层合梁脱层分析的精细解法

张文志, 富明慧, 林敬华

张文志, 富明慧, 林敬华. 层合梁脱层分析的精细解法[J]. 工程力学, 2012, 29(7): 35-41. DOI: 10.6052/j.issn.1000-4750.2010.10.0764
引用本文: 张文志, 富明慧, 林敬华. 层合梁脱层分析的精细解法[J]. 工程力学, 2012, 29(7): 35-41. DOI: 10.6052/j.issn.1000-4750.2010.10.0764
ZHANG Wen-zhi, FU Ming-hui, LIN Jing-hua. A PRECISE METHOD FOR DELAMINATION ANALYSIS ON LAMINATED COMPOSITE BEAMS[J]. Engineering Mechanics, 2012, 29(7): 35-41. DOI: 10.6052/j.issn.1000-4750.2010.10.0764
Citation: ZHANG Wen-zhi, FU Ming-hui, LIN Jing-hua. A PRECISE METHOD FOR DELAMINATION ANALYSIS ON LAMINATED COMPOSITE BEAMS[J]. Engineering Mechanics, 2012, 29(7): 35-41. DOI: 10.6052/j.issn.1000-4750.2010.10.0764

层合梁脱层分析的精细解法

详细信息
    作者简介:

    张文志(1982―),男,安徽人,博士,从事复合材料力学研究(E-mail: manchicheung.sysu@gmail.com);
    林敬华(1984―),男,广东人,硕士,从事数值计算方法研究(E-mail: 10902482r@connect.pdyu.hk).

    通讯作者:

    富明慧(1966―),男,黑龙江人,教授,博士,博导,从事固体力学、数值方法研究(E-mail: stsfmh@mail.sysu.edu.cn).

  • 中图分类号: O241.81;O343.3;TB33

A PRECISE METHOD FOR DELAMINATION ANALYSIS ON LAMINATED COMPOSITE BEAMS

  • 摘要: 提出了层合梁脱层分析的一种半解析模型及相应的精细积分法。首先沿层合梁面内离散,由修正Hellinger-Reissner 变分原理导出各层的半解析方程。然后将各层等分为若干子层,利用相邻子层间状态量的精细积分关系式,将半解析方程转化为一组几乎无离散误差的代数方程。最后,利用各层代数方程系数矩阵的块三对角形式,建立了一种高效的递推消元方法。该文方法不仅具有极高的精度和效率,同时还能处理多种边界条件(包括脱层条件),以及能很好地克服病态的影响。数值算例充分证明了该文方法的有效性。
    Abstract: A semi-analytical model and the corresponding precise method for laminated composite beams are presented. Firstly, dividing the in-plane area evenly and then gives the semi-analytical equations for every layer by using the modified Hellinger-Reissner variational principle. Then divides each layer evenly into several sub-layers, and transforms the semi-analytical equations to a set of algebraic equations which have almost no discrete errors with the precise integration relationship between the adjacent sub-layers. Finally, establishes an efficient reduction method by using the block tridiagonal matrices form of every algebraic equation of layers. The present method not only has high accuracy and efficiency, but also can deal with various boundary conditions including delamination conditions. Furthermore the method overcomes the influence of ill-conditioned matrices. Numerical examples show the validity of the present method efficiently.
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出版历程
  • 收稿日期:  2010-10-18
  • 修回日期:  2010-11-30
  • 刊出日期:  2012-07-24

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