considerations of cutouts in composite cylindrical panels

Computers & .Slrucfures Vol. 29, No. 6. pp. 1101-I I IO. 1988 Printed in Great Britain.

@M-7949/88 s3.00 + 0.00 0 1988 Pergamon Press plc

CONSIDERATIONS OF CUTOUTS IN COMPOSITE CYLINDRICAL PANELS

ANTHONY N. PALAZOTTO and THOMAS W. TISLER Aeronautics and Astronautics Department, Air Force Institute of Technology, Wright-Patterson AFB,

OH 45433, U.S.A.

(Received 27 October 1987)

Abstractqver the past five years the Air Force Institute of Technology has been carrying out an investigation of small and large unreinforced cutout effects on composite cylindrical panels acting under compressive axial loads. Some of the original findings are reviewed and, in addition, new results are presented relating to different loading conditions. In general, not only does a small cutout reduce the panel’s collapse load by at least 50%, but the cutout’s position and size have further effect.

INTRODUCTION

It is well known that the use of composite materials in aerospace structures is only now starting to take on the usage that was originally predicted for this material. Some of the reasons for the long time required to build confidence in its structural use have been in the area associated with nonlinear geometric characteristics related to the many shapes required in the aerospace vehicle. One major feature required for an understanding, which has drawn study within recent years, is in the investigation of collapse via instability of curved composite panels under compressive loading. The phenomenon of buckling of flat composite panels or plates has been well documented [l-3] and will not be discussed herein. The instability of curved composite panels, on the other hand, has attracted a smaller amount of documented research [4-71, and only recently have there been articles written which include work on composite panels requiring nonlinear analysis due primarily to the inclusion of geometric discontinuities, such as cutouts, within their skin surface. Certain research organizations have pursued this area of investigation, i.e. NASA [8] and the Air Force Institute of Technology (AFIT), and the work reported on within this paper is a study carried on at AFIT into unreinforced cutout effects within composite panels. This study included both a finite element investigation using STAGS-Cl as well as experimental results determined with the use of special fixtures made primarily for investigat- ing small panel collapse [9, lo]. The authors will report primarily upon the analysis but will touch on some of the experimental aspects. All of the cutouts considered have been rectangular which makes the results somewhat more severe in nature than a pre- ferred circular opening, but the authors feel this creates a larger reservoir of upper bound characteristics within stress and displacement related functions. Several different boundary and loading conditions have been carried out and will be discussed.

MATHEMATICAL MODELING

As indicated previously, the STAGSC-1 computer code [l l] was used to conduct all the analyses in this study. The nonlinear analysis in this code is based on a finite element displacement model incorporating a total Lagrangian formulation with the assumptions

1 L

1

DIMENSIONS AND MATERIAL PROPERTIES

MATERIAL: GRAPHITE-EPOXY RADIUS: R=12” LENGTH: L=12” NUMBER OF PLIES: 8 ORIENTATION OF PLIES, 0: (O/45/-45/90),

(O/-45/+45/903, THICKNESS: 8 PLIES AT 0.005” = 0.04” ELASTIC MODULI: El = 18850 ksi, Es = 1413.8 ksi SHEAR MODULUS: G = 855 ksi POISSON’S RATIO: qz= 0.3 x, y, z: STRUCTURAL COORDINATES u, v, w: DISPLACEMENTS R,. R,, R,: ROTATIONS

Fig. 1. Panel geometry.

1101

1102 ANTHONY N. PALAZOTTO and THOMAS W. TISLER

_ a, itiiiiiiiiiii

19x19 21x19

Fig. 2. Refined meshes for 2 x 2 in. notch.

of small strains and moderate rotations. A flat 32 degree of freedom (DOF) element (referred to as the 41 I element in the STAG%-I element library) was used to model the panel. Figure 1 represents the panel investigated in this study. The material properties depicted and the orientation of plies are also listed in this figure. It was assumed that the horizontal edges were clamped while the vertical edges were simply supported. The boundaries will be further elaborated upon subsequently. A great deal of work has been associated with the modeling of this panel. Hebert and Palazotto [9] and Janisse and Palazotto [ 121 have shown that maximum mesh dimension equal to I in. can be used for modeling the panel edges as well as the bifurcation of a panel with no cutouts. Lee and Palazotto [13] did an elaborate study of mesh arrangements surrounding cutouts that were either rectangular or square. The resulting mesh arrangements are shown in Fig. 2 in which the minimum size mesh immediately adjacent to the cutout was 0.5 in. Hermsen and Palazotto [I41 verified this mesh arrangement and refined the cutout area of the

4 x 4 in. cutout to 0.33 in. Results were little different from those of Lee’s work. Thus, the mesh size incorporated into this overall study results in a general set of active DOFs equal to approximately 2500 depending on the size of cutouts. One should notice that Lee’s study related to cutouts that were either rectangular or square. Thus, a much needed element dimensional effect was observed relative to individual force functions.

FINITE ELEMENT RESULTS AND DISCUSSION

Janisse and Palazotto [12] carried out the first study of rectangular cutouts in panels. They investigated a 2 x 2 in. opening. Lee and Palazotto [13] followed this with non-square rectangular cutouts ranging size from 2 x 2 in. to 4 x 4 in. Hermsen and Palazotto [ 141 investigated the effects of locating openings eccentric to the panels line of symmetry but with a size equivalent to 2 x 2 in. Finally, Tisler [IS] studied 4 and 5 in. square cutouts located along the line of

Cutouts in composite cylindrical panels 1103

pJ!/W pe0-l le!w


El 6

ml C A

I- 3” -*I

Fig. 7. Location of cutout studied.

symmetry. This section will discuss and compare the results of each study with the respective boundary relations included. It is rather interesting to observe the differences associated with line load conditions. Initially, it will be seen that collapse characteristics are relatively unchanged with loading conditions that are either force or displacement. This is true if the cutouts are small (approximately 3% of the surface area). Further study reveals that as the opening size

4000 T 1

3500

3000

I

increases above a 10% surface area, the effect of the uniform load versus uniform displacement become totally different. It should be kept in mind that each study is relative to a [O/ +45/90], ply layup, but generalized concepts can be observed even from these quasi-isotropic results.

Figures 3 and 4 indicate a load versus edge displacement for various cutouts in which a uniform load has been applied to the upper surface of the panel. The vertical edges are taken to be simply supported with tangential and normal displacement free to move. The panels with 2 x 2 in. and 1 x 2 in. notches have higher collapse load since they both have less material removed compared to the other panels. The 2 x 1 in. notch produces the highest collapse of all since its smallest direction is perpendicular to the applied load and has less stress concentrations than the 1 x 2 in. notch.

Figures 5 and 6 represent contours of radial displacement for a small cutout (2 x 2 in.) and a larger cutout. It is observed by Hermsen [14] that the phenomenon of collapse is tied very closely to linear geometric properties for cutout sizes such as 2 x 2 in. while the 4 x 4 in. is totally nonlinear in displacement properties. The contours represent tenths of the maximum displacements at collapse.

Hermsen [14] carried out further study of the cutout effects, particularly as a result of its location. Figure 7 shows the different positions studied. It was noticed that, compared to the center 2 x 2 in. location, the locations C and D for a [O/45/45/90], had collapse values 26 and 10% less respectively. Location B did produce an increase of collapse load

Uniform Displacement

“‘7

A_ 2500 + Uniform (oad

I 0.000 0.005 0.010 0.012 0.014 0.016

Top Edge Displacement Iin1

Fig. 8. Uniform load vs uniform displacement, 4 in. cutout, I = 0.045 in., tl free.


z 1500 g

I 1000

t

Uniform Displacement

Uniform Load

0-l’: ; : I! I: ;: ;:i: : : 1 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016

Top Edge Displacement (in)

Fig. 9. Uniform load vs uniform displacement, 2 in. cutout, I = 0.045 in., v free.

equal to 1% compared to center location A. Hermsen [14] presented an explanation for the difference between locations C and D tied into the MXY moment resistence.

Tisler [15] recently completed a study in which he investigated the effects of loading conditions along the horizontal edges of the panel. Two conditions were compared; a uniform load and a uniform dis-

placement. It is observed that, with v displacements free along the vertical edges and a 4in. cutout, the collapse load for a uniform displacement is 63% greater than that for a uniform load. It can further be stated that the panel undergoing a uniform load condition will collapse with larger radial displacement near the loading edge (see Fig. 8) while the panel undergoing a uniform displacement edge

Fig. 10. Close up of panel in specialized supports.


Fig. 11. Experimental setup, axial compression.

distribution yields a more symmetric contour plot about a horizontal center line. Tisler [15] also carried out a similar investigation with a 2 in. cutout and found the collapse load comparisons to be 20% of each other (see Fig. 9). It should be noted that in each comparison, a panel thickness of 0.045 in. was used. This thickness was generated from the experimental portion of Tisler’s [ 151 work.

EXPERIMENTATION

For the experimental verification of large cutout results, several panels were tested with 4 x 4 in. and

5 x 5 in. cutouts. Six panels of each cutout size were used: three with t = 0.039 in. and three with t = 0.045 in. Care was taken manufacturing the panels to avoid any damage, including the deveIopment of a new panel clamping device. Once the panels were cut to the proper size, they were fitted in clamps (Fig. 10) and placed in the axial compression setup shown in Fig. 11. The load is slowly applied (0.05 in/min) until the panel collapses. LVDTs measure the radial displacement as well as the applied displacement while a load cell records the total force applied. This allows the formation of load-displacement curves which are compared to the analytical results. The experimental

4 2500

z z 2000

STAGS

o::l::!;:;:f:::;:!: 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.

Radial Displacement (in)

Fig. 12. Radial displacements, experimental and STAGS, 4 in. cutout, t = 0.045 in.

8

1108 AN~ONY N. PALAZOTTO and THOMAS W. TISLER

4000

/

Experimental

@I STAGS

0.62 0.04 0.66 0.08 o.io 0 Radial Displacement (in)

Fig. 13. Radial displacements, experimental and STAGS, 4 in. cutout, f = 0.039 in.

method was the same as used by Janisse [ 121 with some minor modifications to the boundary conditions as described by Horban and Palazotto [lo].

Experimental results tended to confirm some of the results given so far. Horban [IO] tested several similar panels with no cutouts, and found the results to be slightly lower (8-10%) than the bifurcation values. With no cutouts and no initial imperfections, it is expected that the bifurcation results will be very similar to the nonlinear results, and the fact that the experimental results were low is again expected.

The average experimental results for the various thicknesses and large cutout sizes used are compared to analytical results in Figs 12-15. These figures are plots of load versus radial displacements of points adjacent to the cutouts. It is clear that the STAGS model incorporating vertical boundary conditions which assumes freedom of rotation is somewhat softer than the actual experimental results for the large cutouts. Certainly some of this may be attrib- uted to STAGS inability to handle moderately large rotations. Figures 14 and 15 show that the STAGS

5000

4500 -- f/

X Experimental 7 X X 4000 --

.- X X

STAGS

0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20




4000 I

3500

3000 i

;/ ExPerimenta’ -y. x )(

X X

STAGS

I. I. I.,. I .I I I I I I I ’ I ’ I r I ’ t. I ’ I - I * 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0 8



results appear to get worse with increased cutout size. The accuracy also appears to be dependent on thickness to some degree. It is seen that the 5 in. cutout panels have a higher collapse load than the 4 x 4 in. panels. STAGS predicted that the results would be close, but the results from STAGS increase with cutout size, causing STAGS to predict the 4 x 4 in. panels to be slightly stronger. The authors realize that, with hind-sight, the boundary conditions along the vertical edges should have more restraint in the numerical model. This would require more rotational fixity. The results, from the finite element solution, do show similar trends present in the experimentation. In fact, a contribution from this research was the possible judgements made from the physical collapse characteristics which could subsequently be incorporated into further analytical work. It should be pointed out that the present authors investigated the effects of shell geometric imperfection and found it to account for only a small amount of difference in the analytic functions. Furthermore, an investigation into the residual stress present in the cutout area was attempted [IS] and found to have some influence on the shell’s collapse properties. The complete report of these last two studies will be subsequently presented, but at present they are only partially complete and thus documentation is not possible [ 151.

CONCLUSIONS

Based on the analysis conducted within this overall study, the following conclusions can be made as related to the specific conditions considered.

I. A uniform distribution along a horizontal panel edge yields larger collapse loads than if a uniform

load is applied when 2 and 4 in. cutouts are present. This difference is 2@-60% respectively.

2. Panels with rectangular cutouts having the larger dimension parallel to the loading direction yield higher collapse loads than when the larger cutout edge is perpendicular to the load direction.

3. The location of a cutout near a vertical boundary can reduce the collapse load by as much as 25% compared to one located at the panel’s center.

1.

2.

3.

4.

5.

6.

7.

REFERENCES

R. M. Jones, Mechanics of Composite Materials. McGraw-Hill, New York (1975). J. M. Whitney, Shear buckling of unsymmetric cross-ply plates. J. Comp. Mater. 3, 359-363 (1969). A. W. Leissa, Buckling of laminated composite plates and shell panels. Air Force Wright Aeronautical Laboratories, AFWAL-TR-85-3069 (1985). N. F. Knight, J. H. Starnes and W. A. Waters, Post- buckling behavior of selected graphite-epoxy cylindrical panels loaded in axial compression. AIAA Paper No. 86-0881 (May 1986). M. L. Becker, A. N. Palazotto and N. S. Khot, Experi- mental investigation of the instability of composite cylindrical panels. J. exp. Mech. 22, 372-376 (1982). J. M. Whitney, Buckling of anisotropic laminated cylindrical plates. AIAA Jnl 22, 164-1645 (1984). N. R. Bauld and N. S. Khot, A numerical and experimental investigation of the buckling behavior of composite panels. J. Comput. Struct. 15, 393403 (1982). N. F. Knight and J. H. Stames, Postbuckling behavior of axially compressed graphite-epoxy cylindrical panels - _ with circular holes. In Collapse~An&is of Strtkures (Edited bv L. H. Sobel and K. Thomas). ASME PVP- $01. 84, I;p. 13-167 (1984).

II

J. S. Hebert and A. N. Palazotto, Comparison between experimental and numerical buckling of curved cylindrical composite panels. In Proceedings of the Twelfrh


Southeastern Conference on Theoretical and Applied 13. Mechanics, pp. 124-129 (May 1984).

10. B. A. Horban and A. N. Palazotto, The experimental buckling of cylindrical composite panels with 14. eccentrically located circular delaminations. AIAA J.

II.

12.

Spacecr. Rockets 24, 349-352 (1987). B. 0. Almroth, F. A. Brogan and G. M. Stanley, Structural Analysis of General Shells, Vol. II, LMSC-D- 633073. Applied Mechanics Laboratory, Lockheed Palo Alto Research Laboratory, Palo Alto, California (July 15. 1979). T. C. Janisse and A. N. Palazotto, Collapse analysis of composite cylindrical panels with small cutouts. J. Aircr. 21, 731-733 (1984).

C. E. Lee and A. N. Palazotto, Collapse analysis of composite cylindrical panels with small cutouts. J. Comp. Struct. 4, 217-229 (1985). M. F. Hermsen and A. N. Palazotto, The effects of cutout location and material degradation on the collapse of composite cylindrical panels. In Nonlinear Anak_wis and NDE q/ Composite Material Vessels and Components (Edited by D. Hui, J. C. Duke and H. Chung), ASME. PVP-Vol. 115, NDE-Vol. 3, pp. 43-57 (1986). T. W. Tisler, Collapse analysis of cylindrical composite panels with large cutouts under an axial load. MS thesis, AFIT/GAE/AA/86D-18, School of Engineering, Air Force Institute of Technology, Wright-Patterson AFB, OH (1986).

considerations of cutouts in composite cylindrical panels

Documents