摘要
为了提高经典的2节点平面Bernoulli-Euler梁单元在梁杆结构稳定性分析中的计算精度,建立了一种递推凝聚梁单元.将1个杆件当作1个逐级派生的子结构,自顶向下逐级派生,使用静力凝聚方法,消除内部自由度,建立了几何非线性刚度矩阵的递推格式,自底向上逐级递推凝聚.通过递推凝聚得到了一种高精度梁单元,它与经典的2节点梁单元具有相同的自由度数量及分布.推荐进行2次递推,将得到和1个杆件划分为4个经典的2节点梁单元相同的计算精度.对梁杆结构稳定性分析中的几个典型算例进行了分析,1个杆件使用1个单元就可以得到相当准确的临界力.从理论上来说,随着递推次数的增加,其计算精度可以无限逼近精确解.
To enhance the calculation accuracy for frame stability analysis, a recursive condensation beam element is proposed instead of the classical Bernoulli-Euler beam element in a two-node plane. Accordingly, the rod is progressively decomposed into sub-structures. By applying a top-down hierarchical bipartite method, the interior degrees of freedom （IT）OF） are eliminated through static condensation. Afterwards, a geometricallynonlinear rigidity matrix is established in a recursive form. A high-accuracy beam element, which possesses the same DOF and distribution as classical two-node structure, is then obtained. Based on this notion, the twice recursion, which is equivalent to the quadripartite rod calculation accuracy of a classical two-node beam element, is recommended in this study. As a subsequence, the critical forces, which are calculated based on one element per rod, can be accurately obtained via frame stability analysis on some typical examples. Consequently, it is implied that the calculation values can be theoretically converged towards the accurate solutions with the increase of recursion times.
出处
《中国工程机械学报》
2008年第1期1-5,共5页
Chinese Journal of Construction Machinery
基金
国家科技支撑计划资助项目(2006BAJ12B03-2)
关键词
递推凝聚梁单元
静力凝聚
几何非线性
稳定性分析
recursive condensation beam element
static condensation
geometrical nonlinearity
stability analysis
