基于矩阵求逆理论的曲梁单元刚度矩阵解析解

Analytical Solution of Stiffness-Matrix for Curved Girder Elements Based on Theory of Matrix Inversion

基于矩阵求逆理论,提出矩阵求逆的综合法。弹性核法求解曲梁单元的刚度矩阵时,由于柔度矩阵的每个元素表达式繁琐,难以直接求逆得到曲梁单元的刚度矩阵。既有相关文献均指出采用数值方法求逆可得出曲梁单元的刚度矩阵。应用矩阵求逆的综合法,推导出曲梁单元刚度矩阵的解析解,并通过算例分析比较,证明了公式的正确性。由此,在编制曲梁杆系梁段有限元的计算程序时,解析解的应用不但简化了程序的编写,而且节约了计算机工作单元,提高了计算精度。

In this paper, collocation method of matrix inversion is proposed based on its theory. Because each element in flexibility matrix is very complex, it is difficult to solve inverse flexibility matrix directly for getting stiffness matrix of curved girder elements by the spring-center method. Numerical method is used to solve inverse flexibility matrix of curved girder elements in related documents usually. The analytical solution of the stiffness matrix is gotten through the method of matrix inversion by collocation method according to particularity of flexibility matrix. From this, the program of analyzing curved-beam is simplified greatly. At the same time, the working time and storage of computer is saved, and the accuracy of the result is guaranteed.