| 潘树来,王全凤.一种求解有限元问题结点平衡方程的快速方法[J].计算力学学报,2009,26(4):518~522 |
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| 一种求解有限元问题结点平衡方程的快速方法 |
| A speedy solution of the nodal equilibrium equations in the finite-element problems |
| 投稿时间：2007-07-06 |
| DOI：10.7511/jslx20094012 |
| 中文关键词: 系数矩阵 单元最大结点差 结点平衡方程 半等带宽 |
| 英文关键词:coefficients matrix maximum difference of the node number in a element nodal equilibrium equations symmetric half band-width |
| 基金项目:国家自然科学基金(50578066)资助项目. |
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| 中文摘要: |
| 目前随着工程实际问题复杂程度的增加及分析的要求,特别是材料非线性分析的引入,尽管计算机的运算速度、内存、外存容量等不断提高,但并不能完全满足大规模计算的需要,更快、更节省存贮空间的算法一直是有限元法分析过程中的一项核心技术要求。本文针对一些结点及单元均规律化地排列的有限元问题,提出可以透过其相邻结点的关系记录结点平衡方程中系数矩阵的非零元素,无需再像等带宽存贮那样去记录带宽内大量的零元素。此方法可以大大地减少系数矩阵元素的存贮量,从而可以提高计算机读取数据的速度及改善利用迭代法求解的效率。 |
| 英文摘要: |
| With the constant development of finite element method, it is widely used in almost every field of engineering, and has become a powerful technique in solving complex civil engineering. With the increment of complexness and scale in finite element method, the number of unknowns is as large as 104~106, it brings the difficulties in solving stiffness equation by the traditional half-bandwidth storage scheme, one-dimensional various-bandwidth method, or frontal method. The main difficulties exist in the matrix storage and solving CPU time. Although the calculation speed, the volume of EMS memory and external storage of computer increase constantly, the improvement of computer performance doesn’t always keep pace with the increasing requirement of large-scale calculation for more and more complex problem in practical engineering, especially for the nonlinear problem. The algorithm with high efficiency and using less EMS memory is a key technique in finite element method analysis and also an objective of computational mechanics. In this paper an approach is put forward for the finite element problem with regular discretization of elements, in which only the nonzero elements in the global stiffness matrix through the adjacent nodal relations are recorded, unlike in the half-bandwidth storage scheme, a lot of zero elements in the bandwidth of the stiffness matrix are also recorded, so that the large quantity work of storing the coefficients of the matrix can substantially be reduced and the speed of reading computer data information can be increased, giving better improvement on the efficiency of solution by the iteration method. |
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