有限元的神经网络计算方法研究

根据有限元总刚矩阵经修正后具有正定性的特点以及弹性体位能函数的具体形式，提出一种新的神经网络有限元计算模型，即模型中神经网络的能量函数与有限元的优化目标函数相等，从而避免由于神经网络自身结构的原因而带来的计算误差。同时，避免采用基于模拟退火算法等随机神经网络优化计算方法时求解结果的随机性和设定初始退火温度To、内循环次数判据、最终停止判据等人为因素的影响。理论分析和计算机仿真表明，文中提出的方法可靠、有效。

RESEARCH ON NEUROCOMPUTING METHOD ON FINITE ELEMENT ANALYSIS

How to reduce the time in structural analysis and design has been always a remarkable problem for engineers and researchers. Because of the nonlinear and parallel processing ability, neural network has been widely used. Some fundamental problems about the applications of neural network in structural analysis have been studied through theoretical analysis and numerical simulation. A neural network modal is presented, based on the positive characteristic of the modified total stiffness matrix of finite element and the specific form of the elastic potential energy, where the energy function of neural network equals to the objective function of the finite element, which avoids the calculating error of the neural network. Meantime, some human influence, for instance, the randomness from the algorithm of the simulate anneal algorithm and the other random search algorithms, the stop criterion, are avoided. The method is proved to be reliable and effective by theoretical analysis and computer simulation. The neural network method can provide a new approach for structural analysis when considering the complex mechanical behaviors.