Investigation of non-linear boundary value problems belonging to a system of partial equations with employing finite element method

ABSTRACT In this work, we study two-dimensional geometric non-linear boundary value problems and we use finite emenet method to solve the problem. The constitutive relations of the trip material are taken within the framework of the continuum theory by Akbarov and Guz. The problem we discuss here is non-linear partial derivative differential equation system with variable coefficient. Because analytic solutions of the problem is impossible; we solve the problem using numerical analysis -Finite Element- method. Mathematical formulation of the problem is given. Variational formulation of the problem is formed and maden using finite element model. Newton-Raphson method is used non-linear algebraic equations system which forms as result of finite elements. We are tried to determine convergence boundaries of parameters which determined problem by Newton-Raphson method. Numerical results obtained with Newton-Raphson method are being divergent for great values determined this boundary. Numerical results of stress dispersal are given as graphics. Furthermore, this results of comments are maden. Keywords: Non-linear boundary value problem, Finite Element method, Newton-Raphson method, convergence. vn