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# SGBEM-FEM Alternating Method for Analyzing 3D Non-planar Cracks and Their Growth in Structural Components1

G.P.Nikishkov2, J.H.Park3, S.N.Atluri2
This paper is presented in honor of the 90th birthday of the distinguished UCLA Academician, Professor T.H. Lin, whose contributions to the mechanics of fatigue are seminal and monumental.
Center for Aerospace Research & Education, 7704 Boelter Hall, UCLA, Los Angeles, CA 90095-1600, USA
Dept. of Safety Engineering, Chungbuk National University, Chungbuk 361-763, Korea

Computer Modeling in Engineering & Sciences 2001, 2(3), 401-422. https://doi.org/10.3970/cmes.2001.002.401

### Abstract

An efficient and highly accurate, Symmetric Galerkin Boundary Element Method - Finite Element Method - based alternating method, for the analysis of three-dimensional non-planar cracks, and their growth, in structural components of complicated geometries, is proposed. The crack is modeled by the symmetric Galerkin boundary element method, as a distribution of displacement discontinuities, as if in an infinite medium. The finite element method is used to perform the stress analysis for the uncracked body only. The solution for the structural component, containing the crack, is obtained in an iteration procedure, which alternates between FEM solution for the uncracked body, and the SGBEM solution for the crack in an infinite body. Numerical procedures, and the attendant Java code, are developed for the evaluation of stress intensity factors, and fatigue crack growth modeling. Examples for non-planar cracks in infinite media, and for planar cracks in finite bodies, as well as their growth under fatigue, demonstrate the accuracy of the method.

### Keywords

SGBEM, FEM, alternating, 3D non-planar crack.

, G., , J., , S. (2001). SGBEM-FEM Alternating Method for Analyzing 3D Non-planar Cracks and Their Growth in Structural Components1. CMES-Computer Modeling in Engineering & Sciences, 2(3), 401–422.

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