摘要
首先详细论述了一种通过增加棱内"虚节点"和面内"虚节点"方式得到的四边形升阶谱单元及相应的阶谱函数。然后,结合矩阵的一维稀疏存储技术(CSR格式),设计了一种分层四边形高阶亚参元方法,并编制了相应的FORTRAN语言程序进行了实现。该方法具有很好的承袭性,即在生成高阶单元特性矩阵时始终能够承袭低阶单元的特性矩阵,这样可减少计算量,大大提高了编程和计算效率。最后,通过将所设计的方法应用于重力坝/腹拱坝问题的求解,验证了本文方法具有与相应常规有限元方法一样高的计算精度,且当使用分层Q8元和分层Q12元时,随着网格的加密,坝踵及坝趾区产生应力集中的区域明显缩小,坝踵-坝趾线段上的第一主应力和y方向应力也基本重合,能很好地解决坝踵及坝趾区的应力集中,可为数值求解重力坝实际问题提供一种高效分析方法。
A type of hierarchical quadrilateral element and the corresponding hierarchical functions are introduced in detail by properly increasing the"virtual nodes"in the edge and in the face for the finite element analysis of the gravity dam problems.The resulting high-order subparametric element method based on hierarchical quadrilateral elements is then proposed by combing the CSR technology of the stiffness matrix and it is realized by compiling FORTRAN program.This method has a good inheritance,that is,it can always inherit the characteristic matrix of the low-order element while the higher-order element characteristic matrix is generated.And thus,it reduces the amount of calculation and greatly improves the efficiency of programming and calculation.By applying the resulting method to the solution of gravity dam/arch-abdomen dam,it is verified that the method has the same accuracy as the corresponding conventional finite element method.The area of stress concentration near the dam heel and the dam toe obviously decreases with the number of elements increasing when hierarchical Q8 and Q12 elements are used,respectively,and the resulting first principal stress and the stress in the y direction on the line between the dam heel and dam toe are basically identical.This provides an efficient analysis method for the numerical solution of the actual gravity dam problems.
作者
谢凌洁
肖映雄
徐亚飞
Xie Lingjie;Xiao Yingxiong;Xu Yafei(Civil Engineering and Mechanics College,Xiangtan University,411105,Xiangtan,China)
出处
《应用力学学报》
CAS
CSCD
北大核心
2021年第3期902-908,共7页
Chinese Journal of Applied Mechanics
基金
国家自然科学基金项目(10972191)
湖南省教育厅资助科研项目(19A502)。
关键词
重力坝/腹拱坝
非结构四边形网格
阶谱单元
亚参数有限元
一维稀疏存储
gravity dam/arch-abdomen dam
unstructured quadrilateral mesh
hierarchical element
subparametric finite element
sparse storage by one-dimensional array
