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Alternative state space formulations for magnetoelectric thermoelasticity with transverse isotropy and the application to bending analysis of nonhomogeneous plates. (English) Zbl 1059.74518

Summary: By introducing two displacement functions and two stress functions, the governing equations of the linear theory of magneto-electro-thermo-elasticity with transverse isotropy are simplified. On selecting certain physical quantities as the basic unknowns, two new state equations are established. Each of them is order reduced when compared with the one reported recently in literature, leading to a higher numerical efficiency. The material inhomogeneity along the axis of symmetry (\(z\)-direction) can be taken into account and an approximate laminate model is employed to facilitate deriving analytical solutions. The validity of new formulations is examined by considering a laminated magneto-electro-elastic rectangular plate and good agreement is obtained with existent results. A plate with a functionally graded property is then analyzed. The effect of magnetoelectric coupling in a BaTiO\(_3\)–CoFe\(_2\)O\(_4\) composite predicted from the micromechanics simulation is studied quantitatively.

MSC:

74F15 Electromagnetic effects in solid mechanics
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