APPLICATION OF TREFFTZ BEM TO ANTI-PLANE PIEZOELECTRIC PROBLEM

Anti-plane electroelastic problems are studied by the Trefftz boundary element method （BEM） in this paper. The Trefftz BEM is based on a weighted residual formulation and indirect boundary approach. In particular the point-collocation and Galerkin techniques, in which the basic unknowns are the retained expansion coefficients in the system of complete equations, are considered. Furthermore, special Trefftz functions and auxiliary functions which satisfy exactly the specified boundary conditions along the slit boundaries are also used to derive a special purpose element with local defects. The path-independent integral is evaluated at the tip of a crack to determine the energy release rate for a mode Ⅲ fracture problem. In final, the accuracy and efficiency of the Trefftz boundary element method are illustrated by an example and the comparison is made with other methods.

ANTI-PLANE CRACK MOVING ALONG THE INTERFACE OF DISSIMILAR PIEZOELECTRIC MATERIALS

The problem of an anti-plane Griffith crack moving along the interface of dissimilar piezoelectric materials is solved by using the integral transform technique. It is shown from the result that the intensity factors of anti-plane stress and electric displacement around the crack tip are dependent on the speed of the Griffith crack as well as the material coefficients. When the two piezoelectric materials are identical, the present result will be reduced to the result far the problem of an anti-plane moving Griffith crack in homogeneous piezoelectric materials.

A MIXED ELECTRIC BOUNDARY VALUE PROBLEM FOR AN ANTI-PLANE PIEZOELECTRIC CRACK

The analytical continuation method is adopted to solve a mixed electric boundary value problem for a piezoelectric medium under anti-plane deformation.The crack face is partly conductive and partly impermeable.The results show that the stress intensity factor is identical with the mode Ⅲ stress intensity factor independent of the conducting length.But the electric field and the electric displacement are dependent on the electric boundary conditions on the crack faces and are singular not only at the crack tips but also at the junctures between the impermeable part and conducting portions.

Crack tip fields of piezoelectric materials under antiplane impact

THE fracture mechanics of piezoelectric materials is extensively studied under static mechanicalor electrical loads. However, the failure of practical smart structure always happens underdynamic loads, so it is urgently needed to study the fracture dynamics of piezoelectric materi-als. The dynamic Green’s functions for anisotropic piezoelectric materials were proposed byNorris. The dynamic representative formulas and the fundamental solutions were

Non-local theory solution to two collinear limited-permeable mode-I cracks in a piezoelectric/piezomagnetic material plane

The non-local theory solution to two collinear limited-permeable mode-I cracks in a piezoelectric/piezomagnetic medium was investigated by using the generalized Almansi's theorem and the Schmidt method in the present paper. The problem was formulated through Fourier transformation into two pairs of dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces. For solving the dual integral equations, the displacement jumps across the crack surfaces were directly expanded as a series of Jacobi polynomials. Numerical examples were provided to show the effects of the crack length, the distance between the two collinear cracks, the lattice parameter, the electric permittivity and the magnetic permeability of the air inside the crack on the stress fields, the electric displacement fields and the magnetic flux fields near the crack tips in a piezoelectric/piezomagnetic medium. Different from the classical solutions, the present solution exhibits no stress, electric displacement and magnetic flux singularities at the crack tips in a piezoelectric/piezomagnetic medium.