Asymptotic homogenization model for generally orthotropic reinforcing networks in smartcomposite plates

Abstract

A general three-dimensional micromechanical model pertaining to smart composite layerswith wavy boundaries is applied to the case of thin smart plates reinforced with a networkof generally orthotropic bars that may also exhibit piezoelectric behavior. The method usedfor the development of the structural model is that of asymptotic homogenization, whichreduces the original boundary value problem into a set of three decoupled problems, eachproblem being characterized by two differential equations. These three sets of differentialequations, referred to as ‘unit cell problems’, deal, independently, with the elastic,piezoelectric, and thermal expansion behavior of the network-reinforced smart compositeplates. The solution of the unit cell problems yields expressions for effective elastic,piezoelectric and thermal expansion coefficients which, as a consequence of theiruniversal nature, can be used to study a wide variety of boundary value problemsassociated with a smart structure of a given geometry. The model can be used tocustomize the effective properties of a smart structure by changing some materialor geometric parameters such as the size or nature of the reinforcements. Thedeveloped general methodology is applied to smart network-reinforced compositestructures with generally orthotropic reinforcements and actuators. As particularexamples, spatial rectangular, triangular, and rhombic smart network plates areanalyzed. The general orthotropy of materials is very important from the practicalviewpoint and this orthotropy makes micromechanical modeling significantlymore complex. In the limiting case of isotropic reinforcements and absence ofactuators, the above general orthotropic micromechanical model converges to resultsthat are consistent with those of previous models obtained by either asymptotichomogenization, or stress–strain relationships in the isotropic reinforcements.