Transient Thermoelectroelastic Response of a Functionally Graded Piezoelectric Strip with an Annular Crack

Abstract

Transient responsc of an annular crack in a plate of a functionallygraded piezDelectric m 烈 teria1 ( FGPM )is studied under thermal shock load ［ ng collditiolls ． It is assumed that the t［ herm 〔 〕electroelas ・ tic pr 〔 〕 perties of the strip vary continuousIy along the thickness Dfthc strip ， and that the crack faces are completely insulated ． SDme material propcrties are assunled to be exponentially dependent on the distance fromthc crack line paralel † o the boundaries of the plate ． By using b ｛ ｝th the Lapluce and Hankel trallsforms ， the thermal ancl electrome ⊂hallical problems are reduced to a singular integral equa 亡 i〔，n and a system of singular ｛ ntegral equations ． The singular integrul equatiens are solved numerically ， and a numerical method is then enlployed to obtain 出 e 亡 ime dependent solutio 】 rsby way of a Laplace inversiun technique ． The intensity factors versus time are presented for various values of dimensionless paralneters representing the lnaterial nonhoinegeneit ) ・ and the crack positior ／．