Arbitrary Lagrange Eulerian Approach for Bird-Strike Analysis Using LS-DYNA
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Arbitrary Lagrange Eulerian Approach for Bird-Strike Analysis Using LS-DYNA

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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 ...

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.

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Arbitrary Lagrange Eulerian Approach for Bird-Strike Analysis Using LS-DYNA Arbitrary Lagrange Eulerian Approach for Bird-Strike Analysis Using LS-DYNA Document Transcript

  • 2013 American Transactions on Engineering & Applied Sciences. American Transactions on Engineering & Applied Sciences http://TuEngr.com/ATEAS Arbitrary  Lagrange  Eulerian  Approach  for  Bird­Strike Analysis Using LS­DYNA  Vijay K. Goyal a b a* a , Carlos A. Huertas , Thomas J. Vasko b Department of Mechanical Engineering, University of Puerto Rico at Mayagüez, PR 00680 USA Engineering Department, Central Connecticut State University, New Britain, CT 06050 USA ARTICLEINFO 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 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. Keywords: Finite element; Impact analysis; Bird-strike; Arbitrary Lagrange-Eulerian. 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 * Corresponding author (V. Goyal), Tel.: 1-787-832-4040 ext. 2111; E-mail: 2013. American Transactions on Engineering & Applied Sciences. vijay.goyal@upr.edu. Volume 2 No. 2 ISSN 2229-1652 eISSN 2229-1660 Online Available at http://TuEngr.com/ATEAS/V02/109-132.pdf 109
  • 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 110 Vijay K. Goyal, Carlos A. Huertas, and Thomas J. Vasko
  • 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 * Corresponding author (V. Goyal), Tel.: 1-787-832-4040 ext. 2111; E-mail: 2013. American Transactions on Engineering & Applied Sciences. vijay.goyal@upr.edu. Volume 2 No. 2 ISSN 2229-1652 eISSN 2229-1660 Online Available at http://TuEngr.com/ATEAS/V02/109-132.pdf 111
  • 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) 112 Vijay K. Goyal, Carlos A. Huertas, and Thomas J. Vasko
  • 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) * Corresponding author (V. Goyal), Tel.: 1-787-832-4040 ext. 2111; E-mail: 2013. American Transactions on Engineering & Applied Sciences. vijay.goyal@upr.edu. Volume 2 No. 2 ISSN 2229-1652 eISSN 2229-1660 Online Available at http://TuEngr.com/ATEAS/V02/109-132.pdf 113
  • 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. 114 Vijay K. Goyal, Carlos A. Huertas, and Thomas J. Vasko
  • 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 . The mesh displacement is defined as 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. * Corresponding author (V. Goyal), Tel.: 1-787-832-4040 ext. 2111; E-mail: 2013. American Transactions on Engineering & Applied Sciences. vijay.goyal@upr.edu. Volume 2 No. 2 ISSN 2229-1652 eISSN 2229-1660 Online Available at http://TuEngr.com/ATEAS/V02/109-132.pdf 115
  • 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. 116 Vijay K. Goyal, Carlos A. Huertas, and Thomas J. Vasko
  • 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 * Corresponding author (V. Goyal), Tel.: 1-787-832-4040 ext. 2111; E-mail: 2013. American Transactions on Engineering & Applied Sciences. vijay.goyal@upr.edu. Volume 2 No. 2 ISSN 2229-1652 eISSN 2229-1660 Online Available at http://TuEngr.com/ATEAS/V02/109-132.pdf 117
  • 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. 118 Vijay K. Goyal, Carlos A. Huertas, and Thomas J. Vasko
  • 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. * Corresponding author (V. Goyal), Tel.: 1-787-832-4040 ext. 2111; E-mail: 2013. American Transactions on Engineering & Applied Sciences. vijay.goyal@upr.edu. Volume 2 No. 2 ISSN 2229-1652 eISSN 2229-1660 Online Available at http://TuEngr.com/ATEAS/V02/109-132.pdf 119
  • 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 120 Vijay K. Goyal, Carlos A. Huertas, and Thomas J. Vasko
  • 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]. * Corresponding author (V. Goyal), Tel.: 1-787-832-4040 ext. 2111; E-mail: 2013. American Transactions on Engineering & Applied Sciences. vijay.goyal@upr.edu. Volume 2 No. 2 ISSN 2229-1652 eISSN 2229-1660 Online Available at http://TuEngr.com/ATEAS/V02/109-132.pdf 121
  • 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 122 Vijay K. Goyal, Carlos A. Huertas, and Thomas J. Vasko
  • *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. * Corresponding author (V. Goyal), Tel.: 1-787-832-4040 ext. 2111; E-mail: 2013. American Transactions on Engineering & Applied Sciences. vijay.goyal@upr.edu. Volume 2 No. 2 ISSN 2229-1652 eISSN 2229-1660 Online Available at http://TuEngr.com/ATEAS/V02/109-132.pdf 123
  • 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. 124 Vijay K. Goyal, Carlos A. Huertas, and Thomas J. Vasko
  • 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 * Corresponding author (V. Goyal), Tel.: 1-787-832-4040 ext. 2111; E-mail: 2013. American Transactions on Engineering & Applied Sciences. vijay.goyal@upr.edu. Volume 2 No. 2 ISSN 2229-1652 eISSN 2229-1660 Online Available at http://TuEngr.com/ATEAS/V02/109-132.pdf 125
  • 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 126 Vijay K. Goyal, Carlos A. Huertas, and Thomas J. Vasko
  • 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 * Corresponding author (V. Goyal), Tel.: 1-787-832-4040 ext. 2111; E-mail: 2013. American Transactions on Engineering & Applied Sciences. vijay.goyal@upr.edu. Volume 2 No. 2 ISSN 2229-1652 eISSN 2229-1660 Online Available at http://TuEngr.com/ATEAS/V02/109-132.pdf 127
  • 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 128 Vijay K. Goyal, Carlos A. Huertas, and Thomas J. Vasko
  • 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 * Corresponding author (V. Goyal), Tel.: 1-787-832-4040 ext. 2111; E-mail: 2013. American Transactions on Engineering & Applied Sciences. vijay.goyal@upr.edu. Volume 2 No. 2 ISSN 2229-1652 eISSN 2229-1660 Online Available at http://TuEngr.com/ATEAS/V02/109-132.pdf 129
  • 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. 130 Vijay K. Goyal, Carlos A. Huertas, and Thomas J. Vasko
  • 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. Accessed http://www.ibb.uni-stuttgart.de/publikationen/fulltext/2003/linder-2003.pdf 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 * Corresponding author (V. Goyal), Tel.: 1-787-832-4040 ext. 2111; E-mail: 2013. American Transactions on Engineering & Applied Sciences. vijay.goyal@upr.edu. Volume 2 No. 2 ISSN 2229-1652 eISSN 2229-1660 Online Available at http://TuEngr.com/ATEAS/V02/109-132.pdf 131
  • 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 publication according to the guidelines given at the journal’s website. 132 Vijay K. Goyal, Carlos A. Huertas, and Thomas J. Vasko