摘要
作者在之前的研究中利用刚度的二叉树填充元优化算法的结果,在指出结构局部修改在刚度矩阵三角分解因子中的影响沿二叉树回溯至根的基础上,提出了一种全新的结构修改算法。这一算法与现在标准的有限元稀疏矩阵求解器兼容,在不改变求解精度的前提下,可以广泛地用于结构修改的各个领域。与传统的ShermanMorrison-Woodbury(SMW)公式(秩m修正)或其他的直接重分析方法相比,新的方法可以方便与高效地在结构的任何位置修改大量的单元。但是当结构的修改量较少时,这种方法的计算效率可能不及SMW公式。该文在已有研究成果的基础上进一步研究修改后刚度矩阵三角分解的更新步骤,发现更改一些矩阵元素的消元方式可以有效的减少计算量,提高结构重分析的效率。数值算例表明,与之前的重分析算法相比,至多可节约30%的计算量。
Based on the features of binary tree and fill-in＇s reducing, the authors proposed a new algorithm for structural modifications, which indicated that in LDLT factorization, the effect of modification will propagate up to the root along the binary tree. This algorithm is compatible with the standard sparse solver in finite element method, and can be applied to various fields for structural modifications. Compared with traditional Sherman- Morrison-Woodbury formulas or other reanalysis methods, the new algorithm is more efficient if the modications are high-rank. However, if the modications are low-rank, this method might be less efficient. Based on the previous study, the existing procedure of updating triangular factors is improved further in this paper. The alternative formula of recalculating the factors can reduce the amount of calculation significantly and improve the efficiency of reanalysis. Numerical tests show that the improved algorithm can save up to 30% of computation efforts compared with the existing one.
出处
《工程力学》
EI
CSCD
北大核心
2016年第7期1-6,共6页
Engineering Mechanics
基金
国家自然科学基金项目(11472014)
北京市博士后工作经费资助项目(2015ZZ-131)
关键词
有限元法
结构修改算法
结构重分析
结构工程
工程设计软件
finite element method
structure modification algorithm
structural reanalysis
structure engineering
engineering design software
