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Abstract
3D grid-reinforced smart composite structures with periodic or nearly periodic arrangement of reinforcements/actuators that are the subject matter of this Thesis are not only worth considering because of their practical uses in various fields but also due to the obvious advantages they have over other types of composites in being more amenable to analytical and numerical treatments.
The present study predicts 'effective' properties of such structures for a wide range of geometrical and material parameters. Hence, comprehensive micromechanical approaches including analytical and numerical modeling have been developed. The analytical modeling is based on the multiscale Asymptotic Homogenization Method whereas the numerical modeling is based on Finite Element technique. The models presented in this Thesis have adopted general anisotropy given that the anisotropic properties of the constituents are very important from the practical view-point; at the same time however, it renders the analysis more complex.
The AHM transforms original Boundary Value Problems describing piezothermoelastic behavior of such structures into a simpler set of problems characterized by certain 'effective' coefficients. The complexity in the BVPs is a result of the presence of multiple inhomogeneities (in a relatively small length scale) in the composite which implies that its behavior is described by a set of equations with rapidly varying coefficients. The BVPs are fairly complex and can only be simplified by recasting them in the form of modified Unit Cell Problems and by means of the solution of the derived UCPs explicit expressions for the effective piezothermoelastic coefficients of the homogenized 3D grid-reinforced composites have been obtained.
The FE models were also developed and where appropriate a comparison between results obtained by the two approaches was carried out on several examples of practical interest with cubic, conical embedded grids and diagonally reinforced smart structures. The comparison has shown that the asymptotic micromechanical model is an appropriate and effective approach in modeling those effective elastic properties of the 3D grid-reinforced composite structures. These effective coefficients are shown to depend only on the geometric and material parameters of the unit cells and are free from the periodicity complications that characterize their original material counterparts.
The FE models have added a new dimension to the analysis by predicting the effective shear moduli for a wide range of3D grid-reinforced composites.
