Computing Method and Circuit Realization of Neural Network on Finite Element Analysis

Abstract:

The finite element analysis in theory of elasticity is corresponded to the quadratic programming with equality constraint, which can be further transformed into the unconstrained optimization. In the paper, the question is solved by modified Hopfield neural network based on the energy function of the neural network equals to the objective function of the finite element method and the minimum point, which is the stable equilibrium point of the network system, is the solution. In addition the authors present the computer simulation and analogue circuit experiment to verify this method. The results are revealed that: 1) The results of improved Hopfield neural network are reliable and accuracy; 2) The improved Hopfield neural network model has an advantage on circuit realization and the computing time, which is unrelated with complexity of the structure, is constant. It is practical significance for the research and calculation.

• Periodical: Applied Mechanics and Materials (Volumes 195-196)
• Pages: 758-763
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.195-196.758
• Online since: August 2012
• Authors: Li Kun Cui, Wei Wang, Zhuo Li
• Keywords: Analogue Circuit, Finite Element Method (FEM), Hopfield Neural Network, Simulation

References

[1] N. G. Xie, T. T. Yu, W. D. Shao, Network parallel algorithm in optimization computation of engineering structure, Journal of East China University of Metallargy, vol. 18, no. 2, pp.117-120, 2001 (in Chinese).

[2] W. L. Zhang. Studying status and development of computing mechanics, Journal of Anhui institute of architecture, vol. 9, no. 2, pp.7-12, 2001 (in Chinese).

[3] X. Chen, D. H. Sun, H. Z . Huang, Finite element system for structural analysis and neural network, Hoisting and conveying machinery, no. 6, pp.6-8, 1999 (in Chinese).

[4] X. C. Wang , Finite element method, Beijing: Tsinghua University Press, 2003 (in Chinese).

[5] D. H. Sun, Q. Hu, H. Xu , Real-time Neurocomputing Model Used in Elastic Mechanics, China mechanical engineering, vol. 8, no. 2, pp.35-38, 1997 (in Chinese).

[6] H. B. Li, Neurocomputing based structural finite element analysis, Dalian: Dalian university of technology, 2003 (in Chinese).

[7] L. K. Cui, W. Wang, Z. Li, Application of Hopfield neural network in finite element solving, Computer Engineering and Applications, vol. 46, no. 16, pp.46-47+49, 2010 (in Chinese).

[8] H. Z. Huang , H. B. Li, Research on neurocomputing method on finite element analysis, Journal of Mechanical Strength, vol. 25, no. 3, pp.298-301, 2003 (in Chinese).

[9] E. Z. Liang, E. W. Liang, Circuit design and simulation application base on Protel 99 SE , Beijing: Tsinghua University Press, 2000 (in Chinese).