Evaluation of elastic moduli of composite materials by linear programming

A method of applying linear programming to evaluate the elastic moduli of unidirectionally fiber-reinforced composite materials is presented. Based on the theory of elasticity, the stresses and displacements of the fiber and of the resin are expressed in terms of harmonic series. The coefficients of the series are determined by the simplex algorithm to minimize the deviations which occur when the stresses and displacements are matched at the fiberresin interface and at the outer boundary of the representative element of the composite. By applying the energy principle, the Young's modulus in the fiber direction and the major Poisson's ratio of the E-glass/resin composite are found to be in good agreement with existing results, while the gap of the bounds for its bulk modulus is considerably narrowed in comparison to earlier results.