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CivilComp Proceedings
ISSN 17593433 CCP: 81
PROCEEDINGS OF THE TENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING Edited by: B.H.V. Topping
Paper 110
Comparing BEM and FEM Strategies for the Computation of the Stress Intensity Factor using Singular and NonSingular Elements S.P.L. Leme, R.F. Lima, L.M. Bezerra and P.W. Partridge
Department of Civil and Environmental Engineering, University of Brasília, Brazil S.P.L. Leme, R.F. Lima, L.M. Bezerra, P.W. Partridge, "Comparing BEM and FEM Strategies for the Computation of the Stress Intensity Factor using Singular and NonSingular Elements", in B.H.V. Topping, (Editor), "Proceedings of the Tenth International Conference on Civil, Structural and Environmental Engineering Computing", CivilComp Press, Stirlingshire, UK, Paper 110, 2005. doi:10.4203/ccp.81.110
Keywords: fracture mechanics, finite element, boundary element, stress intensity factor, singular and nonsingular elements.
Summary
The determination of the stress intensity factor (K) in Linear Elastic Fracture
Mechanics (LEFM), is very useful [1] for the investigation of crack propagation and
structural integrity in pressure vessels, pipelines, aircraft fuselages, concrete dams
and other structures. Crack propagation can be evaluated using the Fracture
Mechanics parameters such as the Stress Intensity Factor (K) and the JIntegral (J) [2].
Obtaining K experimentally is expensive and time consuming. A fast, low cost,
and economical alternative is the use of numerical methods for the calculation of K.
In this paper, the numerical methods used to this end are the FEM and BEM [3].The BEM
promises to bring improved accuracy as the fundamental solutions employed in
the BEM enable the stresses in areas of high stress gradients to be calculated accurately.
In spite of this, the use of special elements called quarterpoint elements is common,
both in the FEM [4] and the BEM [5] fracture mechanics applications to model the
singularities at the crack tip [6]. Other advantages [3,7] of the BEM are the
reduction of the dimensionality of problems; ease of modelling regions where
parameters such as stresses or strains vary rapidly; ease of remeshing where
necessary, and others. These advantages of the BEM can be fully exploited in fracture
mechanics applications. The ease of remeshing is particularly important for
following the propagation of cracks, as is the fact that it is only necessary to define
elements on the boundary, avoiding the discretization of the complete domain.
In this paper, several techniques are used for the calculation of the Stress Intensity Factor KI (Deformation Mode I) [2] using both the FEM and the BEM. The results obtained lead to some practical conclusions which may be easily employed by engineers in the day to day evaluation of structural integrity. The use of special quarterpoint elements is also considered. The FEM results are obtained using the ANSYS commercial software, which calculates automatically results for KI using the JIntegral [8,9] technique employing both common and quarterpoint quadratic elements. The BEM results are obtained using a classic plane stress FORTRAN code adapted for fracture mechanics problems to employ the COD (Crack Opening Displacement) method, Nodal Stresses and the JIntegral technique to calculate KI. The code employs common quadratic elements, but the calculation of the derivatives of the displacements ( ) and ( ) which appear in the JIntegral is accomplished in an accurate way by differentiating the BEM fundamental solutions [10]. The results obtained here show that accuracy of the results improves when quarter point elements are employed and also if finer discretizations are used. It is noted that the simple methods such as COD and the Nodal Stress method can give reasonable values of KI when refined meshes and quarterpoint elements are employed with the FEM. The technique which relates the value of KI to the JIntegral requires a larger computational effort, but produces much more accurate results. Using the FEM, the results obtained using the JIntegral and employing quarterpoint elements contained only small errors in comparison with solutions available in the literature. Even considering only common elements, the formulation presented for BEM give results compatible with the best results obtained using the FEM. The BEM produced good results for discretizations employing only a few elements using implicit differentiation of the fundamental solutions for the calculation of and in the calculation of the JIntegral. Considering the results obtained one can ask if the search for the singularity at the crack tip in numerical methods is essential for the calculation of K via the JIntegral. References
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