The strict theory of complex variable function method for sextuple harmonic equation and applications

Abstract

The strict theory of the complex variable function method for the sextuple harmonic equation is given in detail, which is a development of the work on the quadruple harmonic equation of the authors. Both of the above mentioned works develop the well-known Muskhelishvili complex variable function method for solving the biharmonic equation used in the classical theory of elasticity. Meanwhile, some applications to the elasticity, plasticity, and fracture theories of quasicrystalline materials have shown that the theory and method are successful and effective.