On the Alternating Method for Cauchy Problems and Its Finite Element Discretisation

2013 ◽  
pp. 183-197 ◽  
Author(s):  
Thouraya N. Baranger ◽  
B. Tomas Johansson ◽  
Romain Rischette
Keyword(s):  
Finite Element ◽  
Cauchy Problems ◽  
Alternating Method

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.

Elastodynamic Fracture Analysis of Multiple Cracks by Laplace Finite Element Alternating Method

1999 ◽  
Vol 67 (3) ◽  
pp. 606-615 ◽  
Author(s):  
W.-H. Chen ◽  
C.-L. Chang ◽  
C.-H. Tsai
Keyword(s):  
Finite Element ◽  
Stress Intensity ◽  
Laplace Transform ◽  
Stress Intensity Factors ◽  
Dynamic Stress ◽  
Multiple Cracks ◽  
Intensity Factors ◽  
Dynamic Stress Intensity Factors ◽  
Alternating Method ◽  
The Laplace Transform

The Laplace finite element alternating method, which combines the Laplace transform technique and the finite element alternating method, is developed to deal with the elastodynamic analysis of a finite plate with multiple cracks. By the Laplace transform technique, the complicated elastodynamic fracture problem is first transformed into an equivalent static fracture problem in the Laplace transform domain and then solved by the finite element alternating method developed. To do this, an analytical solution by Tsai and Ma for an infinite plate with a semi-infinite crack subjected to exponentially distributed loadings on crack surfaces in the Laplace transform domain is adopted. Finally, the real-time response can be computed by a numerical Laplace inversion algorithm. The technique established is applicable to the calculation of dynamic stress intensity factors of a finite plate with arbitrarily distributed edge cracks or symmetrically distributed central cracks. Only a simple finite element mesh with very limited number of regular elements is necessary. Since the solutions are independent of the size of time increment taken, the dynamic stress intensity factors at any specific instant can even be computed by a single time-step instead of step-by-step computations. The interaction among the cracks and finite geometrical boundaries on the dynamic stress intensity factors is also discussed in detail. [S0021-8936(00)02103-6]

Verification of the Combination Rules of Multiple Flaws in ASME B&PV Code Section XI: A Case Study of Two Adjacent Surface Planar Flaws

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
Toshihisa Nishioka ◽  
Guangqin Zhou ◽  
Takehiro Fujimoto
Keyword(s):  
Finite Element ◽  
Cost Effective ◽  
Pressure Vessels ◽  
Surface Cracks ◽  
Combination Rule ◽  
Combination Rules ◽  
Alternating Method ◽  
Vna Solution ◽  
Coplanar Cracks

In nuclear pressure vessels, multiple surface cracks are often found by regular inspection. In order to evaluate the integrity of the vessels, ASME B&PV Code Section XI provides the flaw combination rules; however, its accuracy has not been clarified yet. For the analyses of interacting multiple semi-elliptical surface cracks, in 1983 Nishioka and Atluri developed the Vijayakumar, Nishioka, and Atluri (VNA) solution-finite element alternating method which is highly accurate and cost effective. Using this highly accurate VNA-finite element alternating method, the case of extremely closely located two interacting coplanar cracks was analyzed. From the numerical results, it is found that the B&PV Code Section XI provides a conservative flaw combination rule. Therefore, the B&PV Code Section XI is precisely verified by modern and accurate computational technologies.

The finite element ? Alternating method applied to benchmark No. 1

1982 ◽  
Vol 20 (1) ◽  
pp. R21-R26
Author(s):  
T. E. Kullgren ◽  
G. P. Ganong
Keyword(s):  
Finite Element ◽  
Alternating Method

Analysis of Interaction Behavior of Surface Flaws in Pressure Vessels

1986 ◽  
Vol 108 (1) ◽  
pp. 24-32 ◽  
Author(s):  
P. E. O’Donoghue ◽  
T. Nishioka ◽  
S. N. Atluri
Keyword(s):  
Finite Element ◽  
Stress Intensity ◽  
Pressure Vessels ◽  
Influence Functions ◽  
Surface Cracks ◽  
Intensity Factors ◽  
Alternating Method ◽  
Circumferential Crack ◽  
Magnification Factors ◽  
Surface Flaws

The evaluation of stress intensity factors for surface flaw problems and, in particular, semi-elliptical surface cracks in cylindrical pressure vessels has been well developed using the finite element alternating method. Some of the examples presented here include the interaction effects due to multiple internal longitudinal surface cracks in cylinders as recommended for analysis in the ASME Boiler and Pressure Vessel Code (Section XI). For each crack geometry, several loading cases are considered including internal pressure and polynomial pressure loadings from constant to fourth order. By the method of superposition, the magnification factors for internally pressurized cylinders are rederived using the polynomial influence functions. These influence functions give useful information for design purposes such as in the analysis of a thermally shocked cylinder. The problem of a single circumferential crack in a cylinder is also investigated using the finite element alternating method, and a number of results for such problems are also presented here.

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