The finite-element method (FEM) is a computationally method for solving partial differential equations (PDEs) with specific boundary conditions over a domain. When we applying the FEM to a domain, it has to divide to a finite number of elements and nodes. The collections of the elements and nodes form the finite-element mesh, whose quality is an important part in achieving exact numeric result for all finite-element codes.

To achieve a high-quality mesh, we have to decide on:

• The suitable size and topology of the mesh,

• How it should be placed on the area,

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There are two ways to expound a SOM. Since, the whole weight vectors of a neighborhood nodes move in a same direction, SOM form a map that all close to each other and separating them is impossible. Therefore, we use U-Matrix method to visualize differences in this study.

STEPS SUMMARY:

1. In first step we was modeling and analyzing some square shaped structure with ABAQUS and used results to solve finite-element partial differential equation adaptive to structural analysis. r r t ve a fini l mesh g er ormul n ruc ral analys i to e n sic equ eri lly.

Follo la e s ur lem

̈

( + ) − + − ̈ =

2. In the 2nd step, we start improving our Kohonen algorithm by using Computer

Programming and Math softwares MATLAB and STUDIO-1. During this step, the network must be fed a large number of example vectors that represent the kinds of vectors expected during mapping.

3. In 3rd step, we was applying n-dimensional Toroidal to our algorithm. Toroidal groups play an important part in our research. That is n-dimensional Toroidal have a controlling role to that all elements fit exactly in the assumed

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Application of neural network technique to structural analysis by implementing an adaptive finite-element mesh generation, M.N Jadid, D.R Fairbairn.

Finite-element mesh generation using self-organization neural networks, L Manevitz, M Yousof, D Givoli

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Tony Phillips, Tony Phillips ' Take on Math in the Media, American Mathematical Society, October 2006

"Methods with high accuracy for finite element probability computing" by Peng Long,