2012, 40(7): 117-122.

Peng Hui-fen Meng Guang-wei Fan Sen Zhou Li-ming. Stress Analysis of Laminated Composite Plates with Wavelet Finite Element Method[J]. Journal of South China University of Technology(Natural Science Edition), 2012, 40(7): 117-122.

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