arbitrary lagrange eulerian approach for bird-strike analysis using ls-dyna

* Corresponding author (V. Goyal), Tel.: 1-787-832-4040 ext. 2111; E-mail: [email protected]. 2013. American Transactions on Engineering & Applied Sciences. Volume 2 No. 2 ISSN 2229-1652 eISSN 2229-1660 Online Available at http://TuEngr.com/ATEAS/V02/109-132.pdf

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American Transactions on Engineering & Applied Sciences

http://TuEngr.com/ATEAS

Arbitrary Lagrange Eulerian Approach for BirdStrike Analysis Using LSDYNA Vijay K. Goyal a*, Carlos A. Huertas a, Thomas J. Vasko b

a Department of Mechanical Engineering, University of Puerto Rico at Mayagüez, PR 00680 USA b Engineering Department, Central Connecticut State University, New Britain, CT 06050 USA A R T I C L E I N F O

A B S T RA C T

Article history: Received December 23, 2012 Received in revised form 26 February 2013 Accepted March 01, 2013 Available online March 08, 2013 Keywords: Finite element; Impact analysis; Bird-strike; Arbitrary Lagrange-Eulerian.

In this third and last sequence paper we focus on developing a model to simulate bird-strike events using Lagrange and Arbitrary Lagrange Eulerian (ALE) in LS-DYNA. We developed a standard work for the two-and three-dimensional models for bird-strike events. We modeled the bird as a cylinder fluid and the fan blade as a plate. The case study was that of frontal impact of soft-bodies on rigid plates based on the Lagrangian Bird Model. Results show very good agreement with available test data and within 7% error when compared with the Lagrange and SPH methods. The developed ALE approach is suitable for bird-strike events in tapered plates.

2013 Am. Trans. Eng. Appl. Sci.

1. Introduction As we mentioned in previous two papers, the collisions between a bird and an aircraft are

known as a bird-strike events. With modern computer capabilities, we can try to simulate

bird-strike events and predict the damage to engine components [1–3]. Typically, we use the

Lagrangian method because it is easy to model such events. However, with new methods in the

2013 American Transactions on Engineering & Applied Sciences.

110 Vijay K. Goyal, Carlos A. Huertas, and Thomas J. Vasko

horizon such as Arbitrary Lagrangian Eulerian (ALE), the question is how promising are these new

methods.

When we model the bird and fan blades using the Lagrangian description, we encounter that

there is a loss of bird mass due to the fluid behavior of the bird, which causes large distortions in the

bird model. This loss of mass may reduce the real loads applied to the fan blade, which is the real

motivation to use the Arbitrary Lagrangian Eulerian [4–8] (ALE) in this work. LS-DYNA has

integrated the ALE formulation to model this fluid-structure interaction problem but the bird-strike

events have not been fully studies using this computational tool.

In the Lagrangian model, the numerical mesh moves and distorts with the physical material,

allowing accurate and efficient tracking of material interfaces and the incorporation of complex

material models. One disadvantage of this method is the negative volume error, which occurs as a

result of mesh tangling do to its sensitivity to distortion, resulting in small time steps and

sometimes loss of accuracy.

The simulations of the ALE bird-strike event performed in this work include only two

dimensional cases. The good results in two dimensional ALE simulation of a bird-strike may be

obtained by inputting into our analysis the parameters used by Souli and Olovsson [6]. The

geometrical properties of their work may not match the ones found used here, but the differences

are insignificant. The material properties for the plate have been varied along with the initial

velocity of the void/bird part and the constraints present in the SPC card for the target. The force

plots obtained resemble those generated during the ALE and Lagrangian simulations.

2. Background and Motivation Barber et al. [9] found that bird impacts in rigid targets generated peak pressures independent

of bird size and proportional to the square of the impact velocity, resulting in a fluid-like response.

Barber et al. presented the time-dependent pressure plots for the impact of birds against a rigid

cylindrical wall. This work was taken as reference to create simulations similar to those presented

by Barber et al. [9].

The MacNeal-Schwendler Co. [8] showed that the ALE description of a bird-strike against a


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leading edge is able to simulate and predict the leading edge cusp (deflection). They compared the

results using the ALE description with those of the Lagrangian description and the test data. For the

Lagrangian and ALE solution, results and CPU time were shown. For the contact algorithm, it

was not necessary to use an eroding contact algorithm but a regular Master-Slave contact for panel

bird interaction. The analysis of the Lagrangian technique took a CPU time of 1.7 hours using SGI

R8000 port of MSC/DYTRAN.

The work performed by Moffat et al. [10] was used to reproduce models of impact of birds on

tapered plates. Moffat et al. [10] worked in the use of an ALE description of bird-strike event to

predict the impact pressures and damage in the target plate. This work used the MSC/DYTRAN

code for the simulations instead of LS-DYNA which is the code used in this project. The article

presents some previous work involving rigid plate impacts from Barber et al. [9] and a flexible

tapered plate impacts from Bertke et al. [11]. These two kinds of impacts were reproduced in the

work by Moffat et al. [10] using the finite element description in MSC/DYTRAN. The geometrical

model that was used for the bird was a cylinder with spherical ends with an overall length of 15.24

cm and a diameter of 7.62 cm. The bird density is 950 kg/m3. Moffat et al. [10] found that the

pressures were insensitive to the strength of the bird and a yield stress of 3.45 MPa was taken for

the rigid plate impact analysis. For the viscosity it was necessary to take higher values for impacts

at 25°. The article shows plots of the shock pressures for different velocities and for different bird

sizes. For the tapered plate impact simulation a 7.62 × 22.86 cm plate was used. The plate was

tapered by 4° and the edge thickness was 0.051 cm which blended to 0.160 cm for the majority of

the plate. The work did not specify the kind of element that was used for the tapered plate. For

the LS-DYNA simulation performed in this research the tapered plate will be simulated using shell

elements.

In the case of the ALE formulation an Eulerian material with shear strength was chosen with a

third order polynomial equation of state. The tension cutoff was the same as in the Lagrangian

technique. For the contact algorithm an ALE fluid-structure coupling algorithm was used and an

Eulerian mesh had to be created. The bird that was modeled as an Euler fluid flows thru the

Eulerian mesh. The results showed the same variables as in the Lagrangian model. The time used


for the CPU on SGI R8000 port was one hour. The results obtained with the Lagrange model and

the ALE models were very close to the test data although the ALE simulation employed less CPU

time for the analysis stage. In addition the ALE simulation gave more accurate physical

description of bird slicing and breakup.

After a careful review, very little work was found using ALE formulation to model bird-strike

events. Thus, we developed a standard work for bird-strike events using the ALE method. We

compared the results by those obtained using the Lagrangian formulation [12] and Smooth Particle

Hydrodynamic formulation [13].

3. Impact Analysis We considered the bird at impact as a fluid material. The soft body impact results in damage

over a larger area if compared with ballistic impacts. Now, to better understand, bird-strike events

let us first understand the impact problem and then apply it to the bird-strike event being studied in

this work.

3.1 A Continuum Approach Three major equations are solved by LS-DYNA to obtain the velocity, density, and pressure of

the fluid for a specific position and time. These equations are conservation of mass, conservation

of momentum, and constitutive relationship of the material Cassenti [14]. The conservation of

momentum can be stated as follows:

(1)

where P is a diagonal matrix containing only normal pressure components, ρ the density, and V the

velocity vector. The second equation used in the analysis is the conservation of mass and it is

written as per unit volume as follows:

(2)

We can further express constitutive relation in its general form as follows:

(3)


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3.2 ALE Approach The Lagrangian method uses material coordinates (also known as Lagrangian coordinates) as the

reference. The major advantage of the Lagrangian formulation is that the imposition of boundary

conditions is simplified since the boundary nodes are always coincident with the material

boundary. Each individual node of the mesh follows the associated material particle during

motion. This allows easy tracking of free surfaces, interfaces between materials and

history-dependant relations. The major disadvantage of this method is that large deformations of

the material lead to large distortions and possible entanglement of the mesh. Since in the

Lagrangian formulation the material moves with the mesh, if the material suffers large

deformations, the mesh will also suffer equal deformation and this leads to inaccurate results.

These mesh deformations cause inaccuracy in the simulation results. To correct this problem,

remeshing must be performed which requires extra time.

Figure 1: Description of motion for Lagrange formulation.

The reference coordinates for the Lagrange method are the material coordinates (X). Let us

define RM as the material domain (reference for the Lagrangian domain) and RS as the spatial

domain. The motion description for the Lagrangian formulation is:

(4)

where is the mapping between the current position and the initial position, as shown in

Figure 1. The displacement u of a material point is defined as the difference between the current

position and the initial position:

(5)


Figure 2: Lagrange, Eulerian, ALE Methods.

Figure 3: Maps between material, spatial and referential domains.

The ALE formulation [15] is a combination of the Lagrangian and Eulerian methods. In this

method the reference coordinate is arbitrary and is generally presented as χ. Depending on the

motion, the calculations are Lagrangian based (nodes move with the material) or Eulerian (nodes

fixed and the material moves through the mesh). The user must specify the optimal mesh motion,

which is the major disadvantage of the ALE method. Figure 2 presents the differences between

the mesh motions in the Lagrangian, Eulerian and ALE formulations.


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In the ALE method, the referential domain is denoted as RR and the reference coordinates are

denoted as χ. The position of the particle may be defined as , and the mesh motion

as . The mesh displacement is defined as

(6)

The relationship between material coordinates and ALE coordinates, as shown in Figure 3, is

given by

(7)

where, by composition of functions.

For the Lagrange mesh, the nodes are assigned to material particles; therefore the mesh motion

is equal to the material motion. On the other hand, the nodes in the Eulerian mesh are fixed and the

material flows through the mesh. The ALE formulation is a combination of the Lagrange and

Eulerian, therefore the nodes can be fixed (as in the Eulerian mesh) or moving with the material

(Lagrangian mesh).

Table 1: Comparison of peak pressure for different Lagrange, SPH and ALE simulations.


Figure 4: Beam impact problem.

4. Beam Centered Impact Problem Before studying bird-strike events, we proceeded to solve a beam centered impact problem

[12]. The problem consisted in taking a simply supported beam of length, L, of 100 mm over

which a rigid object of mass, mA, of 2.233 × 10−3

kg impacts at a constant initial velocity of, (vA)

1,100 m/s. The beam has a solid squared cross section of length 4 mm, modulus of elasticity, EB,

of 205 GPa, and a density, ρB, of 3.925 kg/m3. Figure 4 shows a schematic of the problem. The

goal of this problem is to obtain the pressure maximum peak pressure exerted at the moment of

impact. The problem is solved analytically and then compared to the corresponding outputs from

LS-DYNA for the Lagrange method (Table 1).

4.1 Analytical Solution Since the impact occurs at only one point, the problem can be solved by concentrating all the

mass of the beam at the point of impact, i.e., at the center of the beam. Thus will simply the

problem to a problem of central impact between two masses, as shown in Figure 5.

Figure 5: Beam impact problem simplification.


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The impulsive time-average constant force acting during the time of the impact is found

as [12]:

(8)

where ∆ is the time it takes to complete the impact. Equation (8) has two unknowns: the

average force and the impact time. The impact time is taken to match the impact time given by

LS-DYNA, and thus performs a fair comparison. Once the impact time is known, the force is

obtained straight forward using Equation (8).

4.2 ALE Simulation We solved this problem using the Arbitrary Lagrange Eulerian (ALE) description. The major

challenge in this ALE model was that LS-DYNA does not allow the use of rigid material for the

bird and the creation of a reference void mesh around it. As discussed earlier the constitutive

relation for this material varies from that used in the Lagrange case [12].

Figure 6: ALE simulation of transversal beam impact.

Figure 6 shows the progression and the deformation obtained in this simulation. The impulse

time for this simulation was similar to that obtained using Lagrangian approach and was ∆ = 8.10

µs. Using Eq. 8, the analytical impact force was 27.58 kN. The analytical impact force was

27.65 kN and the peak pressure as 1.105 GPa. The peak force in this ALE simulation was 25.94

kN which is 6.2% lower than the analytical value. The pressure from the ALE method is

calculated as 1.037 GPa. The values obtained with the ALE model are within 6% with those


obtained using the Lagrangian model.

5. BirdStrike Impact Problem Barber et al. [9] performed an experimental characterization of bird-strike events and it was

our interest to use the ALE formulation in LS-DYNA to analyze bird-strike against flat and tapered

plates. We use the work by Barber et al. [9] as a mean of comparison. The results within 10%

would be acceptable since the actual testing model is not available.

In order to achieve a fair comparison with the Lagrange, SPH simulations and the test data, we

kept the same bird properties as in the Lagrangian case [12,13]. Two different simulations were

performed: 2D and 3D. The first one is a 2D simulation based on the work done by Souli and

Olovsson [6], which has been proven to yield acceptable results. The second model is a 3D

simulation trying to reproduce the bird strike event in solid rigid plates studied by Barber et al. [9].

Also, a 2D version of this test is created. All computer simulations generated data that are

compared with the experimental work and the Lagrangian case of the same bird-strike event.

Table 2: Bird model used for the ALE simulation.

5.1 BirdModel The bird model establishes the most important variables and parameters that better fit to high

speed bird-strike events when simulated with computer software. The ALE bird model uses

parameters given in Table 2.


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5.2 Bird Impact against a Flat Plate Here we used two different targets: a rigid flat plate and a deformable tapered plate. The

purpose of using a rigid flat plate target is to compare the simulations with the experimental data

obtained from Barber et al. [9]. Barber et al. [9] used a rigid flat plate for their experiments which

was modeled as a circular rigid plate with dimensions of 1 mm thickness and 15.25 cm of diameter.

The material of the target disk was 4340 steel, with a yield strength of 1035 MPa, Rockwell

surface hardness of C45, modulus of elasticity modulus of 205 GPa, and a Poisson’s ratio of 0.29.

These properties of the material will be used in LS-DYNA to model the flat rigid plate. The birds

used in the tests weigh about 100 grams and are fired at velocities ranging from 60 to 350 m/s. To

achieve a better simulation of the bird-strike event the densities of the computer simulated bird

must be calculated based on the masses of the tests and the recommended bird cylinder-like

computer model. The target disk must be modeled as a circular rigid plate.

Figure 7: Geometric model for the Lagrangian bird and target shell.

Figure 8: Deformation of the shell target in the ALE description.


The computer simulations are based on the data given by the Barber et al.[9] research and the

bird model used. The purpose of these simulations is to compare analytical results (computer

simulations) obtained by using the ALE method with experimental results and the current

Lagrange model. LS-DYNA data output parameters such as *DATABASE_RCFORCwere used to

obtain the impact force.

5.2.1 Bird Strike Simulation Using 2D ALE Let us begin with the 2D ALE model. First, we varied the coupling and reference system

parameters inside the *CONSTRAINT_LAGRANGE_IN_SOLIDand

*ALE_REFERENCE_SYSTEM_GROUP cards. By studying the deformations, the best results

are achieved when we take a reference system type parameter of PRTYPE=5 and a coupling type

parameter of CTYPE=5.

Here, we set the initial velocity of the model to 198 m/s (442.9 mph), which is the velocity

used in the Lagrange simulation [12]. This velocity is assigned to a node set containing the bird

and the void mesh using the *INITIAL_VELOCITY card. A moving mesh was simulated without

constraints of expansion. The material used for the target was the *MAT_PLASTIC_KINEMATIC

and for the bird and void the *MAT_ELASTIC_FLUID. A penalty coupling was used to specify

the type of coupling inside the *CONSTRAINED _LAGRANGE_IN_SOLID card. Figure 8

shows the interaction between the bird and the shell and the moving reference for the void mesh.

The void has no constraints of rotation about the z–axis.

The impacting progression for this simulation can be observed in Figure 8. It can be observed

that the modeled bird deforms to the sides although there is no a complete sliding of all of the bird

material on the target. The mesh deforms as the bird impacts the target. The reference system

follows an automatic mesh motion following a mass weighted average velocity in ALE. The

maximum pressure obtained in this.

ALE simulation is approximately 3.5 MPa. The model used in this simulation has smaller

dimensions than the dimensions of the bird tested by Barber in shot 5126A and for this reason it

was not expected to produce the same results as in the test data. However, the behavior of the

pressure between the fluid and the structure is similar to that observed in both Lagrange simulations

and experimental data by Barber et al. [9]. Once again, the steady state for this case is not as well


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captured; instead the zero value is obtained after a short period of time.

The maximum force obtained for this ALE simulation is 0.080 MN in the negative x direction.

This result can not be compared with the Lagrange simulation because the geometrical models in

both cases are not the same. The variables used in the ALE cards for this case will be used as

reference to create an ALE model that fits the geometrical dimensions of a bird strike performed by

Barber et al., specifically shot 5126 A.

5.2.2 2D ALE Simulation of Shot 5126A By changing various bird parameters, a new deformation for the model bird is created. The

deformation is shown in Figure 9. The reference system composed by the surrounding void mesh

translates following an automatic mesh motion using mass weighted average velocity. The

NADV variable (Number of cycles between advection) was changed to the flag of 1 in the

*CONTROL ALE card.

Figure 9: Deformation of the 2D ALE bird impacting a rigid plate.

The peak pressure is approximately 36 MPa, which is 10% lower than the 40 MPa measured

by Barber et al. [9] and 17.54% lower than the 43.66 MPa obtained from the Lagrangian

formulation using the elastic fluid material. In this case there is almost no variation in the impact

area when compared with the SPH and Lagrange methods. Also, in the ALE method there is no

change in the global mass of the model as in the Lagrange method. Hence, there was no change in

the mass, in contrast with the Lagrange model. This suggests that the loads generated with the

ALE method would be more accurate to the real loads generated in a bird-strike event. This also is

supported by the fact that the peak pressure obtained in the ALE method was 10% of the test data

obtained by Barber et al [9].


Figure 10: Pressure contours for the ALE simulation using NADV=1.

Figure 10 shows the pressure contour progression for this simulation at different times of the

impact. The fringe levels changes from one plot to another in different time intervals. As

observed in this figure, a shock pressure is generated at the moment of the impact. This shock

pressure travels from the front to the back of the simulated ALE bird. The highest value obtained

was 278 MPa. This is the pressure calculated for one ALE element inside of the modeled bird and

does not necessarily represent the pressure exerted on the target. The pressure contours also

confirm that the compressive shock waves, shown by Cassenti [14], are also calculated by the 2D

ALE simulation of a bird-strike.

Figure 11: Meshing of the ALE simulation of Shot 5126.

5.2.3 Bird Strike Simulation Using ALE in 3D A three dimensional ALE model in LS-DYNA of shot 5126A Barber et al. is also created.

The simulation is performed by creating a void mesh inside of the bird. The dimensions and

parameters were those corresponding to shot 5126 A. The material used for the bird was the


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*MAT_ELASTIC_FLUID and *MAT_PLASTIC_KINEMATIC for the plate. The formulation

used for the ALE bird and surrounding void mesh simulation was the one-point integration with

single material and void.

Figure 11 shows the meshing of the void material for this simulation. Also the merged nodes

on the common boundaries of the void and the cylinder can be observed. This is a necessary

condition to allow the bird material to flow through the void mesh. The number of cycles between

advection (NADV) variable inside the *CONTROL_ALE was set to one. The continuum

treatment used for this simulation was DCT = 2 (EULERIAN). The void mesh and bird moved

together with an initial velocity of 198 m/s (442.9 mph) against the rigid flat plate. The

deformation of the bird and void mesh started when the ALE bird impacts the Lagrangian target.

The penalty coupling was used to define the coupling. This means that the forces will be

computed as a function of the penetration of the bird in the target.

5.2.4 Variation of the Coupling Type Changes in the type of coupling used in the ALE model were performed in order to study the

influence of this variable in the pressure calculated by LS-DYNA for the bird-strike simulation.

The coupling type variable (CTYPE) is included in the

*CONSTRAINED_LAGRANGE_IN_SOLID card.

Using Acceleration Constraint Coupling

For this case the type of coupling used was an acceleration constraint or CTYPE=1. This

coupling was used to calculate the forces between the Lagrangian target and the ALE bird.

Although we observed a deformation of the plate after the impact, no pressure was calculated when

using acceleration constraint. The simulated ALE bird went through the flat plate without

deformation. Therefore this type of coupling is not recommended for bird-strike modeling.

Using Constrained Acceleration Velocity

The next coupling used is the constrained acceleration velocity that is the default value used by

LS-DYNA (CTYPE=2). We observed that no pressure was computed for the fluid-structure

database. Therefore, this coupling type does not produce good results for this type of problems.


Using Constrained Acceleration Velocity in the Normal direction

For this simulation the coupling type used was an acceleration velocity constraint in normal

direction only (CTYPE=3) for the coupling between the ALE bird and the Lagrangian target. No

pressure was observed.

Figure 12: Average pressure for the 3D ALE simulation of the bird-strike.

Using Penalty Coupling without Erosion

The next coupling type used was the penalty coupling (CTYPE=4). The final shape of the

deformed bird for this case encloses the same behavior to that obtained in the 2D ALE simulation.

The deformation for this simulation was not as accurate as desired and as a consequence the

pressure in the coupling interface registered an approximate value of 95 MPa as seen in Figure 12.

This value is 135% higher than the 40 MPa measured in the test data corresponding to shot 5126A

from Barber et al. [9] and 117% higher to the 43.6 MPa of the Lagrangian case. The reason is that

the equation of state is a function of time and thus the time step scale factor (TSSFAC) needs to be

changed.

5.2.5 Variation of the Time Step Scale Factor The Time Step Scale Factor (TSSFAC) inside the *CONTROL_TIMESTEP was modified in

order to change the time step used for the ALE calculations. It is desired to study how this

variation affects the final results in the time history force and pressure generated by the fluid

structure database output.


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Figure 13: Average pressure for the 3D ALE simulation

of the bird-strike with change in TSSFAC.

Table 3: Comparison of peak forces for different Lagrange, SPH and ALE tapered plate impact simulations at 0 degrees.

The TSSFAC used in the previous 3D ALE simulation was 0.35 which produced a peak

pressure of 95 MPa, as seen in Figure 12. A value of TSSFAC of 0.58 produced similar

deformation however the pressure plot changed. The new peak pressure obtained in this

simulation that was 44.85 MPa 12.25% higher than the experimental value of 40 MPa found by

Barber et al [9]. Another value used was a TSSFAC of 0.90. The deformation obtained again


was similar to previous 3D ALE simulation. The peak pressure for this case is 19.4 MPa, which is

51.4% lower than the experimental value. When the TSSFAC was set to 0.58 the peak pressure

obtained was 44.85 MPa which is 12.12% higher than the experimental value of Barber. Figure

13 shows the influence of the time step scale factor on the maximum peak pressure at the impact

time. The optimum value that for which a steady value is maintained. Thus a value of 0.58 is

selected.

Table 3 shows the comparison of the average peak pressure generated for each of the ALE

simulation with the test data from Barber et al. [9]. As observed when the TSSFAC is increased

from the original value of 0.35 it considerably decrease the error compared with the test data. The

optimum value of the pressure in which the error was the lowest possible, 12%, was obtained when

the TSSFAC was 0.58. Therefore, it can be concluded that for simulation of bird-strike using the

ALE method in 3D a value of 0.58 should be used for the TSSFAC. The error for the Lagrange

and SPH simulations are under 10% and for the 3D ALE simulation with TSSFAC the error

obtained was 12%. The material used for the Lagrange and ALE is the elastic fluid and for the

SPH was material null. The peak pressure using the 2D ALE case has a delay which is irrelevant

because it only depends on the time that takes the bird to impact the plate which is a function of the

distance in which the bird was placed initially.

6. Tapered Plate Impact at 0 Degrees Now, we model a bird striking a tapered plate as was in the case of the Lagrangian model and

SPH model. The bird properties and the tapered plate are taken as the used by Moffat et al. [10].

Two different impact angles for tapered plate are considered: 0 degrees and 30 degrees. The

material used for the bird model is *MAT_ELASTIC_FLUID with a penalty coupling. The

variables for the *REFERENCE_SYSTEM_GROUP were kept the same as in previous

simulations.

First a 2D simulation of the impact of the bird against the tapered plate was performed. The

coupling of the bird and the tapered plate needs to be calculated in all the directions. This can be

obtained setting the value of the DIREC variable inside the

*CONSTRAINT_LAGRANGE_IN_SOLID to 3. The type of coupling used in this simulation

was the penalty coupling (CTYPE=4). The peak force obtained was 0.01461 MN with an error of


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1.4% if compared with the Lagrangian simulation of the same case. It can be observed that the

bird did not go through the plate.

Figure 14: ALE Bird impacting a tapered plate at 0 degrees at different time intervals and the top

view of the tapered plate after the impact.

Table 4: Comparison of peak forces for different Lagrange, SPH and ALE tapered plate impact simulations at 30 degrees.

The results obtained in the ALE simulation of a bird-strike impact against a tapered plate at 0

degrees were similar to that of the Lagrange and SPH cases. Figure 5.22 shows the interaction of

the bird and the plate. As expected, the bird was sliced in two parts and the plate was slightly

deformed as seen in Figure 14. However, the pressure plot generated by the *DATABASE_FSI

shows that there were little interaction between the Lagrangian plate and the ALE bird. It was

necessary to vary the penalty factor in this simulation in order to calibrate the value of the force


calculated in the coupling. The penalty factor (PFAC) is used only when a penalty coupling type

is included in the keyword. The PFAC variable scales the estimated stiffness of the interacting

(coupling) system. A value of 860 was used in our case which was found to be the optimum value.

The maximum value of the average pressure was 0.0112 MN, 20.4% lower than the 0.0141 MN

computed by the Lagrange case using material elastic fluid.

The comparison for the peak force and the maximum normal deflection obtained in the

simulations of the impact of a bird against a tapered plate using Lagrange, SPH and ALE

formulations are shown in Table 4.

Figure 15: ALE Bird impacting a tapered plate at 30 degrees at different time intervals and the top

view of the tapered plate after the impact.

6.1 Tapered Plate Impact at 30 Degrees

The maximum deflection for this case was measured to be 1.18 in, 11.9% higher than the value

obtained by Moffat et al. [10]. The maximum force obtained in this simulation was 0.05319 MN

which is 6.06% higher than the Lagrange case. This value was obtained using a penalty coupling

with a penalty factor of 120.

The 3D simulation of the bird impact at 30 degrees against the deformable tapered plate


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showed that the deformation in the ALE simulation has a similar behavior as in the Lagrangian

case [12]. The maximum normal deflection shown in Figure 14 for this ALE simulation was 1.25

in which is 19.8% higher than the value found by Moffat et al. [10] and 5.65% lower than the

Lagrange case using elastic fluid material. In addition, the ALE bird suffered a little change in

dimensions only without any loss of mass.

The peak force obtained in the ALE simulation was about 0.04761 MN, 15.9% lower than

0.0566 MN obtained in the Lagrange simulation [12]. For this simulation also was necessary to

calibrate the value of the penalty factor PFAC to a value of 170, which was the optimum value.

As previously stated, the main reason for the difference is the type of material used in the ALE

method. Another reason for this could be that in the ALE simulation the bird did not presented

any loss of mass as in the Lagrangian case. Also, the SPH formulation [13] the particles of the

modeled SPH bird interact in the impact, which could be one of the causes of the low force

obtained. The difference in the time in which the peak pressure occurs for each case is irrelevant

because the time parameters and the distance from the initial position of the bird to the target were

different for each formulation.

The comparison for the peak force and the maximum normal deflection obtained in the

simulations of the impact of a bird against a tapered plate using Lagrange, SPH and, ALE

formulations are shown in Table 4.

7. Final Remarks The three computational methods (Lagrangian, SPH and ALE) used in LS-DYNA have shown

to be robust for the one-dimensional beam centered impact problem. The peak pressure from all

three cases has an error smaller than 7% when compared to the analytical results. For the

Lagrangian and SPH the error is less than 5%. Thus, the three methods can be used to study

soft-body impact problems, such as bird-strike events. For the frontal bird-strike impact against a

flat rigid plate, the best contact was the eroding contact type and the best Lagrangian material was

material elastic fluid, which is a material specialized to model a fluid-like behavior taking in

consideration the deviatoric stresses which are not considered for the null material. The Lagrangian


simulations show that the results are in within 10% when compared to already available

experimental data in the literature. The 2D ALE simulation, using an automatic mesh motion

following a mass weighted average velocity and a penalty coupling produced a peak pressure of 36

MPa, and the results were within 10% with the pressure measured by Barber et al. [9]. The peak

pressure using the 3D ALE simulations showed sensibility to the time-step scale factor (TSSFAC).

It was shown that the best time scaled parameter is that of TSSFAC=0.58 which produces an error

of 12.12% when compared with that by Barber et al. [9]. Both Lagrangian and ALE models used

the material elastic fluid which can explain the convergence in their results. For flat plate impact

simulation using a SPH bird constructed using two different mesh resolutions, if the contact

*CONTACT_CONSTRAINT_NODE_TO_SURFACE the pressure obtained is 37.3 MPa with an

error of 6.75% over the test data. Therefore, it is recommended to use the above type of contact

when studying SPH bird-strike events against rigid flat plate impacts simulations because it better

represents the deformations and pressure obtained with the test data.

For the 0 degree bird impact against a tapered plate, there was a small fluid-structure

interaction because the bird is basically sliced in two parts. This behavior is observed by all three

approaches. For the 30 degrees bird impact against a tapered plate, the Lagrangian and SPH

produce peak forces within 10% error and the maximum normal deflection are found within 13.3%

when compared to the maximum normal deflection found by Moffat. However, the maximum

normal deflection found in this ALE simulation was 1.25 in, 19.73% higher than the value found by

Moffat et al. [10]. Therefore, based on these simulations the ALE approach can be used for

bird-strike events in tapered plates.

8. Acknowledgments This work was performed under the grant number 24108 from the United Technologies Co.,

Pratt & Whitney. The authors gratefully acknowledge the grant monitors for providing the

necessary computational resources. The research presented herein is an extension of the work

presented at the 47th AIAA/ASME/ACE/AHS/ASC SDM Conference, Rhode Island, May 2006,

AIAA-2006-1759.


131

9. References [1] T. Vasko, “Fan Blade Bird-Strike Analysis and Design”, Proceedings 2000 of the 6th

International LS-DYNA Users Conference, 2000. Detroit, USA, pp.(9-13)–(9-18). http://www.dynalook.com/international-conf-2000/session9-2.pdf Accessed December 2012.

[2] C. Shultz, J. Peters, Bird Strike Simulation Using ANSYS LS/DYNA. 2002 ANSYS users conference. Pittsburgh, PA, 2002.

[3] J. Metrisin, B. Potter, Simulating Bird Strike Damage in Jet Engines, ANSYS Solutions 3 (4) (2001) 8–9.

[4] C. Linder, “An Arbitrary Lagrangian-Eulerian Finite Element Formulation for Dynamics and Finite Strain Plasticity Models”, Master’s thesis, Department of Structural Mechanics, University Stuttgart, Stuttgart (2003). 115p. http://www.ibb.uni-stuttgart.de/publikationen/fulltext/2003/linder-2003.pdf Accessed December 2012.

[5] M. Melis, Finite Element Simulation of a Space Shuttle Solid Rocket Booster Aft Skirt Splashdown Using an Arbitrary Lagrangian-Eulerian Approach. NASA/TM--2003-212093. 2003. http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20030016601_2003020325.pdf Accessed December 2012.

[6] L. Souli, M. and Olovsson, “ALE and Fluid-Structure Interaction Capabilities in LS-DYNA”, in: Proceedings of the 6th International LS-DYNA Users Conference, Detroit, USA, 2000, http://www.dynalook.com/international-conf-2000/session15-4.pdf Accessed December 2012.

[7] C. Stoker, “Developments of the Arbitrary Lagrangian-Eulerian Method in non-linear Solid Mechanics.”, PhD thesis, Universiteit Twente, The Netherlands (1999): 152. http://doc.utwente.nl/32064/1/t0000013.pdf Accessed December 2012.

[8] T. M.-S. Corporation, Bird Strike Simulation Using Lagrangian & ALE Techniques with MSC/DYTRAN.

[9] J. P. Barber, H. R. Taylor, J. S. Wilbeck, “Characterization of Bird Impacts on a Rigid Plate: Part 1”, Technical report AFFDL-TR-75-5, Air Force Flight Dynamics Laboratory, Wright-Patterson Air Force Base, OH (1975).

[10] W. Moffat, Timothy J. and Cleghorn, “Prediction of Bird Impact Pressures and Damage using MSC/DYTRAN”, in: Proceedings of ASME TURBOEXPO, Louisiana, 2001.

[11] R. S. Bertke, J. P. Barber, “Impact Damage on Titanium Leading Edges from Small Soft Body Objects”, Technical Report AFML-TR-79-4019, Air Force Flight Dynamics


Laboratory, Wright-Patterson Air Force Base, OH (1979).

[12] V. K. Goyal, C. A. Huertas, T. J. Vasko, Bird-Strike Modeling Based on the Lagrangian Formulation Using LS-DYNA. American Transactions on Engineering & Applied Sciences, 2(2): 57-81. (2013) http://TuEngr.com/ATEAS/V02/057-081.pdf Accessed March 2013.

[13] V. K. Goyal, C. A. Huertas, T. R. Leutwiler, J. R. Borrero, T. J. Vasko, Smooth Particle Hydrodynamics for Bird-Strike Analysis Using LS-DYNA. American Transactions on Engineering & Applied Sciences, 2(2): 57-81. (2013) http://TuEngr.com/ATEAS/V02/083-107.pdf Accessed March 2013.

[14] B. N. Cassenti, Hugoniot Pressure Loading in Soft Body Impacts. United Technologies Research Center, East Hartford, Connecticut, 1979.

[15] T Belytschko, WK Liu, B Moran, Nonlinear Finite Elements for Continua and Structures, John Wiley & Sons, New York, 2000.

Dr. V. Goyal is an associate professor committed to develop a strong sponsored research program for aerospace, automotive, biomechanical and naval structures by advancing modern computational methods and creating new ones, establishing state-of-the-art testing laboratories, and teaching courses for undergraduate and graduate programs. Dr. Goyal, US citizen and fully bilingual in both English and Spanish, has over 17 years of experience in advanced computational methods applied to structures. He has over 15 technical publications with another three in the pipeline, author of two books (Aircraft Structures for Engineers and Finite Element Analysis) and has been recipient of several research grants from Lockheed Martin Co., ONR, and Pratt & Whitney.

C. Huertas completed his master’s degree at University of Puerto Rico at Mayagüez in 2006. Currently, his is back to his home town in Peru working as an engineer.

Dr. Thomas J. Vasko, Assistant Professor, joined the Department of Engineering at Central Connecticut State University in the fall 2008 semester after 31 years with United Technologies Corporation (UTC), where he was a Pratt & Whitney Fellow in Computational Structural Mechanics. While at UTC, Vasko held adjunct instructor faculty positions at the University of Hartford and RPI Groton. He holds a Ph.D. in M.E. from the University of Connecticut, an M.S.M.E. from RPI, and a B.S.M.E. from Lehigh University. He is a licensed Professional Engineer in Connecticut and he is on the Board of Directors of the Connecticut Society of Professional Engineers

Peer Review: This article has been internationally peer-reviewed and accepted for

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arbitrary lagrange eulerian approach for bird-strike analysis using ls-dyna

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