摘要
提出空间杆系几何构造分析的有限单元法,构造了两种单元(链杆单元和准梁单元)的几何约束矩阵,集成为整体矩阵并引入支承条件后,通过对其阶数与秩的比较分析确定体系的几何可变性及静定性.本法原理简单,便于计算机实施,结果完备:对于几何不变体系,可指出多余约束的数 目;对于几何可变体系,可给出体系的自由度数及相应的运动模态,并确定自由度的常变瞬变性质.
In this paper, the finite element method was applied to geometric stability analysis of three-dimensional skeletal structures. Two types of element geometric constraint matrices were derived. After assembling element matrices to form the corresponding global matrix and emposing the required displacement constraints, the geometric stability of a system can be analyzed by comparing the order and rank of the global geometric matrix. The method is found to be simple in concept, easy in implementation on a computer and complete in its computed results. For example, for geometrically stable systems, the number of redundant constraints is easily available, and for geometrically unstable system, the number of degrees of freedom (DOF) of the system and the corresponding displacement modes can also easily be calculated.
出处
《力学与实践》
CSCD
北大核心
2003年第1期23-26,共4页
Mechanics in Engineering
基金
清华大学基础研究基金(JC2000001)
清华大学土木系基础基金项目资助.
关键词
空间杆系
几何构造
单元分析
几何约束矩阵
有限元法
FEM, 3D skeletal structures, geometric stability, element analysis, geometric constraint matrix
