THE FUNDAMENTAL SOLUTIONS FOR THE PLANE PROBLEM IN PIEZOELECTRIC MEDIA WITH AN ELLIPTIC HOLE OR A CRACK

1.IntroductionItiswell-knownthatthefundame,ltalsolutionsorGreen'sfunctionsplayanimportantroleilllinearelasticity.Forexample,theycanbeusedtoconstructmanyanalyticalsolutionsofpracticalproblems.Itismoreimportantthattheyareusedasthefundamentalsolutionsintheboundaryelementmethod(BEM)tosolvesomecomplicatedproblem.Withthewidely-increasingapplicationofpiezoelectricmaterialsinengineeringproblems,thestudyregardingtheGreen'sfLlnctionsinpiezoelectricsolidshasreceivedmuchinterest.The3DGreen'sfunctionsi…

The fundamental solutions for the plane problem in piezoelectric media with an elliptic hole or a crack

Based on the complex potential method, the Green's functions of the plane problem in transversely isotropic piezoelectric media with an elliptic hole are obtained in terms of exact electric boundary conditions at the rim of the hole. When the elliptic hole degenerates into a crack, the fundamental solutions for the field intensity factors are given. The general solutions for concentrated and distributed loads applied on the surface of the hole or crack are produced through the superposition of the fundamental solutions. With the aid of these solutions, some erroneous results provided previously in other works are pointed out. More important is that these solutions can be used as the fundamental solutions of boundary element method to solve more practical problems in piezoelectric media.