Asymptotic homogenization modeling of thin composite network structures

Asymptotic homogenization models for composite plates reinforced with orthotropic bars are developed and the effective elastic coefficients are obtained. The original problem for the regularly non-homogeneous composite structure reduces to a system of two simpler types of problem, called "unit cell" problems. It is precisely these unit cell problems that enable the determination of the aforementioned coefficients. These effective coefficients are universal in nature and can be used to study a wide variety of boundary value problems associated with a composite structure of a given geometry. The derived model is applied to a number of practical cases involving composite plates reinforced with different networks of orthotropic bars. It is shown that the model can be used to tailor the effective properties of a given composite structure to meet the requirements of a particular application by changing some material or geometric parameters. In the limiting case of isotropic reinforcements, the results are shown to converge to those of previous models obtained by means of asymptotic homogenization or stress-strain relationships in the reinforcements