absolute value of electric potential in the MEE cylinder. Moreover, increasing the temperature and moisture concentration on the outer surface decreases the magnetic potential through the thickness of the cylinder as shown in Fig.3.8e. As mentioned earlier, in uncoupled hygrothermomagnetoelectroelasticity, temperature and mois- ture distributions are independent of other multiphysicalfields. As seen in Fig.3.8f and g, the non-dimensional temperature and moisture concentration distribution increase through the thickness in the same manner as the applied temperature and moisture concentration on the outer surface increases.
investigation reveals that the coupling effects of magneto-electro-elasticfields cannot be ignored when the material properties exhibit piezomagnetic/piezoelectric effects simultaneously. Although the governing and constitutive equations of the magnetic and electric potentials are similar to each other, their distributions are not the same due to the different coupling coefficients. Furthermore, it is seen that imposing a proper magneticfield can reduce the hoop stress in a rotating FGPM cylinder, and as a result can make the smart structures more reliable. Finally, the investigation shows that moisture concentration and temperature have similar effects on the multiphysical responses of an MEE cylinder in uncoupled hygrothermomagnetoelectroelasticity. It is observed that hygrothermal loading can change the radial stress, hoop stress, axial stress, and electric potential significantly for both hollow and solid MEE cylinders. It is worth mentioning that a theoretical micromechanical model or a computational homogenization technique can be used to obtain the effective properties of smart materials to be used in the closed-form solutions obtained in this chapter for multi- physical analysis of smart materials and structures [49,50].
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