有限元结构动力分析的广义特征值的神经计算

Finite element approach for structural dynamic analysis using generalized eigenvalue-based neurocomputing

广义特征值问题是结构动力分析计算的关键之一.应用Reyle igh极小值原理,将神经网络的能量函数的极小点对应于广义特征值问题的最小特征值所对应的特征向量,在神经网络朝着能量函数极小点运动的同时得到了最小特征值所对应的特征向量的精确解答.从特征值的变分特性出发,给出了基于罚函数法的其他特征值的神经网络求解方案,从而在理论上给出了广义特征值问题的所有特征值的神经网络求解方法.仿真计算表明,该方法正确、有效可行.

The generalized eigenvalue problem is a crucial problem for structural dynamic calculations. Based on Reyleigh＇s theorem of minimum, the global minimum of the energy function for neural network is mapped to the eigenvector corresponding to the minimal eigenvalue of the generalized eigenvalue problem. A precise solution for the minimal eigenvector corresponding to the minimal eigenvalue is obtained while the neural network is moving to the minimum of energy function. According to the variational characteristic of eignvalue, a neural network method using penalty function for solving other eigenvalues is also presented. Thus, neural network solving methods of all eigenvalues are derived in theory. Theoretical analysis and numerical simulation results indicate that this method is accurate and effective.