Validation of Computational Structural Dynamics Models for Parachute Systems

Transcription

1 20th AIAA Aerodynamic Decelerator Systems Technology Conference and Seminar<BR> 4-7 May 2009, Seattle, Washington AIAA Validation of Computational Structural Dynamics Models for Parachute Systems Matthew Pruett 1 and Michael Accorsi 2 University of Connecticut, Storrs, CT, and Richard D. Charles 3 U.S. Army Natick Soldier Research, Development & Engineering Center, Natick, MA, A validation study was performed to evaluate the ability of two computational structural dynamics models (TENSION and LS-DYNA) to accurately simulate the mechanical behavior of fabric structures such as parachute systems. The validation tests involved large shape changes of fabric structures and therefore evaluated the ability of the models to simulate fabric anisotropy and wrinkling in a geometrically nonlinear analysis. Experimental results from three distinct laboratory tests were used to perform the validation study. The first test was a fabric cylinder that was loaded biaxially through internal pressure and axial extension. The second test was a square airbag that was internally pressurized. The third test was a round parachute model with hydrostatic loading. Validation of these computational models will provide the parachute industry with the required technical evidence that these tools are appropriate for design of parachute systems. I. Introduction arachute Decelerator Systems (PDS) have traditionally been designed using semi-empirical formulas P 1 supplemented by full-scale drop tests and wind tunnel tests to insure that the design is adequate. This approach to design is expensive due to the cost of physically testing parachute systems and can hamper progress on a project due to the time required to perform tests. The ability to accurately model a deceleration system without having to build and test prototypes would greatly benefit the parachute community and facilitate the development of new parachute designs. The use of computational simulations, based on Finite Element Analysis (FEA), to analytically model parachute systems has emerged as the most promising technique to fulfill this need. Although FEA has been commercially available for decades, the application of FEA to parachute systems is not trivial. As with any modeling method, there is a need to validate the model by comparing its predictions to results obtained by physical testing. To date, much of the work applying FEA to parachute systems has been qualitative and there still exists a strong need to perform validation studies in this area. The general operation of a parachute system involves strong dynamic interaction of a highly flexible fabric structure (i.e. the parachute) with the surrounding airflow. In general, a computational structural dynamics (CSD) model is needed to model the fabric structure, a computational fluid dynamics (CFD) model is needed to model the airflow, and a coupling algorithm is needed to capture the fluid-structure interaction (FSI) effects. Therefore, comprehensive validation studies are needed that not only validate the composite FSI simulations but also validate the constituent CSD and CFD models. The focus of the current study is validation of two CSD models for parachute systems. Structural modeling of parachute systems is not trivial due to the large, geometrically nonlinear (GNL) motion of the system and the characterization of fabric behavior and properties for GNL analysis. In general, the mechanical properties of fabrics are not only anisotropic but also the fabric anisotropy can evolve with motion of the structure. 1 Graduate Research Assistant, Department of Civil & Environmental Engineering. 2 Professor, Department of Civil & Environmental Engineering, Senior Member 3 Research Aerospace Engineer, Airdrop Technology Team, Senior Member 1 Copyright 2009 by the, Inc. All rights reserved.

2 Modeling of the evolving fabric anisotropy is critical to accurately capture the load carrying capacity of the structure. Another important attribute of fabric behavior is their inability to support compressive stresses, commonly referred to as wrinkling. Therefore, a CSD model for parachute systems requires accurate methods to model wrinkling of anisotropic fabrics within a geometrically nonlinear framework. These complex issues contribute to the uncertainties associated with structural modeling of parachute systems and highlight the need for validation studies. To date, TENSION and LS-DYNA have been the two FEA codes most widely used for simulation of parachute systems. The TENSION code was developed jointly by personnel at the University of Connecticut and U.S. Army Natick Soldier Research, Development, and Engineering Center and the underlying theory and various verification and application problems have previously been presented 2-4. LS-DYNA is a general purpose commercial FEA code that is used extensively in industry 5 and the application of LS-DYNA to a variety of parachute problems has previously been published 6-8. In the current study, a validation study of TENSION and LS-DYNA for CSD modeling of parachute systems is performed. Both codes are used to perform simulations corresponding to three different fabric structures that were tested experimentally. The simulation results are then compared to the test results to perform the validation study. II. Methodology Standard biaxial tension tests were first performed on parachute fabrics to evaluate its mechanical behavior and to provide the mechanical properties needed for the FEA models. Figure 1 shows the apparatus used to perform the biaxial tension tests and Figure 2 shows a typical stress-strain curve obtained from the test. Although the fabrics showed some material nonlinearity, the stress-strain behavior can reasonably be characterized as linear elastic for the tested range. Figure 2 illustrates that the elastic moduli in the warp and fill directions are significantly different. Additional tests indicated that both the shear modulus and Poisson s ratio were negligible. Therefore, the fabric was characterized as a linear elastic, orthotropic material with distinct moduli in the warp and fill directions with negligible shear modulus and Poisson s ratio. It should also be noted that the fabrics were tested up to approximately 7% strain in these tests. Stress vs. Strain oz / sq. yd. fabric 30 warp stress, warp extension 25 fill stress, fill extension 20 Stress (N/cm) Strain Figure 1. Biaxial fabric testing setup Figure 2. Stress versus strain curves for the 1.1 oz fabric The validation tests were performed at the University of Massachusetts Lowell and are classified into three different types based upon the test configuration 9. In the first test, a cylinder of fabric is internally pressurized then pulled in the axial direction which is an alternate means to conduct biaxial testing 10. In the second test, an initially square fabric airbag is internally pressurized. In the third test, a small scale parachute is suspended upside down and incrementally filled with water. Multiple trials were conducted for each test type including variations in the fabric orientation, loading, and configuration size depending upon the test type. An ARAMIS digital imaging system was used to measure full field displacements of the fabric structures during the tests 9. This system images the test structure from one side and, therefore, can only capture the visible portion of 2

3 a three-dimensional structure. Drop-offs in data occur in regions not visible to the cameras. The coordinates of unstructured points on the deformed surface are the primary output data. To facilitate processing of the results, the raw output data was interpolated over a uniform grid of points. The series of cylinder tests consisted of hollow fabric cylinders measuring 13 in. (33.0 cm.) long and 4 in. (10.2 cm) in diameter fixed at each end by clamps, as shown in Figure 3. The cylinders were pressurized to 4, 8, and 12 psi (27.6, 55.2 and 82.7 KPa). Once pressurized, one end of the cylinder was displaced away from the other end, elongating the cylinder axially. This was done until failure of the material or the maximum displacement of the machine was reached. During this displacement, the internal pressure was kept constant. This was carried out for two fabric orientations with (1) the fabric warp direction in the circumferential direction of the cylinder and (2) the fabric fill direction in the circumferential direction of the cylinder. The cylinder was imaged when the cylinder was pressurized and then for every in. (0.1 mm) of axial displacement throughout the tests. The main item for comparison in these tests is the cylinder radius. The airbag test consists of a square airbag measuring 38 in. by 38 in. (96.5 cm. by 96.5 cm.) and pressurized to specific values as shown in Figure 4. The specific values of pressure varied between fabrics depending on their porosity. The material orientation was not varied in these tests. The fabric warp and fill directions were aligned with the edges of the square. The deformed shape and contours plots of the transverse displacement will be one comparison of the analyses. Cross sections through the deformed airbag in the vertical, horizontal, and diagonal directions will also be compared. The canopy test consisted of two different size canopies connected to a support by 16 suspension lines which were loaded with increasing amounts of water as shown in Figure 5. One setup used a circular fabric pattern with a diameter of in. (28.6 cm) and 12 in. (30.5 cm.) suspension lines that were attached to a 1 (2.5 cm.) diameter mounting disk. The larger setup had a diameter of (59.1 cm.) and 24 in. (61.0 cm.) suspension lines. A coating was applied to the fabric so that it could contain the water without leaking. The effect of this coating was not included in the FEA models but is expected to be negligible. The main measurements obtained from this test were the volume of water introduced into the canopy and the resulting height of water as well as the shape of the loaded canopy. Figure 3. Test setup for the cylinder trials Figure 4. Test setup for the airbag trials 3

4 Figure 5. Test setup for the canopy trials III. Results The cylinder tests are characterized by relatively small displacements but large strains in both the circumferential and axial directions. The stresses and strains are fairly uniform over the surface (except near the boundaries) and there is no wrinkling in this problem. Because of the large strains, accurate measurement of the elastic moduli is important in this validation test. The standard biaxial test (Figure 1) used to determine the elastic moduli and all the validation tests (Figure 3) were performed in two different labs with different operating conditions (temperature, humidity, etc) which could affect the mechanical properties of the fabric. Despite this, the properties measured from the standard biaxial tests were used for all the validation simulations. The experimental data obtained from this test were coordinates on a portion of the deformed cylinder surface. Data was only obtained for the portion of the surface that was visible to the digital imaging cameras. The data was processed by fitting circles to the experiment data at each section along the axis of the cylinder. The average of the radii of these circles was then reported as the deformed radius for the test. Figure 6 is a plot of the deformed cylinder radius versus cylinder pressure with the fill thread in the circumferential direction and zero axial extension. Radii are plotted for a simple analytical solution, TENSION, DYNA, and the experiments. The simple analytical solution corresponds to a linear solution for the radial expansion of an unrestrained circular cylinder under internal pressure 11 u r pr Et 2 where u r is the radial displacement, p is the internal pressure, r is the radius, E is Young s modulus in circumferential direction and t is the fabric thickness. It should be noted that the circumferential strains in this test run from approximately 7% to 15% for the range of pressures used. These values are considerably higher than the biaxial tests used to determine the material properties. Despite this difference, reasonable agreement between the experimental results and FEA results are achieved in this test. 4

5 Figure 6. Radius versus pressure for inflated cylinder with fill thread in circumferential direction (analytical, experimental, and FEA results). Figure 7 is a similar plot for the case where the warp thread is in the circumferential direction. In this test, the circumferential strains vary from approximately 4% to 10% for the range of pressures used. These strain levels are much closer to those used to measure the fabric material properties. In this test, agreement of the experiment results with the FEA results is quite good. Figure 7. Radius versus pressure for inflated cylinder with warp thread in circumferential direction 5

6 (analytical, experimental, and FEA results). The relationship between the deformed radius and axial extension is shown in Figure 8 and Figure 9 for the fill and warp threads oriented in the circumferential direction, respectively. It can be seen that overall, in both the computational and experimental results, the radius does not change significantly when the ends are displaced axially. Figure 8. Radius versus axial displacement for inflated cylinder pressurized to 8 psi with fill thread in circumferential direction (experimental and FEA results). 6

7 Figure 9. Radius versus axial displacement for inflated cylinder pressurized to 8 psi with warp thread in circumferential direction (experimental and FEA results). In general, the comparisons between the experimental and FEA results for the cylinder tests show good correlation. The FEA results correctly predict the observed behavior with regard to increasing internal pressure and axial extension. Differences between the measurements and simulations are attributable to several factors. First, the tests to determine input properties and the cylinder tests were performed in two different labs. Second, the change in radius compared to the original radius is small and therefore subject to measurement error. Third, the experimental results did not correspond to perfectly cylindrical shapes indicating that physical setup and execution of the tests introduced some inaccuracy. Finally, the cylinder tests with the fill fibers in the circumferential direction have significantly higher strains than the fabric characterization tests. Despite these differences, the correlation between the tests and simulations were quite good. The airbag problem is characterized by large displacements and relatively small strains with a considerable amount of wrinkling over the airbag surface. The shape of the inflated airbag is the primary result for comparison which accounts for displacements in both the in-plane and transverse directions. Both FEA codes have specific algorithms to account for fabric wrinkling so they should have been able to successfully model the airbag. As with the cylinder tests, the experimental data for the airbag was difficult to use in its raw form so some data processing was needed to extract the required data for comparisons. The experimental data was interpolated over a square grid of uniformly spaced points. Figure 10 shows the top view of the deformed shape of the airbag predicted by TENSION and LS-DYNA (center and right, respectively). The color contours correspond to the magnitude of the transverse displacement. It is seen that these two FEA results agree extremely well. The shape of the deformed airbag which is determined by the in-plane displacements agree very well. The contours which indicate the transverse displacements also agree very well. On the left, there is a contour plot of the transverse displacement obtained from the interpolated experimental data over the entire grid. It can be seen that the experimental data around the perimeter of the deformed airbag is not clear due to imaging limitations and data drop-off. It can also be seen that positioning of the airbag within the Cartesian grid is slightly skewed. In general, however, the transverse displacement contours of the experimental data agree very well with the FEA contours. Figure 11 is a plot of the raw test data (red) and the interpolated data (blue) which more clearly shows the skewing of the airbag. 7

8 Figure 10. Contour plot of airbags showing experimental (left), TENSION (center), and LS-DYNA (right) results Figure 11. Plot showing orientation and skew of experimental data and grid of interpolated data Cross sections were taken through the experimental and numerical results to compare the deformed shapes at various sections. Vertical, horizontal and diagonal sections across the airbag and through the center point were used. The diagonal sections are shown in Figure 12. The experimental results (solid blue lines) are not perfectly symmetric due to the skew in the airbag position. Despite this, agreement between the experimental results and FEA results (blue and green symbols) is excellent. Figure 13 shows sections taken vertically and horizontally across the airbag. Again, the agreement between experimental and FEA results is excellent. 8

9 Figure 12. Shape of the inflated airbag along the diagonal sections (solid blue line is experiment, blue symbol is TENSION and green symbol is LS-DYNA) Figure 13. Shape of the inflated airbag along vertical and horizontal sections (solid blue line is experiment, blue symbol is TENSION and green symbol is LS-DYNA) The canopy test gives the opportunity to evaluate the ability of the codes to predict large displacements with regions that are taut, wrinkled and slack. In a taut region, there is tension in both principal directions. In a wrinkled 9

10 region, there is tension in only one principle direction and wrinkling occurs in the second principle direction. In a slack region, there is no tension in either principle direction resulting in wrinkling in both directions. Similar to the airbag, the canopies have large displacements with relatively low strain due to the fluid loading. The wrinkling/slack aspect of the canopy is more extensive because the tests with low fluid depths are almost entirely wrinkled or slack with only the portions of the canopy leading to the suspension lines under stress. The relationship between the added fluid volume and the resulting fluid height is measured experimentally and provides a good metric for the validation study. The results showing the relationship between fluid height and fluid volume for the 12 in. (30.5 cm.) canopy is shown in Figure 14. The correlation between LS-DYNA, TENSION, and the test data is excellent demonstrating that both of FEA codes were able to model the canopy well. Figures 15 and 16 show side and bottom views of the deformed 12 in. (30.5 cm.) canopy with 9.3 cm of water for LS-DYNA and TENSION, respectively, with the experimental results overlaid in green. The test data is very limited in this case. The binocular nature of the imaging system has a larger drop-off effect in the canopy than in the airbag due to the large extent of wrinkling and overall curvature of the canopy. Although specific comparisons are made difficult by the lack of experimental points, it appears that both FEA results are similar to the experimental data. The outside dimensions of the partially loaded canopy in the bottom views of Figures 15 and 16 predicted by DYNA and TENSION, respectively, are quite similar. However, the specific shapes are somewhat different in their details. The TENSION result preserves the cyclic symmetry created by the 16 suspension lines more clearly than the DYNA result. This is most likely because much of the canopy is fully slack and the canopy shape does not have a single unique solution. The specific shapes calculated by the two FEA codes depend on the nuances of the codes in modeling slack regions as well as the mesh used. A significant difference between the two FEA codes is that DYNA uses an explicit time integration scheme whereas TENSION uses an implicit scheme. Although the problem is inherently static, the FEA static solutions were calculated as the steady state of a dynamic problem with moderate damping. Since explicit methods do not iterate to achieve convergence within a specified tolerance, the solution accuracy may not be sufficient to retain the highly cyclic symmetric response in this case where extensive slack regions exist. 12" canopy - Water volume vs. Water depth Water volume (cm^3) LS-DYNA TENSION UMASS Water depth (cm) Figure 14. Water volume versus water depth for the 12 in. canopy 10

11 Figure 15. LS-DYNA nodal points (magenta) and experimental results (green) for the 12 in. canopy loaded to a depth of 9.3 cm Figure 16. TENSION nodal points (blue) and experimental results (green) for 12 in. canopy loaded to a depth of 9.3 cm Profiles of the 12 in. (30.5 cm.) canopies loaded to 3.3 cm of fluid are shown in Figures 17 and 18 for DYNA and TENSION, respectively. These results are similar to the previous case but somewhat more extreme in that the amount of slack regions present is greater. Again, the TENSION solution is able to retain the cyclic symmetry imposed by the 16 suspension lines which is not apparent in the DYNA solution. 11

12 Figure 17. LS-DYNA nodal points (magenta) and experimental results (green) for the 12 in. canopy loaded to a depth of 3.3 cm Figure 18. TENSION nodal points (blue) and experimental results (green) for the 12 in. canopy loaded to a depth of 3.3 cm The relationship between water volume and water height for the 24 in. (61.0 cm.) canopy is given in Figure 19. Agreement between the two FEA predictions and the experimental results is excellent. The increased size of this canopy allowed for more of the surface profile to be imaged. Figures 20 and 21 show the LS-DYNA and TENSION profiles, respectively, along with the experimental data for the 24 in. (61.0 cm.) canopy loaded to a depth of 16.2 cm. In general, the FEA surface profiles agree well with the experimental profile for this case. Figures 22 and 23 show the LS-DYNA and TENSION surface profiles, respectively, along with the experimental data for the large canopy loaded to a depth of 6.0 cm. The difference between the two codes is clearer here. Although both codes give the correct volume/height relation, the TENSION code is better able than DYNA to predict the highly wrinkled/slack profile for this case. 24" Canopy - Water volume vs. Water depth Water volume (cm^3) LS-DYNA TENSION UMASS Water depth (cm) Figure 19. Water volume versus water depth for the 24 in. canopy 12

13 Figure 20. LS-DYNA nodal points (magenta) and experimental results (green) for the 24 in. canopy loaded to a depth of 16.2 cm Figure 21. TENSION nodal points (blue) and experimental results (green) for the 24 in. canopy loaded to a depth of 16.2 cm 13

14 Figure 22. LS-DYNA nodal points (magenta) and experimental results (green) for the 24 in. canopy loaded to a depth of 6.0 cm Figure 23. TENSION nodal points (blue) and experimental results (green) for the 24 in. canopy loaded to a depth of 6.0 cm IV. Conclusions The goal of this study was to experimentally validate the ability of TENSION and LS-DYNA to accurately predict the nonlinear behavior of fabric structures using three test configurations. Simulations of the three test configurations were performed using input data obtained from basic material characterization tests. Simulation results were compared to data obtained through digital imaging of the test structures. In general, the correlation between the simulations results and experimental data was quite good for both FEA codes and both codes are deemed to be acceptable for structural modeling of fabric structures such as parachutes. The cylinder tests, which involved large strains, illustrate the need for reliable characterization of the material properties. The material properties of fabrics depend on many factors, such as strain level, temperature and humidity, and therefore this task is not trivial. Since accurate stress predictions ultimately depend on material properties, characterization of fabric properties should be a high priority for the parachute industry. The airbag tests and canopy tests were both characterized by large shape changes but relatively small strain. Correlation between the FEA simulations and test results was extremely close since these tests rely less on the material properties. Acknowledgments This work was supported by the U.S. Army Natick Soldier RD&E Center as part of their Airdrop Modeling and Simulation Validation and Verification program. The authors would like to gratefully acknowledge the work and contributions of data and images of Dr. Thomas Godfrey of the Natick Soldier RD&E Center, Macromolecular Science Team, for the fabric material properties data and images, and Dr. Christopher Niezrecki of the University of Massachusetts Lowell for the experimental data and images of the inflated test cases. References 1 Ewing, E., Bixby, H. and Knacke, T., Recovery System Design Guide, Technical Report AFFDL-TR , Air Force Flight Dynamics Laboratory, Wright-Patterson Air Force Base, OH, Accorsi, M., Leonard, J., Benney, R. and Stein, K., Structural Modeling of Parachute Dynamics, AIAA Journal Vol. 38, Issue 1, Pages , Lu, K., Accorsi, M., and Leonard, J., Finite Element Analysis of Membrane Wrinkling, International Journal for Numerical Methods in Engineering, Vol. 50 Issue 5, Pages ,

15 4 Zhang, W., Leonard, J., and Accorsi, M., Analysis of Geometrically Nonlinear Anisotropic Membranes: Theory and Verification, Finite Elements in Analysis and Design, Volume 41, Issues 9-10, May 2005, Pages Hallquist, J., LS-DYNA Theory Manual, Livermore Software Technology Corporation, Livermore, CA, Tutt, B., and Taylor, A., The Use of LS-DYNA to Simulate the Inflation of a Parachute Canopy, AIAA Paper , 18th AIAA Aerodynamic Decelerator Systems Technology Conference and Seminar, May 23-26, 2005, Munich, Germany 7 Tutt, B., Taylor, A., Berland, J., and Gargano B., The Use of LS-DYNA to Assess Candidate ATPS Main Parachutes, AIAA Paper , 18th AIAA Aerodynamic Decelerator Systems Technology Conference and Seminar, May 23-26, 2005, Munich, Germany 8 Lingard, J.S., and Darley, M., Simulation of Parachute Fluid Structure Interaction in Supersonic Flow, AIAA Paper , 18th AIAA Aerodynamic Decelerator Systems Technology Conference, May 23-26, 2005, Munich, Germany 9 Carney, A., Niezrecki, C., Niemi, E., and Chen, J., Parachute Strain and Deformation Measurements using Imaging and Polymer Strain Sensors, AIAA Paper , 19th AIAA Aerodynamic Decelerator Systems Technology Conference, May 21-24, 2007, Williamsburg, VA. 10 Bassett, R., Postleand R., and Pan, N., Experimental Methods for Measuring Fabric Mechanical Properties: A Review and Analysis, Textile Res. J. 69(11), (1999) 11 Urgural, A., Stress in Plates and Shells -, McGraw-Hill Science/Engineering/Math; 2nd edition (June 30, 1998). 15