M. Repka

Analysis of Cracks in Functionally Graded Piezoelectric Materials by a Frequency-Domain BEM

Time-harmonic crack analysis in two-dimensional piezoelectric functionally graded materials (FGMs) is presented in this paper. A frequency-domain boundary element method (BEM) is developed for this purpose. Since fundamental solutions for piezoelectric FGMs are not available, a boundary-domain integral formulation is derived. This requires only the frequency-domain fundamental solutions for homogeneous piezoelectric materials. The radial integration method is adopted to compute the resulting domain integrals. The collocation method is used for the spatial discretization of the frequency-domain boundary integral equations. Adjacent the crack-tips square-root elements are implemented to capture the local square-root-behavior of the generalized crack-opening-displacements properly. Special regularization techniques based on a suitable change of variables are used to deal with the singular boundary integrals. Numerical examples will be presented and discussed to show the influences of the material gradation and the dynamic loading on the intensity factors.