Premium
The perturbation method and the extended finite element method. An application to fracture mechanics problems
Author(s) -
GRASA J.,
BEA J. A.,
RODRÍGUEZ J. F.,
DOBLARÉ M.
Publication year - 2006
Publication title -
fatigue and fracture of engineering materials and structures
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.887
H-Index - 84
eISSN - 1460-2695
pISSN - 8756-758X
DOI - 10.1111/j.1460-2695.2006.01028.x
Subject(s) - finite element method , discretization , discontinuity (linguistics) , extended finite element method , smoothed finite element method , mixed finite element method , fracture mechanics , mathematics , monte carlo method , perturbation (astronomy) , finite element limit analysis , computer science , mechanics , mathematical analysis , structural engineering , boundary knot method , engineering , physics , boundary element method , statistics , quantum mechanics
The extended finite element method has been successful in the numerical simulation of fracture mechanics problems. With this methodology, different to the conventional finite element method, discretization of the domain with a mesh adapted to the geometry of the discontinuity is not required. On the other hand, in traditional fracture mechanics all variables have been considered to be deterministic (uniquely defined by a given numerical value). However, the uncertainty associated with these variables (external loads, geometry and material properties, among others) it is well known. This paper presents a novel application of the perturbation method along with the extended finite element method to treat these uncertainties. The methodology has been implemented in a commercial software and results are compared with those obtained by means of a Monte Carlo simulation.