Optimization of Material Composition of Functionally Graded Beam due to Partial Heating for Thermal Stress Relaxation : A Neural Network Approach

Abstract

In this study, a neural network is applied to optimization problems of material compositions for a functionally graded beam with arbitrarily distributed and continuously varied material properties due to a partial heat supply. Using the analytical procedure of a laminated composite beam model, the analytical two-dimensional transient temperature solution for the beam is derived approximately. Furthermore, the thermal stress component is formulated under the mechanical condition as being traction-free and making use of the elementary beam theory. As a numerical example, the finitely beam composed of zirconium oxide and titanium alloy is considered. And, as the optimization problem of minimizing the thermal stress distribution, the numerical calculations are carried out making use of neural network, and the optimum material composition is determined at arbitrary heat area and heat transfer coefficient. Furthermore, the results obtained by neural network and ordinary nonlinear programming method are compared.