Computational approach for optimum compressive strengths of glass fibre reinforced polyester composites

Abstract

This Paper presents finite difference method and method of separation of variables as computational approaches for optimization of compressive failure response of Glass fibre reinforced polyester (GRP). A two dimensional multiple linear regression model obtained by subjecting replicated samples of GRP composites to compressive failure was found to be a two dimensional Laplace function , through transformation to partial differential equation(PDE). By passing the Finite difference model of the function through nine interior grid or mesh points of a composite region a system of nine by nine linear equations was developed and solved by Leibman method (Gauss-Seidel iteration). The Leibman method algorithms result was optimized by Visual Basic (VB) language Programme. The separation of variables method was employed to obtain three product solution models that solve the approximate 2-D PDE (Laplace) function. While both the finite difference method and method 0f separation of variables gave the ultimate compressive strength as 154 MPa, the method of separation of variables gave the minimum strength as 100MPa.Both the finite difference method and method of separation of variables showed that the compressive failure response of GRP composites could be represented by either elliptical model or exponential model.