Green’s functions of steady-state transversely isotropic hygro-thermo-magneto-piezoelectric cones

Abstract

Green’s functions of transversely isotropic hygro-thermo-magneto-piezoelectric (HTMP) cones are established. The governing equations of transversely isotropic HTMP media are first simplified by introducing two displacement functions. Steady-state general solutions of transversely isotropic HTMP media expressed by seven quasi-harmonic functions are obtained by the operator theory, superposition principle, and generalized Almansi’s theorem. Furthermore, the three-dimensional problems of a semi-infinite HTMP cone subjected to a point moisture source and a point heat source are analyzed by introducing the potential functions which are determined by moisture, thermal, electric, magnetic equilibrium relationships and boundary conditions. Furthermore, the fundamental solutions of the HTMP cones under the action of the point sources are obtained. The numerical examples and the contours of the coupled fields of HTMP cones are presented, and the variation regularity of stress, electric displacement, and magnetic induction are discussed. The effects of different apex angles of cones on the coupled fields are also analyzed.