Cong Gu, Goong Chen, and Tomasz Wierzbicki. Structural Failure of Aircraft Fuselage in Water Entry

Transcription

1 Structural Failure of Aircraft Fuselage in Water Entry

2 Hydrodynamic Computation and Examples

3 Hydrodynamic Computation and Examples

4 Introduction In [1], water entry process of an aircraft is simulated using CFD techniques. The aircraft is assumed to be a rigid body with free motion in a mixture of air and water. The current study aims to answer the question whether the aircraft can survive the water entry process described in the simulation. Ideally, a couple fluid-structural interaction simulation is required to fully understand the process. However, such a simulation, especially involving rapid fracture and disintegration can be quite challenging. The strategy employed here is an uncoupled structural analysis. Data are obtained from CFD simulation to serve as external load in the structural analysis. Some choices made here. A full-blown 3D analysis is avoided in this study, since such an analysis would require a more detailed description of the aircraft structure to be useful. Analysis based on rigid beam theory is used here as a simplified model. To this end, beam theory will be described and applied to the fuselage of the aircraft in the following.

5 Free-Free Rigid Beam I Dynamic failure of free-free beam was studied in [2, 3]. Plastic failure is predicted when the bending moment developed in the beam exceeds a critical value. Here, the fuselage of the aircraft is described as a rigid beam. It takes into account the bending moment, lateral displacement and rotary inertia, but not deformation of any kind. The governing equations are, for x [, L], V x + q z = λa z, N x + q x = λa x, M x V + τ = ηα, Free-free boundary condition, namely zero forcing at both ends, is used as M() = M(L) =, N() = N(L) =, V () = V (L) =.

6 Free-Free Rigid Beam II Figure 1: Direction of axes. Figure 2: Beam element subject to forces and moments.

7 Free-Free Rigid Beam III (x, y, z) are body-local axes for roll, pitch and yaw respectively (see Figure 1), q z and q x (N/m) are external force in z and x direction per unit length, τ (N m/m) is external pure torque in y direction per unit length measured at the center of cross section, V (N) is internal shear force, M (N m) is internal bending moment, N (N) is internal axial (x) force, η (kg m) is sectional moment of inertia in y direction measured at the neutral position, λ (kg/m) is linear mass density, a z and a x (m/sec 2 ) are the acceleration in z and x direction respectively, and α (1/sec 2 ) is the angular acceleration in y direction. See Figure 2 for an illustration of a beam element. All other motion are ignored.

8 Global Motion I Since CFD data is available only at certain snapshots in time, acceleration terms in the equation have to be evaluated using information from the current time instance only. This is also essential for satisfaction of boundary condition at both ends simoutaneously, which will be shown in when the equations are integrated. In general, neutral positions of cross sections should be given. But for estimation purposes, they are aligned to a line parallel to x-axis (ignored). The instantaneous global motion is described by the following rigid body dynamics,

9 Global Motion II m = T = J = L L L α = T/J, λ(x 1 ) dx 1, F x = L [ ] τ(x 1 ) q z (x 1 )(x 1 x ) dx 1, [ ] λ(x 1 )(x 1 x ) 2 + η(x 1 ) dx 1, a x (x) = ω 2 (x x ) + F x /m, q x (x 1 ) dx 1, F z = where ω is the angular velocity (1/sec) in y direction. L q z (x 1 ) dx 1, a z (x) = α(x x ) + F z /m,

10 Data Processing I Values needed for the above calculation are q z, q x, τ, λ, η and ω. Angular velocity ω is directly read from the simulation, since it won t interfere with boundary condition. Other Data input from CFD are the aircraft geometry and the external stress σ on the aircraft surface at each snapshot in time. Figure 3 shows an example of instant pressure distribution on the geometry. Figure 3: Pressure distribution on aircraft surface. Black line is the three-phase contact line.

11 Data Processing II To perform a numerical beam analysis along the x-axis, the aircraft surface is partitioned, equally in x-axis, into n segments S j, j = 1, 2,..., n. Figure 4 shows an example of partitioning into 1 segments. Piecewise constant values are assumed for numerical caluculation. Figure 4: Partition of the aircraft surface along the x-axis. Number of segments n = 1.

12 Data Processing III First, the center in z direction is calculated by z j = 1 z ds. S j This z j serves as the neutral position. Values of z j are shown in Figure 5. The distribution of mass and rotary inertia are calculated also using the available geometry. Since detailed interior model of the aircraft is not available, for simplicity, we assume mass is distributed to each segment proportional to the surface area S j. S j λ j = c l Sj, where l = L/n, and coefficient c (kg/m 2 ) is determined by matching a given total mass of the aircraft. As for the sectional moment of inertia, we assume half of the mass is uniformly distributed on the surface, and the other half is located near the neutral position, thus does not have much contribution, η j = c 2l S j (z z j) 2 ds. Values of λ and η are shown in Figure 6 and 7

13 Data Processing IV 2 15 n=1 n=25 z (m) x (m) Figure 5: Center in z direction along the aircraft body. 1 n=1 n=25 3 n=1 n= λ (kg/m) 6 4 η (kg-m) x (m) x (m) Figure 6: Distribution of mass λ along the aircraft body. Figure 7: Distribution of rotary inertia η along the aircraft body.

14 Data Processing V It is assumed that there is a pressure of p in the cabin, therefore, the external load on the beam is calculated as q j = 1 1 (σ p I)ˆn ds, τ j = (z z j)ˆk (σ p I)ˆn ds. l l S j S j q j is then projected to x and z directions as q x,j and q z,j respectively. Figures 8 1 show the distributions of external force load q x, q z and torque τ for the example given in Figure 3. Data is smoothed out a little and peak values are reduced if there is a smaller number of segments n. Relative magnitude and direction of the load along aircraft body is illustrated in Figure 11, to be compared with Figure 3.

15 Data Processing VI 2.5e+6 n=1 n=25 2.5e+6 n=1 n=25 2e+6 2e+6 1.5e+6 1.5e+6 q x (N/m) 1e+6 q z (N/m) 1e x (m) x (m) Figure 8: Distribution of external load q x along the aircraft body for the example given in Figure 3. Figure 9: Distribution of external load q z along the aircraft body for the example given in Figure 3.

16 Data Processing VII 5 n=1 n=25 τ (N-m/m) -5-1e+6-1.5e+6-2e x (m) Figure 1: Distribution of external pure torque τ along the aircraft body for the example given in Figure 3.

17 Data Processing VIII Figure 11: Relative magnitude and direction of the external load obtained in data processing is added as vector arrows to Figure 3. Note that the vertical center z j is only considered in this subsection. As mentioned previously, neutral positions are artificially aligned to a line parallel to x-axis in order to simplify calculation.

18 Direct Integration of the Beam Equations I Integration of the beam equations with boundary condition at x = gives V (x) = N(x) = M(x) = x x x [ ] q z (x 1 ) + λ(x 1 )a z (x 1 ) dx 1 [ ] q x (x 1 ) + λ(x 1 )a x (x 1 ) dx 1 [ ] V (x 1 ) τ(x 1 ) + αη(x 1 ) dx 1. The problem is to make sure the boundary condition is also satisfied at the other end x = L. In fact, by direct calculation as in Appendix, it is automatically satisfied. Figures show the strength of internal forces and bending moment for the example given in Figure 3. The comparison between n = 1 and n = 25 reveals that results do not depend much on the choice of n if n is as large as 1.

19 Direct Integration of the Beam Equations II 3e+6 3e+6 n=1 n=1 n=25 n=25 2e+6 2e+6 1e+6 1e+6 V (N) N (N) -1e+6-1e+6-2e+6-2e+6-3e x (m) -3e x (m) Figure 12: Internal shear force V along aircraft body. Figure 13: Internal axial force N along aircraft body.

20 Direct Integration of the Beam Equations III 2e+7 n=1 n=25 1.5e+7 1e+7 M (N-m) 5e+6-5e x (m) Figure 14: Internal bending moment M along aircraft body

21 Bending of Cylindrical Shell I Buckling caused by excessive compressive stress is considered here. As proposed in [4], critical compressive stress for a cylindrical shell before buckling failure is given by σ cr = Et eq R 3(1 ν 2 ), where E is the Young s modulus, t eq is shell wall thickness, R is radius of the cylinder and ν is Poisson s ratio. The maximum compressive stress induced by M and N is given by σ max = M N. πr 2 t eq 2πRt eq Therefore, we compare the effective bending moment with critical value M = M NR/2, M cr = πert2 eq 3(1 ν2 ), This is regarded as a good estimation for short cylinders. Using values from Table 1, we get M cr = N m.

22 Bending of Cylindrical Shell II Geometry Radius of cylinder R = 3.1 m Equivalent thickness t eq = 1 cm (?) Material (Aluminum 224-T351) Poisson s ratio ν =.33 Young s modulus E = 73.1 GPa Table 1: Parameters for critical bending moment calculation.

23 Bending of Cylindrical Shell III Now we find the maximum of effective bending moment M over the whole fuselage for each time snapshot t, getting M max(t). They are then plotted versus t in Figures in comparison with the critical bending moment M cr. Here are some interpretations for those four scenarios. 1e+8 M max 1e+8 M max M cr M cr 8e+7 8e+7 6e+7 6e+7 M (N-m) M (N-m) 4e+7 4e+7 2e+7 2e t (s) Figure 15: Maximum effective bending moment M max for the scenario with 8 pitch angle t (s) Figure 16: Maximum effective bending moment M max for the scenario with 3 pitch angle.

24 Bending of Cylindrical Shell IV 1e+8 1e+8 M max M cr M max M cr 8e+7 8e+7 6e+7 6e+7 M (N-m) M (N-m) 4e+7 4e+7 2e+7 2e t (s) Figure 17: Maximum effective bending moment M max for the scenario with 3 pitch angle t (s) Figure 18: Maximum effective bending moment M max for the scenario with 9 pitch angle.

25 Bending of Cylindrical Shell V Scenario with 8 pitch angle (Figure 15). Plane is generally safe from structural failure. The process is also known as ditching. Large temoprary bending moment can be observed if ditching on a wavy sea and when the speed of the aircraft is still high, for example, at around t =.7 s. See Figure 19. Scenario with 3 pitch angle (Figure 16). The plane might recover to the ditching posture. However, it have to overcome a period of large bending moment when the middle or tail parts of the fuselage hit water, for example, at around t =.78 s. See Figure 2. Scenario with 3 pitch angle (Figure 17). The plane is subject to large axial compression and asymmetric external load, for example, starting from t =.4 s. Therefore the aircraft is most likely to suffer global failure. See Figure 21. Scenario with 9 pitch angle (Figure 18). The plane is subject to axial compression, but not much bending due to the symmetric external load. This lasts until wings reach the water, which is not simulated. See Figure 22.

26 Bending of Cylindrical Shell VI Figure 19: External load and axial stress for the scenario with 8 pitch angle at t =.7 s. Figure 2: External load and axial stress for the scenario with 3 pitch angle at t =.78 s.

27 Bending of Cylindrical Shell VII Figure 21: External load and axial stress for the scenario with 3 pitch angle at t =.5 s. Figure 22: External load and axial stress for the scenario with 9 pitch angle at t =.2 s.

28 Other Failure Modes Tearing, shear, stringers, rings, etc.

29 Appendix: Boundary Condition at x = L M(L) L L L = V (x 2 ) dx 2 τ(x 1 ) dx 1 + α η(x 1 ) dx 1 L x 2 [ ] L L = qz (x 1 ) + λ(x 1 )az (x 1 ) dx 1 dx 2 τ(x 1 ) dx 1 + α η(x 1 ) dx 1 L [ ][ ] L L = (L x ) (x 1 x ) qz (x 1 ) + λ(x 1 )az (x 1 ) dx 1 τ(x 1 ) dx 1 + α η(x 1 ) dx 1 L [ ( )] = (L x ) qz (x 1 ) + λ(x 1 ) α(x 1 x ) + Fz /m dx 1 L [ ( )] L L (x 1 x ) qz (x 1 ) + λ(x 1 ) α(x 1 x ) + Fz /m dx 1 τ(x 1 ) dx 1 + α η(x 1 ) dx 1 L L L = (L x ) qz (x 1 ) dx 1 α λ(x 1 )(x 1 x ) dx 1 + (Fz /m) λ(x 1 ) dx 1 L [ ] L [ τ(x 1 ) qz (x 1 )(x 1 x ) dx 1 + α λ(x 1 )(x 1 x ) 2 ] + η(x 1 ) dx 1 L (Fz /m) λ(x 1 )(x 1 x ) dx 1 [ ] = (L x ) Fz + (Fz /m) m T + αj =

30 G. Chen, C. Gu, P. J. Morris, E. G. Paterson, A. Sergeev, Y.-C. Wang, and T. Wierzbicki. Malaysia airlines flight MH37: water entry of an airliner. In: Notices of the AMS 62.4 (215), pp N. Jones and T. Wierzbicki. Dynamic plastic failure of a free-free beam. In: International Journal of Impact Engineering 6.3 (1987), pp J. Yang, T. Yu, and S. Reid. Dynamic behaviour of a rigid, perfectly plastic free free beam subjected to step-loading at any cross-section along its span. In: International journal of impact engineering 21.3 (1998), pp S. Timoshenko and J. M. Gere. Theory of elasticity stability. McGraw, 1961.

31 Study of Impact of Aircraft on Solids: Applications of LS-DYNA and ANSYS Explicit Dynamics Goong Chen 1, Yi-Ching Wang 2, and Alain Perronnet 3 1: Goong Chen is professor of mathematics at Texas A&M University (TAMU) and Texas A&M University at Qatar (TAMUQ). He is also a member of the Institute for Quantum Science and Engineering at TAMU. His address is gchen@math.tamu.edu. 2: Yi-Ching Wang is a Ph.D. student in the mathematics department of TAMU. Her address is ycwang@math.tamu.edu. 3: Alain Perronnet is professor of applied mathematics at Université Pierre et Marie Curie, Paris, France. His address is perronnet@ljll.math.upmc.fr. Goong Chen 1, Yi-Ching Wang 2, and Alain Perronnet 3 Study of Impact of Aircraft on Solids: Applications of LS-DYNA and

32 Abstract Numerical simulation can help us comprehend and control man-made disasters. Air craft crashworthiness and human survivability are of utmost concerns in any emergency landing situation. Motivated by the air incident, Germanwings Flight 9525 crash in March 215, we use Computational Structural Dynamics (CSD) software LS-DYNA and ANSYS Explicit Dynamics to try different numerical simulations of Airbus A32 crashing into a wall and compare the results to the reality. Goong Chen 1, Yi-Ching Wang 2, and Alain Perronnet 3 Study of Impact of Aircraft on Solids: Applications of LS-DYNA and

33 1. Introduction On March 24, 215, one deliberate air incident, Germanwings Flight 9525, an Airbus A32-2, crashed into the French Alps during the fight from Barcelona to Düsseldorf. The co-pilot locked the captain out of the cockpit during the flight and began a rapid descent intensionally. The aircraft descended from 38 ft to 6 ft in 8 minutes and crashed into the mountain peak with 43 mph. Due to this high speed, the impact was very hard so there were no big pieces like wings or cockpit, only a lot of little pieces in the crash site. All 15 passengers and crew members were killed in this crash. Goong Chen 1, Yi-Ching Wang 2, and Alain Perronnet 3 Study of Impact of Aircraft on Solids: Applications of LS-DYNA and

34 Figure 1: Crash Site. Wreckage and debris lie on the French Alps mountain everywhere after the crash of the Germanwings Airbus A32 on March Goong Chen 1, Yi-Ching Wang 2, and Alain Perronnet 3 Study of Impact of Aircraft on Solids: Applications of LS-DYNA and

35 The paper, Computer simulation of an F-4 Phantom crashing into a reinforced concrete wall by M. Itoh, M. Katayama and R. Rainsberger, presents a numerical simulation of an aircraft F-4 Phantom jetfighter crashing into a reinforced concrete wall by using a general-purpose hydrocode AUTODYN. It also compares computational results with the experimental ones of a full-scale aircraft impact test which was conducted by Sandia National Laboratories in New Mexico, USA, in Snapshots of crushing behaviour of the aircraft are illustrated in the next two pages. Goong Chen 1, Yi-Ching Wang 2, and Alain Perronnet 3 Study of Impact of Aircraft on Solids: Applications of LS-DYNA and

36 Figure 2: Deformed mesh configurations after impact. Goong Chen 1, Yi-Ching Wang 2, and Alain Perronnet 3 Study of Impact of Aircraft on Solids: Applications of LS-DYNA and

37 Figure 3: Deformed mesh configurations after impact. (cont.) Goong Chen 1, Yi-Ching Wang 2, and Alain Perronnet 3 Study of Impact of Aircraft on Solids: Applications of LS-DYNA and

38 2. What s LS-DYNA LS-DYNA is a finite element analysis software package developed by Livermore Software Technology Corporation (LSTC) to solve complex real world problems. It combines both implicit and explicit solvers. It provides the capabilities to simulate different engineering problems in the automobile, aerospace, construction, military, manufacturing, and bioengineering industries. Goong Chen 1, Yi-Ching Wang 2, and Alain Perronnet 3 Study of Impact of Aircraft on Solids: Applications of LS-DYNA and

39 3. How to use LS-DYNA There are three steps to run LS-DYNA: create geometry and generate mesh by its own preprocessor, LS-PrePost. set up the models in an input file (.k) and run calculation. view the results and make animation videos in LS-PrePost Goong Chen 1, Yi-Ching Wang 2, and Alain Perronnet 3 Study of Impact of Aircraft on Solids: Applications of LS-DYNA and

40 End time in.k file of the airplane crash problem: Goong Chen 1, Yi-Ching Wang 2, and Alain Perronnet 3 Study of Impact of Aircraft on Solids: Applications of LS-DYNA and

41 Initial velocity in.k file of the airplane crash problem: Goong Chen 1, Yi-Ching Wang 2, and Alain Perronnet 3 Study of Impact of Aircraft on Solids: Applications of LS-DYNA and

42 One example of plastic material airplane and rigid granite in.k file of the airplane crash problem: Goong Chen 1, Yi-Ching Wang 2, and Alain Perronnet 3 Study of Impact of Aircraft on Solids: Applications of LS-DYNA and

43 4. What s ANSYS Explicit Dynamics ANSYS Explicit Dynamics is a computational structural dynamics (CSD) software package developed by vendor ANSYS to simulate the impacts or short-duration high-pressure loadings problems. It uses the Finite Element Method to solve the governing equations. There are three steps to run Explicit Dynamics: create geometry and generate mesh. determine and select the settings of both material and mechanical model and run calculation. display results. Goong Chen 1, Yi-Ching Wang 2, and Alain Perronnet 3 Study of Impact of Aircraft on Solids: Applications of LS-DYNA and

44 There are many property models and parameters for materials. We need to choose carefully for our case. It is important to choose efficient mesh methods for the aircraft. Goong Chen 1, Yi-Ching Wang 2, and Alain Perronnet 3 Study of Impact of Aircraft on Solids: Applications of LS-DYNA and

45 Goong Chen 1, Yi-Ching Wang 2, and Alain Perronnet 3 Study of Impact of Aircraft on Solids: Applications of LS-DYNA and

46 5. Supercomputer Simulations and Examples of Video Animations The representative aircraft model we use here is Airbus A32. We use the aircraft speed 2 m/s and the pitch angle. The physical parameter values of the aircraft are listed in the following Table. Total weight kg Wing span 35.8 m Height 11.76m Overall length m Box 1: Parameter values for Airbus A32 used in our calculations. Goong Chen 1, Yi-Ching Wang 2, and Alain Perronnet 3 Study of Impact of Aircraft on Solids: Applications of LS-DYNA and

47 We simulate three cases by LS-DYNA and ANSYS Explicit Dynamics on Texas A&M Supercomputing Facility s Eos, an IBM idataplex Cluster 64-bit Linux, Intel Nehalem processors. For LS-DYNA, it takes CPU time 24 hours to run for.19 second with 2 CPUs. For ANSYS Explicit Dynamics, it takes CPU time 2 hours to run for.1 second with 8 CPUs. All of these three cases are under the same physical material properties. Case 1: Aircraft crashes into a mountain by LS-DYNA Case 2: Aircraft crashes into a wall by LS-DYNA Case 3: Aircraft crashes into a wall by ANSYS Explicit Dynamics Goong Chen 1, Yi-Ching Wang 2, and Alain Perronnet 3 Study of Impact of Aircraft on Solids: Applications of LS-DYNA and

48 Case 1: Aircraft crashes into a mountain by LS-DYNA The aircraft mesh is made up of nodes and quadrangles by LS-DYNA. The dynamic motions of animation videos can be viewed in the following links: aircraftmountain1.avi mesh version aircraftmountain2.avi different angle aircraftmountain3.avi Goong Chen 1, Yi-Ching Wang 2, and Alain Perronnet 3 Study of Impact of Aircraft on Solids: Applications of LS-DYNA and

49 Case 2: Aircraft crashes into a wall by LS-DYNA The wall mesh is composed of 424 hexahedra and the aircraft mesh is made up of nodes, 2448 quadrangles by LS-DYNA. The dynamic motions of animation videos can be viewed in the following links: different angle: http: // http: // http: // http: // Goong Chen 1, Yi-Ching Wang 2, and Alain Perronnet 3 Study of Impact of Aircraft on Solids: Applications of LS-DYNA and

50 View from inside of the aircraft: http: // View from inside of the wall: http: // Goong Chen 1, Yi-Ching Wang 2, and Alain Perronnet 3 Study of Impact of Aircraft on Solids: Applications of LS-DYNA and

51 Case 3: Aircraft crashes into a wall by ANSYS Explicit Dynamics The aircraft and wall mesh are made up of 8419 nodes, elements by ANSYS Explicit Dynamics. The dynamic motion of animation video can be viewed in the following links: different angles: (the eroded nodes which show up as red dots) Goong Chen 1, Yi-Ching Wang 2, and Alain Perronnet 3 Study of Impact of Aircraft on Solids: Applications of LS-DYNA and

52 6. Concluding Remarks Our computations and numerical simulations are still in progress. These are highly challenging simulations and there are many difficulties we need to overcome. There are hundreds of parameters for material models in LS-DYNA and ANSYS Explicit Dynamics. We need to determine and adjust values of parameters carefully to get reasonable results. We also need to add more structures of aircraft such as rings, seats, engine, and fuel tank. The explosion caused by fuel tank during the crash needs to be considered as well. We would also like to include cases with different pitch angles and velocities. Our simulations still need to be improved to be close to the real case. Goong Chen 1, Yi-Ching Wang 2, and Alain Perronnet 3 Study of Impact of Aircraft on Solids: Applications of LS-DYNA and