| 四边简支各向同性矩形厚板的插值矩阵法解 |
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| 引用本文： | 杨智勇,牛忠荣,伍章健,周焕林.四边简支各向同性矩形厚板的插值矩阵法解[J].固体力学学报,2011(Z1). |
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| 作者姓名： | 杨智勇 牛忠荣 伍章健 周焕林 |
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| 作者单位： | 合肥工业大学工程力学系;英国曼切斯特大学机械、航空与土木工程学院; |
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| 基金项目： | 国家自然科学基金(11072073); 安徽省自然科学基金(090414153)资助 |
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| 摘 要： | 针对强厚度矩形板四边简支情况,论文根据状态变量法思想,基于三维弹性理论基本方程,以3个位移分量及3个应力分量按双三角级数展开,将三维弹性力学控制方程转化为常微分方程边值问题.尽管一些各向异性弹性矩形厚板早已由状态空间法获得分析解,可是各向同性厚板的分析解至今难以获得,因为状态空间解法中特征方程有重根问题而不易于收敛.论文提出采用插值矩阵法直接对常微分方程进行求解,获得各向同性矩形厚板在四边简支边界条件下三维理论的位移和应力解,并与有限元精细结果进行比较,证明了本文解的准确性.
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| 关 键 词： | 厚矩形板 四边简支 各向同性 三维弹性理论 插值矩阵法 |
SOLUTIONS OF 3-D ELASTIC THEORY OF SIMPLY SUPPORTED ISOTROPIC RECTANGULAR THICK PLATES BY INTERPOLATING MATRIX METHOD |
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| Zhiyong Yang Zhongrong Niu Zhangjian Wu Huanlin Zhou.SOLUTIONS OF 3-D ELASTIC THEORY OF SIMPLY SUPPORTED ISOTROPIC RECTANGULAR THICK PLATES BY INTERPOLATING MATRIX METHOD[J].Acta Mechnica Solida Sinica,2011(Z1). |
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| Authors: | Zhiyong Yang Zhongrong Niu Zhangjian Wu Huanlin Zhou |
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| Institution: | Zhiyong Yang1 Zhongrong Niu1 Zhangjian Wu2 Huanlin Zhou1(1School of Civil Engineering,Hefei University of Technology,Hefei 230009,China)(2School of Mechanical,Aerospace and Civil Engineering,University of Manchester M13 9PL,UK) |
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| Abstract: | The analytical solutions to some anisotropic elastic rectangular thick plates have already been obtained by state space method.The analytical solutions of 3-D isotropic thick plates,however,are not yet available so far.The problem is mainly associated with the characteristic equation of state space analysis for the isotropic rectangular plate.There exist the repeated eigenvalues,which leads to the difficulty to find a closed-form solution.In this paper,the solutions of the isotropic rectangular thick plates... |
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| Keywords: | thick rectangular plate simply supported on four sides isotropy 3-D elasticity interpolating matrix method |
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