| Many problems of engineering mechanics that have large computation scale haven't been solved due to the bottleneck between the computation and memory of the Von Neumann computer. And there still haven't breakthrough in some new or pendent problems because of such reason as computation, etc. Therefore, new theory and method of computational mechanics need to be developed to solve above problems.With the increasingly perfecting of numerical calculation theory of definite structure, people are not satisfied with the analysis of definite structure, and begin to take the uncertain factors of structure into account when analyzing the structure. Uncertainty of structure can be classed into two different categories. One is stochastic uncertainty. The other is fuzzy uncertainty. Finite element method is adopted to analyze the uncertain structure the same as to analyze the definite structure. Up to now, the research of stochastic finite element is mature basically. However, the application of finite element in analysis and computation of uncertain structure is to be limited because there hasn't a satisfying solving method to fuzzy equations and interval equations. So, studying on real-time computation of structural analysis and on the solving method of fuzzy finite element not only has important theory significance, but also has important application value in engineering.Point to above problems, under the financial support of the National Natural Science Foundation (exploration of high tech and new concept and new conceive), the Excellent Young Teachers Program of Ministry of Education and National Excellent Doctoral Dissertation Special Foundation, the static and dynamic real-time computation of elasticity-plastic mechanics, solving method of fuzzy finite element and other problems were studied in this paper. And some achievement was gained as following:(1) Based on the positive definiteness of system stiffness matrix of finite element that was modified and the form of potential energy function of elastic body, the linear system of saturation mode (LSSM) was introduced into the neural computation of finite element, by which the no-error solving of finite element neural net computation was realized in theory. The circuit realization of neural computation of finite element was presented.(2) Eigenvalue is very important to dynamic analysis and computation of structure. Based on the theory of Reyleigh minimum, the minimum of energy function of neural network was mapped to the eigenvector that was mapped to the minimal eigenvalue of the generalized eigenvalue problem, by which the precise solution of minimal eigenvalue was gained while the neural network moving to the minimum of energy function. Based on the variational characteristic of eigenvalue, the neural network solving method of other eigenvalues based on penalty function method was presented. Thus, the neural network solving method of all eigenvalues was presented in theory.(3) In practical engineering, plastic deformation occurs frequently. Compared with elastic structural analysis, more time is used to analyze the plastic deformation structure. So, the real-time computation of plastic structure is more important than that of elastic structure.Point to the limitation of existing method, the neural computation method of finite element of elasticity-plastic mechanics was studied on the base of variational principle of the second order minimal potential energy in plastic theory. The neural network solving method of elasticity-plastic mechanics based on variational principle of the second order minimal potential energy was presented, and the neural network computation model of finite element of plastic mechanics was given.(4) Due to the imperfectness of solving the fuzzy equations, complexity in computation of fuzzy finite element equations and imbalance in the two sides of fuzzy finite element equations while the solution was lead back to the original equations, the fuzzy finite element method based on fuzzy coefficient programming was...
|
PDF Full Text Request