Dynamic fiber inclusions with elliptical and arbitrary cross-sections and related retarded potentials in a quasi-plane piezoelectric medium. (Q1430791)

The paper deals with quasi-static electroelastic fields in an infinite piezoelectric composite with transversely isotropic matrix material and with a continuous fiber inclusion parallel to the axis of material symmetry. The inclusion of arbitrary cross-sections that has the same electroelastic moduli and mass density as the piezoelectric material is taken to undergo a spatially uniform time-domain transformation. All the field variables are assumed to be dependent only on the plane coordinates, and they are determined in terms of three potentials that are convolutions of retarded Green functions. Compact integral formulae are derived for the potentials by means of Fourier transform, and they are shown to recover the potentials of continuous circular fiber inclusions and fiber tubes as special cases. A numerical procedure based on Gauss quadrature technique is applied for evaluations of fiber inclusions with arbitrary cross-sections. Numerical examples are given for homogeneous fiber inclusions with circular and elliptical cross-sections.