Size-Dependent Deformation for Thermo-Magneto-Electro-Elastic (TMEE) Timoshenko Micro-/Nano-Beam Based on Deviatoric Couple Stress Theory

Static deformation for thermo-magneto-electro-elastic (TMEE) micro-/nano-beams subjected to applied load is investigated in this paper based on Timoshenko beam model incorporating the extended modified couple stress theory (MCST). Conventional material coefficients are converted into alternative ones, electric potential, magnetic potential, and thermal entropies are solved analytically based on Maxwell equations and heat equation. Governing equations for the TMEE Timoshenko micro-/nano-beams are derived for the first time by using the principle of minimum total potential energy, a 50% BaTiO 3 –CoFe 2 O 4 bilaminate is demonstrated as an example, validity and efficiency are examined. It is found that microstructure effect (MCST) causes the deflections to decrease, and extra equivalent rigidity due to the existence of thermal/pyroelectric/pyromagnetic terms tends to weaken the beam structure. Meanwhile, the magnitude for electric/magnetic potential is bigger than that based on pure MEE modeling, in addition, deflections with couple stress are found to be smaller than those without couple stress especially for very thin structures.