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基于高阶剪切变形理论的四边形求积元板单元及其应用

申志强 夏军 宋殿义 程盼

申志强, 夏军, 宋殿义, 程盼. 基于高阶剪切变形理论的四边形求积元板单元及其应用[J]. 力学学报, 2018, 50(5): 1093-1103. doi: 10.6052/0459-1879-18-225
引用本文: 申志强, 夏军, 宋殿义, 程盼. 基于高阶剪切变形理论的四边形求积元板单元及其应用[J]. 力学学报, 2018, 50(5): 1093-1103. doi: 10.6052/0459-1879-18-225
Shen Zhiqiang, Xia Jun, Song Dianyi, Cheng Pan. A QUADRILATERAL QUADRATURE PLATE ELEMENT BASED ON REDDY'S HIGHER-ORDER SHEAR DEFORMATION THEORY AND ITS APPLICATION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(5): 1093-1103. doi: 10.6052/0459-1879-18-225
Citation: Shen Zhiqiang, Xia Jun, Song Dianyi, Cheng Pan. A QUADRILATERAL QUADRATURE PLATE ELEMENT BASED ON REDDY'S HIGHER-ORDER SHEAR DEFORMATION THEORY AND ITS APPLICATION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(5): 1093-1103. doi: 10.6052/0459-1879-18-225

基于高阶剪切变形理论的四边形求积元板单元及其应用

doi: 10.6052/0459-1879-18-225
基金项目: 1)国家自然科学基金(51508562,51809271)和 学校科研计划(ZK2017-03-40)资助项目.
详细信息
    作者简介:

    2)宋殿义,副教授,主要研究方向:新型结构抗冲击与抗爆研究. E-mail:changshasong@nudt.edu.cn

    通讯作者:

    宋殿义

  • 中图分类号: O343.1;

A QUADRILATERAL QUADRATURE PLATE ELEMENT BASED ON REDDY'S HIGHER-ORDER SHEAR DEFORMATION THEORY AND ITS APPLICATION

  • 摘要: 近年来由各类新型复合材料或功能梯度材料构成的板结构在工程领域得到了广泛应用,其显著特点是材料性能沿板厚变化.为合理考虑横向剪切应变,许多学者基于Reddy高阶剪切变形理论,构建了不同的有限元单元对该类板结构进行分析,但其中满足$C^{1}$连续条件的单元相对较少.本文基于Reddy高阶剪切变形理论,采用求积元方法,建立了$C^{1}$连续的四边形板单元.利用该单元对均质材料、复合材料、功能梯度材料构成的等厚度矩形板、变厚度矩形板及等厚度斜板的线弹性弯曲和自由振动问题进行了计算分析,并与现有文献中的相应计算结果进行了对比.研究表明:基于高阶剪切变形理论的四边形求积元板单元具有较高的计算效率和良好的适应性,文中各类材料构成的等变厚度矩形板及等厚度斜板均只需1个单元即可得到理想的计算结果.对于等/变厚度矩形板,可仅使用9$\times$9个积分点,而对于等厚度斜板,随着斜角的增大,所需积分点的数目逐渐增多至15$\times $15.该四边形求积元板单元可进一步用于新型复合材料板的非线性分析.

     

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出版历程
  • 收稿日期:  2018-07-10
  • 刊出日期:  2018-09-18

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