BEM Formulation for 3D Static Analysis in Magnetoelectroelastic Solids

The three-dimensional static boundary element method formulation is presented in this chapter. Both piezoelectric and piezomagnetic phases are present in considered magnetoelectroelastic materials. These materials are able of converting energy among electric, magnetic and mechanical fields. The boundary element technique is based on the displacement boundary integral representation. Static fundamental solutions are employed in the form of the integrals along a unit circumference. The point collocation scheme with the mixed boundary elements is used for spatial discretization. The generalized displacements and tractions are interpolated by the linear and constant shape functions, respectively. Boundary geometry is approximated by eight-node quadrilateral elements with quadratic shape functions. Simple numerical example with known exact solutions is considered to validate the proposed boundary element formulation. To establish versatility of the present approach a more complex example is presented.