Iterative method for solving a problem with mixed boundary conditions for biharmonic equation arising in fracture mechanics

Dang Quang A; Mai Xuan Thao

doi:10.5269/bspm.v31i1.11728

Dang Quang A Vietnam Academy of Science and Technology Institute of Information Technology
Mai Xuan Thao Hong Duc University

DOI: https://doi.org/10.5269/bspm.v31i1.11728

Keywords: Iterative method, Biharmonic equation, Mixed boundary conditions, Crack problem

Abstract

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.

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Author Biographies

Dang Quang A, Vietnam Academy of Science and Technology Institute of Information Technology

Head of Department of Mathematical methods in Information Technology,

Mai Xuan Thao, Hong Duc University

Head of Department of Natural Sciences

Thanh Hoa City