A coupled fictitious stress method and Eshelby inclusions as a meshless technique for inhomogeneity problems. (1st January 2022)

• Record Type: Journal Article
• Authors: Kamal, M.A.; Rashed, Youssef F.
• Is Part Of: Engineering analysis with boundary elements. Volume 134(2022)
• Page Start: 117
• Page End: 138
• Publication Date: 2022-01-01
• Subjects: Meshless techniques -- Fictitious stress method -- Eigenstrain -- Eshelby's equivalent inclusions -- Particular solution; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2021.09.031
• Languages: English
• ISSNs: 0955-7997

Abstract

Highlights: The fictitious stress method is employed as a meshless method. The fictitious stress method is applied to inhomogeneous problems. Eshelby's equivalent inclusion theory is used to model inhomogeneities within the proposed method. Two solution algorithms are proposed, i.e. direct and iterative. Abstract: In this paper, the fictitious stress method (FSM) as a meshless technique is extended to solve problems with inhomogeneities. The Eshelby's equivalent inclusion theory is coupled with the FSM as a set of particular solutions. There is no domain discretization as analytical solutions for inclusions are employed. The coupling procedure is presented, and the solution is carried out either in a direct or in an iterative approach. Numerical examples are presented to verify accuracy of the developed formulations.