Micromechanical analysis of thermoelastic and magnetoelectric composite and reinforced shells

Abstract

A comprehensive micromechanical model for the analysis of structurally periodic and fully coupled magneto-electric and thermoelastic smart composite and reinforced thin shells is developed on the basis of Asymptotic Homogenization. Starting with the quasi-static approximation of Maxwell’s equations as well as force and thermal balance the model is decomposed into a macroscopic and a microscopic problem which are treated separately and sequentially even though the two scales are inherently coupled and co-existent in the original structure. The microscopic problem allows the computation of the effective coefficients and the macroscopic problem determines an asymptotic approximation of the field variables (stress, electric displacement, heat flux etc.). It is shown that in the limiting case of a thin elastic shell whereby any magnetoelectric and thermal behavior is suppressed, the derived model converges to the familiar classical shell model. As illustrated, the results of the model constitute an important refinement over previously established work.