Determination of the effective stiffness of a unidirectional layer by the finite element method and approximate formulas

Abstract

Layered composites formed by unidirectional layers are widely used in aviation in the most loaded areas of the aircraft. Data on the elastic properties of the layers are required for the strength and stiffness calculation of structural elements made of such materials. There are two possible approaches to address the problem. The first approach is based on solving the problem of micromechanics using methods of the theory of elasticity. The second approach consists in developing a simplified model of a unidirectional layer. Analysis of the model can provide for fairly simple formulas for determination of the effective stiffness of a unidirectional layer. A comparative analysis of the results obtained in both approaches revealed the limits of applicability of approximate formulas derived for evaluating the effective characteristics of the different types of composites depending on the volume content of fibers. The effective elastic characteristics of unidirectional composites are determined by the finite element method in the framework of the linear theory of elasticity. The boundary value problem is solved for a characteristic representative element selected in accordance with the physical and geometric parameters of the medium of an ordered structure. A set of algorithm-programs has been developed under ANSYS environment which automates calculations of the elastic characteristics of materials depending on the volume content of fibers at different ratios of the elastic properties of fibers and binder, and on the parameters of the curvature of the fiber cross-sectional profile. The results obtained by the numerical method are compared with the data obtained experimentally and by approximate formulas.