Complex Variables Method For Several Classes Of Anti-plane Crack Problems Of Piezoelectric Materials

In this thesis, the static ant-plane crack problems of an infinite piezoelectric materials are investigated by using complex variables method on the basis of linear macroscopic theory of piezoelectric materials.Firstly, by continuation technology and conformal mapping, the periodic collinear crack problems are studied in the two cases of permeable and impermeable boundary conditions, and solutions in closed form are obtained, then the formulae for the stress intensity factors and electric displacement intensity factors are derived, and the interaction effects and scale effects of periodicity are shown by figures.secondly, using continuation technology on circular domain, the circular arc crack problem is investigated subjected to anti-plane shear and inplane electric loading at infinity, the explicit form solutions are obtained and the formulae for intensity factors of both mechanics and electric are presented with impermeable boundary condition.Finally, by using series expansion of complex variables, the general solution of multiple circular holes is discussed subjected to uniform loading at infinity. By conformal mapping, the parabolic curve crack are investigated with permeable boundary condition, and the formulae for intensity factors of both mechanics and electric are obtained.