scholarly journals Alternating method applied to edge and surface crack problems

1973 ◽  
pp. 179-238 ◽  
Author(s):  
R. J. Hartranft ◽  
G. C. Sih
Keyword(s):  
Surface Crack ◽  
Alternating Method ◽  
Crack Problems

Analysis of Surface Flaw in Pressure Vessels by a New 3-Dimensional Alternating Method

1982 ◽  
Vol 104 (4) ◽  
pp. 299-307 ◽  
Author(s):  
T. Nishioka ◽  
S. N. Atluri
Keyword(s):  
Finite Element ◽  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Surface Crack ◽  
Crack Surface ◽  
Pressure Vessels ◽  
Pressure Loading ◽  
Intensity Factors ◽  
Alternating Method ◽  
Magnification Factors

An alternating method, in conjunction with the finite element method and a newly developed analytical solution for an elliptical crack in an infinite solid, is used to determine stress intensity factors for semi-elliptical surface flaws in cylindrical pressure vessels. The present finite element alternating method leads to a very inexpensive procedure for routine evaluation of accurate stress intensity factors for flawed pressure vessels. The problems considered in the present paper are: (i) an outer semi-elliptical surface crack in a thick cylinder, and (ii) inner semi-elliptical surface cracks in a thin cylinder which were recommended for analysis by the ASME Boiler and Pressure Vessel Code (Section III, App. G, 1977). For each crack geometry of an inner surface crack, seven independent loadings, such as internal pressure loading on the cylinder surface and polynomial pressure loadings from constant to fifth order on the crack surface, are considered. From the analyses of these loadings, the magnification factors for the internal pressure loading and the polynomial influence functions for the polynomial crack surface loadings are determined. By the method of superposition, the magnification factors for internally pressurized cylinders are rederived by using the polynomial influence functions to check the internal consistency of the present analysis. These values agree excellently with the magnification factors obtained directly. The present results are also compared with the results available in literature.

Surface crack problems in plates

1989 ◽  
Vol 41 (2) ◽  
pp. 105-131 ◽  
Author(s):  
P. F. Joseph ◽  
F. Erdogan
Keyword(s):  
Surface Crack ◽  
Crack Problems

Application of combined-mode fracture criteria to surface crack problems

1986 ◽  
Vol 24 (1) ◽  
pp. 127-144 ◽  
Author(s):  
Xiao-Ming Chen ◽  
Gui-Qiong Jiao ◽  
Zhen-Yuan Cui
Keyword(s):  
Surface Crack ◽  
Fracture Criteria ◽  
Mode Fracture ◽  
Crack Problems ◽  
Combined Mode

Elasto-Plastic Analysis of 3-D Inner Cracks Using the Finite Element Alternating Method

2007 ◽  
Vol 345-346 ◽  
pp. 881-884
Author(s):  
Sang Yun Park ◽  
Jai Hak Park
Keyword(s):  
Finite Element ◽  
Stress Fields ◽  
The Finite Element Method ◽  
Infinite Body ◽  
Alternating Method ◽  
Crack Problems ◽  
Finite Body ◽  
Initial Stress Method ◽  
Galerkin Boundary Element Method ◽  
Element Method

The finite element alternating method (FEAM) was extended to obtain fracture mechanics parameters and elasto-plastic stress fields for 3-D inner cracks. For solving a problem of a 3-D finite body with cracks, the FEAM alternates independently the finite element method (FEM) solution for the uncracked body and the solution for the crack in an infinite body. As the required solution for a crack in an infinite body, the symmetric Galerkin boundary element method formulated by Li and Mear was used. For elasto-plastic numerical analysis, the initial stress method proposed by Zienkiewicz and co-workers and the iteration procedure proposed by Nikishkov and Atluri were used after modification. The extended FEAM was examined through comparing with the results of commercial FEM program for several example 3-D crack problems.

Comparison of SGBEM-FEM Alternating Method and XFEM Method for Determining Stress Intensity Factor for 2D Crack Problems

2014 ◽  
Vol 891-892 ◽  
pp. 345-350 ◽  
Author(s):  
Subhasis Sarkar ◽  
Nicole Apetre ◽  
Nagaraja Iyyer ◽  
Nam Phan ◽  
Kishan Goel ◽  
...  
Keyword(s):  
Finite Element Analysis ◽  
Stress Intensity Factor ◽  
Finite Element ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Boundary Element ◽  
Degrees Of Freedom ◽  
Element Analysis ◽  
Alternating Method ◽  
Crack Problems

The two most promising approaches to determine Stress Intensity Factor (SIF) developedover the past decade are the Symmetric Galerkin Boundary Element Method - Finite Element Method(SGBEM-FEM) based alternating method and the Extended Finite Element (XFEM) method. Thepurpose of this paper is to determine the SIFs for a number of 2-D crack problems by the two ap-proaches and measure their relative effectiveness in terms of accuracy, speed and computational re-sources.In the SGBEM-FEM alternating method, a finite element analysis is carried out on the un-crackedbody using the externally applied loading and next a boundary element analysis is performed byreversing the stresses found on the crack location from the finite element analysis, and the residualstresses on the boundary of the finite body are determined. The steps are repeated until convergenceis achieved where the residual stresses on the boundaries and traction on the crack surfaces are closeto zero.In the XFEM method, the mesh is created without considering the topology of the crack configura-tion and the discontinuities are handled by special discontinuity enrichment functions. The enrichmentfunctions increase the degrees of freedom and the regular stiffness matrix is augmented by additionalterms corresponding to the extra degrees of freedom but the increase in computational requirement isoffset by not having the burden of remeshing the finite elements.Both SGBEM-FEM alternating method and XFEM method are used to solve a number of crackproblems and the example cases clearly show the computational efficiency of the SGBEM-FEM al-ternating method over the XFEM method.

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