Application of the Unified Formulation to bending analysis of magnetostrictive unimorph microbeams

Bending of magnetostrictive unimorph microbeams is investigated using a one-dimensional refined finite element model based on the Carrera Unified Formulation. Since these type of smart devices are usually being used in low magnetic fields, the linear coupled magnetomechanical constitutive relations are used to characterize their coupling behavior. With the use of the principle of virtual displacement, components of the fundamental nucleus matrix are obtained and the gov- erning equations are discretized. 2, 3 and 4-node beam elements are used for modelling the beam major axis while linear 4-node and quadratic 9-node Lagrange elements are used as expansion functions over the cross-section. Two examples of unimorph micro-devices are considered and the results of present work are compared with those of experimental and conventional finite element works existing in the literature. It is shown that the one-dimensional refined finite element model, which is capable of generating three-dimensional results, can accurately catch the experimental data with a lower computational cost than the classical models.