连拱的矩阵分析

• 作 者: 杨高中
• 出 处: 重庆交通学院学报
• 发表日期: 1983年03期
• 关键词: 矩阵分析 连拱 逆阵 迭代法求解 未知变量 迭代矩阵 位移矩阵 对称矩阵 计算工作量 内力影响

对n+1孔连拱如采用刚度矩阵法分析时,当每一节点的未知变量为3时则要计算一个3n×3n阶的逆阵,当每一节点的未知变量为2时,则要计算一个2n×2n阶的逆阵。本文将3n×3n或2n×2n阶逆阵运算化为3×3或2×2阶的矩阵运算,各有关矩阵均采用重复迭代法求解,因而不仅计算工作量少,且计算方便表达简单,不仅适于电算求解也适于手算。此外这个方法不仅可用于连拱也适用于其他用形变法求解的条形结构。

For the n + 1 hole arches, such as the use of stiffness matrix analysis, when each node of the unknown variable is 3, then to calculate a 3n × 3n order inverse matrix, when each node of the unknown variable is 2, then Calculate a 2n × 2n order inverse matrix. In this paper, the matrix operations of 3n × 3n or 2n × 2n orders are transformed into matrix operations of 3 × 3 or 2 × 2 orders. All the relevant matrices are solved by iterative iterative method, which not only reduces the workload but also has the advantages of easy computation, simple expression, Not only suitable for calculating the solution is also suitable for hand calculations. In addition, this method can be used not only for arches but also for other bar structures that are solved by the deformation method.