3-DIMENSIONAL PIEZOELECTRIC BOUNDARY-ELEMENT METHOD

The boundary element method is applied to problems of three-dimensiona l linear piezoelectricity. The continuum equations for conservation of linear momentum and charge are combined into one governing equation f or piezoelectricity. A single boundary integral equation is developed from this combined field equation and Green's solution for a piezoelec tric medium. Green's function and its derivatives are derived using th e radon transform, and the resulting solution is represented by a line integral that is evaluated numerically using standard Gaussian quadra ture. The boundary integral equation is discretized using eight-node i soparametric quadratic elements, resulting in a matrix system of equat ions. The solution of the boundary problem for piezoelectric materials consists of elastic displacements, tractions, electric potentials, an d normal charge flux densities. The complete field solutions can be ob tained once all boundary values have been determined, The accuracy of this linear piezoelectric boundary element method is illustrated with two numerical examples. The first involves a unit cube of material wit h an applied mechanical load. The second example consists of a spheric al hole in an infinite piezoelectric body loaded by a unit traction on its boundary. Comparisons are made to the analytical solution for the cube and an axisymmetric finite element solution for the spherical ho le. The boundary element method is shown to be an accurate solution pr ocedure for general three-dimensional linear piezoelectric material pr oblems.