Micromechanical analysis of piezo-magneto-thermo-elastic T-ribbed and Π-ribbed plates

Abstract

This article determines the closed-form expressions for the effective properties of fully coupled piezo-magneto-thermo-elastic T-ribbed and Π-ribbed plates consisting of arbitrary orthotropic constituents. To evaluate these properties, the authors invoke a general, previously developed asymptotic homogenization model. Of particular interest and practical importance are the product properties, i.e., the pyroelectric, pyromagnetic, and magnetoelectric coefficients; these properties are manifested in the macroscopic composite but are usually absent from the micromechanical behavior of the individual constituents; they are a consequence of the coupling between mechanical, electrical, magnetic, and thermal fields and are realized through strain transfer between the various constituents. The practical importance of the work lies in the fact that it can be successfully employed to tailor the effective properties of a smart composite T- or Π-ribbed plate to the requirements of a particular engineering application by changing certain geometric or material parameters of interest. The validity of the results is illustrated via comparison with other models. Finally, it is shown that in the limiting case of a thin elastic plate of uniform thickness, the derived model converges to the familiar classical plate model.