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分析复合材料层合板弯曲和振动的一种有效无网格方法

王伟 伊士超 姚林泉

王伟, 伊士超, 姚林泉. 分析复合材料层合板弯曲和振动的一种有效无网格方法[J]. 应用数学和力学, 2015, 36(12): 1274-1284. doi: 10.3879/j.issn.1000-0887.2015.12.006
引用本文: 王伟, 伊士超, 姚林泉. 分析复合材料层合板弯曲和振动的一种有效无网格方法[J]. 应用数学和力学, 2015, 36(12): 1274-1284. doi: 10.3879/j.issn.1000-0887.2015.12.006
WANG Wei, YI Shi-chao, YAO Lin-quan. An Effective Meshfree Method for Bending and Vibration Analyses of Laminated Composite Plates[J]. Applied Mathematics and Mechanics, 2015, 36(12): 1274-1284. doi: 10.3879/j.issn.1000-0887.2015.12.006
Citation: WANG Wei, YI Shi-chao, YAO Lin-quan. An Effective Meshfree Method for Bending and Vibration Analyses of Laminated Composite Plates[J]. Applied Mathematics and Mechanics, 2015, 36(12): 1274-1284. doi: 10.3879/j.issn.1000-0887.2015.12.006

分析复合材料层合板弯曲和振动的一种有效无网格方法

doi: 10.3879/j.issn.1000-0887.2015.12.006
基金项目: 国家自然科学基金(11172192;11572210)
详细信息
    作者简介:

    王伟(1981—),女,江苏大丰人,博士生,讲师(E-mail: wangw@suda.edu.cn);伊士超(1983—),男,江苏淮安人,博士(通讯作者. E-mail: shichaoyi@just.edu.cn).

  • 中图分类号: O343.8

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

Funds: The National Natural Science Foundation of China(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.
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出版历程
  • 收稿日期:  2015-09-23
  • 修回日期:  2015-10-23
  • 刊出日期:  2015-12-15

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