ANN Based Solution of Static Structural Problem with Fuzzy Parameters

Abstract

Usual finite element method for static analysis of structures with crisp parameters converts the problem into an algebraic system of linear equations. In actual sense, the structural parameters do involve uncertainties due to various causes and then the governing equations become uncertain which may not be handled by usual methods. It may be noted that the uncertainty here has been taken as fuzzy. As such, one will get then fuzzy system of linear equations in case of static problems. There exist various methods to solve the crisp system of equations such as Gauss elimination, Gauss Jacobi, Gauss–Seidel, and SOR method. But we have very few methods to solve these when uncertainty in term of fuzzy is involved in particular to the tilted problems. In view of the above, this chapter incorporates a new method, viz. the concept of artificial neural network (ANN) in solving the fuzzy linear system of equations corresponding to the static problem of structure. Detail procedure is presented followed by simulation for different example problems of civil structures. Algorithm is also illustrated by solving few numerical examples, and the obtained results are compared in special cases.