弹性力学的实时神经计算原理与数值仿真  

REAL TIME NEUROCOMPUTING THEORY AND NUMERICAL SIMULATION ON ELASTIC MECHANICS 1)

作　　者：孙道恒[1,2] 胡俏[1,2] 徐灏 

机构地区：[1]西南交通大学应用力学与工程系 [2]东北大学机械工程学院

出　　处：《力学学报》1998年第3期348-353,共6页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金;辽宁省博士点基金

摘　　要：针对现代结构分析的特点，提出了基于神经网络结构的弹性力学分析原理；给出求解该问题的网络———改进的Ｈｏｐｆｉｅｌｄ和ＴＨ网络．提出用ＢＰ网络来实现单元刚度矩阵的实时计算．最后。ow to reduce the time in structural analysis and design has been alwaysa remarkable problem for engineers and researchers. Because of the nonlinear and parallel processing ability, Neural Networks (NN) has been widely used. In this paper, some fundamental problems about the applications of NN in structural analysis have been studied through theoretical analysis and numerical simulation. Based on the Hopfield NN, the concept of Energy Functional and the Minimal Potential Principle, the computation of elastic mechanics was transmitted into a quadratic programming. The corresponding architecture and the parameters of the NN(M TH, M Hopfield) were given, and the networks' dynamic stability was analyzed. Solving an elastic mechanical problem is equal to NN's dynamic stabilization, and the ultimate stable state of NN is the solution of related mechanical problem. A NN can be mapped to an dynamic circuit, in which the information is processed parallelly and the time spent has nothing to do with the complexity of a problem. It can been seen from the two examples given that the neurocomputed outputs are in agreement with the classical FEM, the relative errors are all below 1/1 000. It will take about 10 -12 s to analyze the structure by using neural FEM, and it has no relation with the structure's complexity. The input parameters ( R i, C i and β i ) of the M Hopfield and M TH net effect directly on computing speed and precision. In engineering,the parameters can be determined according to the need of engineering and the complexity of the net. When the M Hopfield or M TH net is used to solve a mechanical FE problem, the linking weights should be given.Actually, the linking weight matrix is the total stiffness matrix of the structure to be analyzed. The computation of element stiffness matrix may be considered as a mapping from the dimension and material properties of element to element stiffness coefficient. This mapping can be realized by using BP net. In the training process, the error tolerance can

关 键 词：神经网络 弹性力学 有限元 实时计算 数值仿真 

分 类 号：O343[理学—固体力学] TP18[理学—力学]