梁杆结构稳定性分析中的传递矩阵模型缩减法

A model reduction technique of transfer matrix in the stability analysis of beam structures

摘要:

为了准确地分析梁杆结构的稳定性问题并降低系统刚度阵的阶数,提出了基于传递矩阵法和精确有限元的模型缩减法.将具有弹性支撑的非共线链式分支子结构当作一个超单元,结合梁单元精确刚度阵,使用传递矩阵法联系两端载荷和位移关系,得到该超单元在整体坐标系下的刚度阵,且该刚度阵为与普通梁单元同阶的对称方阵,可直接组装到系统刚度阵中.求解该缩减后系统刚度阵的行列式可得到结构的欧拉临界力.由于子结构的内部自由度不出现在系统刚度阵中,在保证计算精度的同时极大降低了系统刚度阵的阶数.典型算例的稳定性分析验证了方法的正确性和有效性.

Abstract:

To analyze the stability of beam structures accurately and reduce the order of the system stiffness matrix,a model reduction technique based on transfer matrix method and exact finite element method is presented.The noncollinear branch chain substructure with elastic supports is modeled as a super element.In combination of exact stiffness matrix of beams,the force-displacement relation between both ends is developed by the transfer matrix method.The symmetrical stiffness matrix of the super element in the global coordinate system is derived,which has the same order as the classic beam element and can be assembled into the system stiffness matrix directly.The Euler critical force of the structure can be obtained from the determination of the reduced system stiffness matrix.The internal DOFs of the substructure are not used in the model,so the order of the model is greatly reduced and the accuracy of the computation is guaranteed.The validity and efficiency of the proposed method are shown by solving various numerical examples found in the literature.