| 马旭,杨炫峥,李坦.具有Drilling自由度的八节点四边形混合壳单元[J].计算力学学报,2025,42(3):462~470 |
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| 具有Drilling自由度的八节点四边形混合壳单元 |
| Eight-node quadrilateral hybrid shell element with Drilling degrees of freedom |
| 投稿时间：2023-12-20 修订日期：2024-01-31 |
| DOI：10.7511/jslx20231220001 |
| 中文关键词: 非对称有限元法 杂交应力元 Airy应力函数 平板壳单元 |
| 英文关键词:unsymmetric finite element method hybrid stress element airy stress function flat shell element |
| 基金项目:国家自然科学基金(11702242);河北省自然科学基金(A2019203403)资助项目. |
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| 中文摘要: |
| 构造了一个八节点四边形混合壳单元QFUQA8,其中精化非协调膜部分具有Drilling自由度,采用两种位移场改进了组合质量矩阵,通过选取不同的精化元参数,来提高单元的计算精度,根据Airy应力函数的解析解得到的单元应力场构造插值函数,将Drilling旋转添加到八节点等参元的位移场确定测试函数;板部分以任意阶的Timoshenko梁函数构造单元的边界位移插值,Airy应力函数作为假定应力函数,通过向平均面投影的方式修正了存在翘曲结构的单元。数值算例表明,构造的平板壳单元能通过非零常剪力分片检验,并且在壳体结构分析中具有良好的精度和收敛性。 |
| 英文摘要: |
| In this paper,an eight-node quadrilateral hybrid shell element QFUQA8 is constructed,in which the refined uncoordinated membrane part has drilling degrees of freedom.The combined mass matrix is improved by using two kinds of displacement fields,and the computational accuracy of the element is improved by selecting different parameters of the refined elements.The interpolation function is constructed based on the stress field of the element obtained from the analytical solution of the Airy stress function,and the drilling rotation is added to the displacement field of the eight-node isotropic element to determine the test function;the boundary displacement interpolation of the element is constructed in the plate part with the Timoshenko beam function of arbitrary order,and the Airy stress function is used as the assumed stress function,which is corrected for the presence of a warped structure of the element by means of the projection to the mean surface.Numerical examples show that the constructed flat plate-shell elements pass the non-zero constant shear patch test and have good accuracy and convergence in structural analysis of shells. |
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