基于零空间基的非线性结构分析方法

Nonlinear structural analysis algorithm based on the null space basis

根据零空间基和 M- P广义逆理论 ,推导了结构非线性增量平衡方程极值点与非临界点解的统一形式 ,并直接表示为增广矩阵零空间基的形式。研究了基于 M- P逆、奇异值分解和伪上三角分解确定零空间基的三种数值方法 ,以及据此求增量平衡方程增量解的方法。利用 Matlab语言 ,在Matlab集成环境下实现了非线性结构分析算法 ,并研究了算法的效率与稳定性。最后 ,给出了两个详细的数值分析算例 ,结果表明该方法正确有效 。

Based on the basis of null space and M-P inverse theorem, a unified incremental solution formulae, expressed as the null space basis of the augmented matrix, were firstly formulated herein for the incremental equilibrium equation at the limit point and non-critical points. Three numerical analysis techniques, based on the M-P inverse, singular value decomposition (SVD) and pseudo up-triangular decomposition (PUTD), respectively, were developed to compute the null space basis for the augmented equilibrium matrix. Numerical implementations were presented. A specialized nonlinear analysis program were developed with Legend P II 300 in Matlab integrated development environment (IDE) using Matlab language. Finally, two classical numerical examples were used to verify the accuracy of the method aforementioned. Efficiency and accuracy, i.e. computation time and buckling load differences, have been compared in detail for various numerical approaches. The algorithm and program were proved to be efficient. This method can be used for medium scale engineering project.