局部刚度修正的快速算法

A Fast Analysis Method of the Structures with Local Stiffness Changed

研究结构局部刚度改变时的结构重分析方法 .结构局部刚度改变问题在结构有限元计算时常会遇到 ,例如 :结构物个别构件的破坏或损伤 ,构件的局部屈服等等 .本文推导了一种新的算法 ,利用原结构刚度矩阵的 L DL T分解因子 ,通过代数运算获得新结构的解 .该算法的结果是精确且通用的 ,不仅可用于杆系结构也可用于连续体 ,而计算量与目前已有的各种与专用近似方法相同 .算例表明 ,新方法是有效的 .

This paper studied the reanalyzes method of the structure when stiffness changed in local area.The problem often arrived when finite element analyses for the structure with a few components damaged or some elements yield,etc.In this paper,a new solution algorithm is derived,which used the LDLT factors of the stiffness matrix of the old structure with some algebraically calculating.It need not reanalyze the whole new structure,but the result is exact.It takes the same calculation time as the methods that presented in other literature.In addition,the method preaented in this paper is general.It can be used to analyses any type of structure,example,bar's structure system or contimuum problem.The example in this paper shows that the new algorithm is effective in calculating the structure with local stiffness changed.