Iterative method for solving a problem with mixed boundary conditions for biharmonic equation arising in fracture mechanics
Dang Quang A, Mai Xuan Thao · Boletim da Sociedade Paranaense de Matemática · 2011
In this paper we consider a mixed boundary value problem for biharmonic equation of the Airy stress function which models a crack problem of a solid elastic plate. An iterative method for reducing the problem to a sequence of mixed problems for Poisson equations is proposed and investigated. The convergence of the method is established theoretically and illustrated on many numerical experiments.