20120003395_Composite Structures Damage Tolerance Analysis Methodologies
Boundary Element Method for Damage Tolerance Analysis
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A NEW GENERATION OF BOUNDARY ELEMENT METHOD FOR DAMAGE TOLERANCE ASSESSMENT OF AEROSTRUCTURES M H Aliabadi Department of Aeronautics, Imperial College London South Kensignton Campus, London SW7 2BY, United Kingdom [email protected] ABSTRACT This paper describes the considerable progress made in recent years in the development of boundary element technology for modelling and simulation of fracture and damage behaviour in complex structural parts. The analyses that include geometric and materials nonlinearities are robust companion to the established finite element method. Recent advances in modelling cracks in thin walled plates and shells are a clear and distinct progress in damage tolerance analysis for aerostructures. 1. INTRODUCTION In order to ensure a reasonable cost for the design and maintenance of aircraft structures, it is generally accepted that computational analysis and simulation must partially replace full scale and laboratory testing. This is the case not only for designing new parts but also in maintaining aging structures. In any method for lifetime prediction of flawed structures, the effect of the geometry of components, or structures, and its interaction with the growing crack must be considered. A new generation of boundary element formulations known as the Dual Boundary Element Method was developed by Aliabadi and his students [1-3] for modelling crack growth in two- and three-dimensional linear elastic problems. The formulation was subsequently extended to nonlinear and transient problems [4-13]. More recently, a new generation of boundary element method has been developed which allows for the application of the BEM to thin walled structures. The extension of the dual boundary element method to thin-walled problems has provided for the first time a comprehensive modelling tool using BEM. In this paper application of the BEM to linear and nonlinear problems are reviewed. Here attention is paid to the application of the method rather than the detailed formulation. Readers interested in the mathematical formulations should refer to the cited references. 2. TWO-DIMENSIONAL MODELLING In 1991, a new boundary element integral equation formulation for modelling cracks was reported by Aliabadi and portela[1]. The formulation was called the dual boundary element method due to its utilisation two integral equations; the displacement integral equation and the traction integral equation [2]. This development was a milestone in the developments of the boundary element method as for the first time allowed for automatic mixed mode crack growth simulation without a remeshing that is not posible with other numerical methods, most notable the finite element method. In figure 1, the application of the method to typical problem od multiple site damage is presented. As it can be seen from the figure, it is posible to model crack growth and coalesence without a need for remeshing. Furtermore, the crack paths are not inflenced with the distribution of internal meshes, which is inhenerent in domain type methods [3]. Figure 1: Multiple site damage. 3. THREE-DIMENSIONAL MODELLING The BEM formulation for three-dimensional crack growth modelling was reported by Mi and Aliabadi and later Cisilino and Aliabadi. The strategy they developed for modelling crack growth consists of two parts. The first relates to the crack extension itself and is simply done by adding new elements along the crack front, whose dimensions and orientation are respectively given by the crack extension increment ∆a and propagation vectors computed at geometrical points along the crack front. The second part is concerned with the modification of mesh around the crack front. Consider a prismatic bar containing two identical offset semi-circular parallel edge cracks. The dimensions of the bar, as well as the relative positions of the crack, scaled to the original crack radius are shown in figure 2. The bar is subjected to a remote tensile stress at its ends. Crack growth is estimated (see Cisilino and Aliabadi [6]) using Paris law. Anales de Mecánica de la Fractura Vol. I (2006) 3
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Transcript of Boundary Element Method for Damage Tolerance Analysis
7/18/2019 Boundary Element Method for Damage Tolerance Analysis
http://slidepdf.com/reader/full/boundary-element-method-for-damage-tolerance-analysis 1/4
A NEW GENERATION OF BOUNDARY ELEMENT METHOD FOR DAMAGE TOLERANCE
ASSESSMENT OF AEROSTRUCTURES
M H Aliabadi
Department of Aeronautics, Imperial College London
South Kensignton Campus, London SW7 2BY, United [email protected]
ABSTRACT
This paper describes the considerable progress made in recent years in the development of boundary elementtechnology for modelling and simulation of fracture and damage behaviour in complex structural parts. The analysesthat include geometric and materials nonlinearities are robust companion to the established finite element method.Recent advances in modelling cracks in thin walled plates and shells are a clear and distinct progress in damagetolerance analysis for aerostructures.
1. INTRODUCTION
In order to ensure a reasonable cost for the design andmaintenance of aircraft structures, it is generallyaccepted that computational analysis and simulationmust partially replace full scale and laboratory testing.This is the case not only for designing new parts butalso in maintaining aging structures. In any method forlifetime prediction of flawed structures, the effect of thegeometry of components, or structures, and itsinteraction with the growing crack must be considered.
A new generation of boundary element formulations
known as the Dual Boundary Element Method was
developed by Aliabadi and his students [1-3] for
modelling crack growth in two- and three-dimensional
linear elastic problems. The formulation was
subsequently extended to nonlinear and transient
problems [4-13]. More recently, a new generation of
boundary element method has been developed which
allows for the application of the BEM to thin walled
structures. The extension of the dual boundary element
method to thin-walled problems has provided for the
first time a comprehensive modelling tool using BEM.In this paper application of the BEM to linear and
nonlinear problems are reviewed. Here attention is paidto the application of the method rather than the detailed
formulation. Readers interested in the mathematicalformulations should refer to the cited references.
2. TWO-DIMENSIONAL MODELLING
In 1991, a new boundary element integral equationformulation for modelling cracks was reported byAliabadi and portela[1]. The formulation was called thedual boundary element method due to its utilisation twointegral equations; the displacement integral equationand the traction integral equation [2]. This developmentwas a milestone in the developments of the boundaryelement method as for the first time allowed for
automatic mixed mode crack growth simulation withouta remeshing that is not posible with other numericalmethods, most notable the finite element method. In
figure 1, the application of the method to typical
problem od multiple site damage is presented. As it can be seen from the figure, it is posible to model crackgrowth and coalesence without a need for remeshing.Furtermore, the crack paths are not inflenced with thedistribution of internal meshes, which is inhenerent indomain type methods [3].
Figure 1: Multiple site damage.
3. THREE-DIMENSIONAL MODELLING
The BEM formulation for three-dimensional crackgrowth modelling was reported by Mi and Aliabadi andlater Cisilino and Aliabadi. The strategy they developedfor modelling crack growth consists of two parts. The
first relates to the crack extension itself and is simplydone by adding new elements along the crack front,whose dimensions and orientation are respectivelygiven by the crack extension increment ∆a and propagation vectors computed at geometrical pointsalong the crack front. The second part is concerned withthe modification of mesh around the crack front.
Consider a prismatic bar containing two identical offsetsemi-circular parallel edge cracks.The dimensions of the bar, as well as the relative positions of the crack, scaled to the original crack radiusare shown in figure 2. The bar is subjected to a remotetensile stress at its ends. Crack growth is estimated (seeCisilino and Aliabadi [6]) using Paris law.
Anales de Mecánica de la Fractura Vol. I (2006)
3
7/18/2019 Boundary Element Method for Damage Tolerance Analysis
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Figure 2: Growth of two offset semi-elliptical cracks.
2. REINFORCED PANEL UNDER
TRANSVERSE SHEAR LOAD
A flat square panel reinforced with three Z-stringers(from the wing box of the B-52 Stratofortress) issubjected to the transverse load q=0,06MPa and it isconsidered to be simply supported on all sides. Thematerial is aluminium 7075-T6 of Young Modulus
E=71016MPa and Poisson's ratio v=0.33. The panel and
the stringers are modelled with 13 thin plates in total.
Each plate is divided into 32 quadratic elements. InFig.3. deflection contours obtained by using a lrage
deflection dual boundary element method is shown.
3. CURVED STIFFENED PANELS
Dirgantara and Aliabadi carried out a nonlinear fracturemechanics analysis of stiffened curved panel. The properties of the panel are as follows: thickness = 0.05m; crack length 1 m, b=1m and 1/R = 0.1m-
1. Two
stiffeners, with A =0.0175 m2 and I=3.5989*10-4 m4,located at y = ± 0.5 m are attached to the shell. In theanalysis, BEM shell mesh has 64 boundary elements
and the stiffener is modeled with 5 nodal points each.
Figure 3: Modelling crack growth in a stiffened panel
Figure 4: Skin bulging in a reinforced fuselaje panel.
4. BUCKLING OF THIN CRACKED
PLATES
Recently Purbolaksono and Aliabadi[8] presented adual boundary element formulation for bucklinganalysis of plates with cracks. They presented the problem of a rectangular plate with longitudinal centralcrack subjected to compression. Figure 5 presents thechanges in the buckling mode of rectangular plate withaspect ratio 2. For the case of the short cracks (aspectratio of crack length to width up to 0.25), the bucklingmodes are illustrated in figure 2c.
Figure 5. Buckling of a thin cracked plate.
a
Anales de Mecánica de la Fractura Vol. I (2006)
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5. MODELLING OF WING BOX SECTION
Recently Di Pisa and Aliabadi presented the application
of the DBEM to modelling a wing section reinforced
with stiffeners which are riveted to the skin.. The
analysis which included nonlinear deflection werecarried including a crack in a lower skin. The contour
plot of the deflection is shown in figure 6.
Figure 6. A damaged wing box section.
In figure 7, result for the analysis of bonline flaw in a
super plastic diffusion bonded section is shown.
Figure 7. A bondline crack in a SPFDB.
6. SUMMARY
In this paper a brief review of the recent advances in the
application of the boundary element method to Damage
Tolerance Assessment of Aerostructures structures was
presented. The method is shown to be capable of
analyzing linear and nonlinear problems with boundary
only discretization.
REFERENCES
[1] Aliabadi,M.H. and Portela, A., Dual boundaryelement incremental analysis of crack growth in rotatingdis., Boundary Element Technology VII, BoundaryElement Technology VII, Computational MechanicsPublications, Southampton, 607-616, 1991.
[2] Portela,A., Aliabadi,M.H. and Rooke,D.P. The dual boundary element method: efficient implementation forcracked problems, Int. J. Numer. Methods in Engng, 32 ,1269-1287, 1992.
[3] Portela,A., Aliabadi,M.H. and Rooke,D.P. Dual boundary element incremental analysis of crack propagation. Computers and Structures, 46 , 237-247,1993.
[3] Mi,Y and Aliabadi,M.H. Dual boundary elementmethod for three-dimensional fracture mechanicsanalysis, Engineering Analysis, 10 , 161-171, 1992.
[4] M.H.Aliabadi A new generation of boundary
elements in fracture mechanics, Int. J. Fracture, 86 , 91-125, 1997.
[5] Mi,Y. and Aliabadi,M.H. Three-dimensional crackgrowth simulation using BEM, Computers and structures, 52 , 871-878, 1994.
[6] Salgado,A. and Aliabadi,M.H. Boundary elementanalysis of fatigue crack propagation in stiffened panels, AIAA Journal of Aircraft, 35 , 122-130, 1998.
[7] Cissilino,A.P. and Aliabadi,M.H. Three-dimensional BEM analysis for fatigue crack growth in
welded components, Int. J.Pressure Vessel and Pipping,70 , 135-144, 1997.
[8] Aliabadi,M.H. The Boundary Element Method,applications in solids and structures, Wiley, Chichester,2002,
[10] Dirgantara,T and Aliabadi,M.H. Numericalsimulation of fatigue crack growth in pressurized shells, International Journal of Fatigue, 24, 725-738, 2002.
[11] Wen,P.H., Aliabadi,M.H. and Young,A. Crackgrowth analysis for multi-layered airframe structures by boundary element method, Engineering Fracture
Mechanics, 71, 619-632, 2004
X
Y
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Uy
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Anales de Mecánica de la Fractura Vol. I (2006)
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[12] Purbolaksono,J and Aliabadi,M.H., Dual boundaryelement analysis of cracked plates under buckling loads, Int.J.Numer. Meth. Engng., 62, 537-563 2005
[13] DiPisa,C, Aliabadi,M.H. and Alaimo,A. NonlinearAnalysis of a reinforced panel undegoing largedeformation, Proceeding of the 5th InternationalConference on Boundary Element Techniques, edited by Leitao,V and Alaiabdi,M.H., EC Publications, 2004.
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