The Semi-analytical Analysis For The Magnetoelectroelastic Coupling Problem

In this paper, we study the application of semi-analytical method in two kinds ofmaterials. Firstly, based on the basic equations of two-dimensional piezoelectric materialproblem and the basic idea of the scaled boundary finite-element method, set up the scaledboundary finite-element control equation to solve the two-dimensional piezoelectric problem.From the basic plane problem equations of transverse isotropic piezoelectric materials, use thevirtual work formulation, reference with the scaled boundary finite-element method ofelastostatics, derive the piezoelectric scaled boundary finite-element control equationexpressed with generalized displacement and stress, then, solve the equation. In this method,only the boundary of the domain is discrete, use analytical method in the radical direction, hasan accuracy calculation. The paper provides an example to illustrate the versatility, accuracyand efficiency of the scaled boundary finite-element method. In addition, this paper alsodisscussed the different discrete elements and scaled center locations influence on the results.Secondly, based on the basic equations of two-dimensional magnetoelectroelastic solidsproblem and the basic idea of the mixed state Hamiltonian elementary method, set up themixed state Hamiltonian elementary control equation to solve the two-dimensionalmagnetoelectroelastic solids problem. In this problem, Hamiltonian dual equation of planetransversely isotropic magnetoelectroelastic solids is derived from variational principle andmixed state Hamiltonian elementary equations are established. Similar to the Hamiltonianformulation in classic dynamics, the z coordinate is treated analogous to the time coordinate.Then the x-direction is discreted with the linear elements to obtain the governing equations,which are a set of first order differential equations in z and are solved by the analyticalapproach.Finally, a summary of the above methods has been given and the advantages anddisadvantages of these methods have been discussed. Some further works also have beenintroduced.