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At least 325 records · Page 18

Mode interaction in stiffened composite shells under combined mechanical and thermal loadings

Stiffened shells of various configurations fabricated out of composite materials find extensive applications in aircraft structures. Two distinctive modes of buckling dominate structural response of stiffened panels, viz. the short-wave local mode in which the shell skin buckles essentially between the stiffeners and the long-wave overall mode in which the shell skin buckles carrying the stiffeners with it. In optimized designs, the critical stresses corresponding to these modes of buckling would be close to each other. This leads to a nonlinear mode interaction which is recognized to be the principal cause of the failure of stiffened structures. If the structure is subjected to through-the-thickness thermal gradients, then large-wave bending effects would begin to occur well below the overall critical load and these would play the role of overall imperfections. The load carrying capacity would be significantly diminished as a result of interaction of local buckling with overall thermal distortions. The analysis of this problem using standard finite element techniques can be shown to be prohibitively expensive for design iterations. A concept which would greatly facilitate the analysis of mode interaction is advanced. We note that the local buckling occurs in a more or less periodic pattern in a structure having regular spacings of stiffeners. Thus it is a relatively simple matter to analyze the local buckling and the second order effects (which are essential for modeling postbuckling phenomena) using a unit cell of the structure. Once analyzed, these dormations are embedded in a shell element. Thus, a shell element could span several half-waves of local buckling and still be able to depict local buckling effects with requisite accuracy. A major consequence of the interaction of overall buckling/bending is the slow variation of the local buckling amplitude across the structure - the phenomenon of 'amplitude modulation' - and this is accounted for in the present model by letting the scaling parameter of the local mode vary according to a 'slowly varying' function. The construction of the analytical model involves essentially two stages and these are described briefly.

Sridharan, Srinivasan↗

The NASA Monographs on Shell Stability Design Recommendations: A Review and Suggested Improvements

A summary of existing NASA design criteria monographs for the design of buckling-resistant thin-shell structures is presented. Subsequent improvements in the analysis for nonlinear shell response are reviewed, and current issues in shell stability analysis are discussed. Examples of nonlinear shell responses that are not included in the existing shell design monographs are presented, and an approach for including reliability based analysis procedures in the shell design process is discussed. Suggestions for conducting future shell experiments are presented, and proposed improvements to the NASA shell design criteria monographs are discussed.

Nemeth, Michael P.↗

SOME TYPICAL SHELL STABILITY PROBLEMS ENCOUNTERED IN THE DESIGN OF BALLISTIC MISSILES

Investigations carried out at STL on three current problems involving instability of thin shells in applications to aerospace vehicles are discussed. The first concerns the experimental determination of the buckling behavior of longitudinally stiffened pressurized cylinders; the second, the analytic prediction and experimental confirmation of the buckling behavior of multi-layer cylinders and the third involves the behavior of cylinders under combined axial load and lateral pressure. In each case the background of the application is reviewed, followed by a short description of the work. It is indicated that the longitudinally stiffened cylinder shows considerable promise in taking maximum advantage of the strengthening effect of internal pressure, that the use of an external low modulus layer as an insulator can have a significant effect on the buckling capability of a shell, and that the assumption of a linear interaction for pressure and axial load is unnecessarily conservative.

SHELL STABILITY↗

The NASA Monographs on Shell Stability Design Recommendations: A Review and Suggested Improvements

A summary of the existing NASA design criteria monographs for the design of buckling-resistant thin-shell structures is presented. Subsequent improvements in the analysis for nonlinear shell response are reviewed, and current issues in shell stability analysis are discussed. Examples of nonlinear shell responses that are not included in the existing shell design monographs are presented, and an approach for including reliability-based analysis procedures in the shell design process is discussed. Suggestions for conducting future shell experiments are presented, and proposed improvements to the NASA shell design criteria monographs are discussed.

Nemeth, Michael P.↗

Future Directions and Challenges in Shell Stability Analysis

An answer is sought to the question of today, in 1997, after so many years of concentrated research effort in designing buckling critical thin walled shells, why one cannot do any better than using the rather conservative Lower Bound Design Philosophy of the sixties. It will be shown that with the establishment of Initial Imperfection Data Banks and the introduction of Probabilistic Design Procedures one has a viable alternative, that when used judiciously, may lead to improved shell design recommendations.

Arbocz, Johann↗

Structural Concepts Study of Non-circular Fuselage Configurations

A preliminary study of structural concepts for noncircular fuselage configurations is presented. For an unconventional flying-wing type aircraft, in which the fuselage is inside the wing, multiple fuselage bays with non-circular sections need to be considered. In a conventional circular fuselage section, internal pressure is carried efficiently by a thin skin via hoop tension. If the section is non-circular, internal pressure loads also induce large bending stresses. The structure must also withstand additional bending and compression loads from aerodynamic and gravitational forces. Flat and vaulted shell structural configurations for such an unconventional, non-circular pressurized fuselage of a large flying-wing were studied. A deep honeycomb sandwich-shell and a ribbed double-wall shell construction were considered. Combinations of these structural concepts were analyzed using both analytical and simple finite element models of isolated sections for a comparative conceptual study. Weight, stress, and deflection results were compared to identify a suitable configuration for detailed analyses. The flat sandwich-shell concept was found preferable to the vaulted shell concept due to its superior buckling stiffness. Vaulted double-skin ribbed shell configurations were found to be superior due to their weight savings, load diffusion, and fail-safe features. The vaulted double-skin ribbed shell structure concept was also analyzed for an integrated wing-fuselage finite element model. Additional problem areas such as wing-fuselage junction and pressure-bearing spar were identified.

Mukhopadhyay, Vivel↗

A shear deformable theory of laminated composite shallow shell-type panels and their response analysis. I - Free vibration and buckling

This paper deals with the substantiation of a shear deformable theory of cross-ply laminated composite shallow shells. While the developed theory preserves all the advantages of the first order transverse shear deformation theory it succeeds in eliminating some of its basic shortcomings. The theory is further employed in the analysis of the eigenvibration and static buckling problems of doubly curved shallow panels. In this context, the state space concept is used in conjunction with the Levy method, allowing one to analyze these problems in a unified manner, for a variety of boundary conditions. Numerical results are presented and some pertinent conclusions are formulated.

Librescu, L.↗

Nonlinear Buckling Analysis of Tow-Steered Composite Cylinders with Cutouts

The buckling and postbuckling behavior of two composite tow-steered shells with cutouts of different sizes is assessed using nonlinear finite element (FE) analysis and compared to experimental measurements. The cylindrical shells are manufactured using an automated fiber placement system, where the shells’ fiber orientation angles vary continuously around the shell circumference from 10 degrees on the crown and keel to 45 degrees on the sides. One shell features thickness variations due to tow overlaps that result from application of all 24 tows during each pass of the fiber placement system. The second shell uses the system’s tow drop/add capability to achieve a more uniform wall thickness without overlaps. Unreinforced cutouts of two different sizes—the first smaller cutout representing a passenger door on a commercial aircraft and the second larger cutout a cargo door—were machined into each of the two cylinders resulting in a total of four test cases. These cylinders were tested in axial compression and buckled elastically in previous work and are now analyzed using nonlinear FE models to compare bifurcation buckling loads as well as the load-displacement response in the prebuckling and postbuckling regimes. For all four shells analyzed, the prebuckling stiffness, buckling load, and deformation mode sequence throughout the loading-unloading cycle is accurately reproduced by the models. In particular, the shells first buckle locally around the cutouts in a stable (super-critical) manner with only a slight decrease in axial stiffness, which occurs due to the favorable load redistribution facilitated by tow steering. The shells then buckle globally in an unstable (sub-critical) manner with diamond-shaped buckles forming to the left and right of the cutouts. The buckling load of all shells with cutouts is at least 82% of the buckling load of the pristine shells without cutouts. Overall, the ability to sustain local buckling phenomena, and the relatively small reductions in global buckling load compared to pristine shells without cutouts, demonstrates the great potential of using tow steering to mitigate the adverse effects of cutouts in axially-compressed shell structures.

Buckling↗

Nonlinear Buckling Analysis of Tow-Steered Composite Cylinders with Cutouts

The buckling and postbuckling behavior of two composite tow-steered shells with cutouts of different sizes is assessed using nonlinear finite element (FE) analysis and compared to experimental measurements. The cylindrical shells are manufactured using an automated fiber placement system, where the shells’ fiber orientation angles vary continuously around the shell circumference from ±10 degrees on the crown and keel to ±45 degrees on the sides. One shell features thickness variations due to tow overlaps that result from application of all 24 tows during each pass of the fiber placement system. The second shell uses the system’s tow drop/add capability to achieve a more uniform wall thickness without overlaps. Unreinforced cutouts of two different sizes—the first smaller cutout representing a passenger door on a commercial aircraft and the second larger cutout a cargo door—were machined into each of the two cylinders resulting in a total of four test cases. These cylinders were tested in axial compression and buckled elastically in previous work and are now analyzed using nonlinear FE models to compare bifurcation buckling loads as well as the load-displacement response in the prebuckling and postbuckling regimes. For all four shells analyzed, the prebuckling stiffness, buckling load, and deformation mode sequence throughout the loading-unloading cycle is accurately reproduced by the models. In particular, the shells first buckle locally around the cutouts in a stable (super-critical) manner with only a slight decrease in axial stiffness, which occurs due to the favorable load redistribution facilitated by tow steering. The shells then buckle globally in an unstable (sub-critical) manner with diamond-shaped buckles forming to the left and right of the cutouts. The buckling load of all shells with cutouts is at least 82% of the buckling load of the pristine shells without cutouts. Overall, the ability to sustain local buckling phenomena, and the relatively small reductions in global buckling load compared to pristine shells without cutouts, demonstrates the great potential of using tow steering to mitigate the adverse effects of cutouts in axially-compressed shell structures.

composites↗

Structural Performance of Advanced Composite Tow-Steered Shells With Cutouts

The structural performance of two advanced composite tow-steered shells with cutouts, manufactured using an automated fiber placement system, is assessed using both experimental and analytical methods. The shells' fiber orientation angles vary continuously around their circumference from +/-10 degrees on the crown and keel, to +/-45 degrees on the sides. The raised surface features on one shell result from application of all 24 tows during each fiber placement system pass, while the second shell uses the system's tow drop/add capability to achieve a more uniform wall thickness. These unstiffened shells were previously tested in axial compression and buckled elastically. A single cutout, scaled to represent a passenger door on a commercial aircraft, is then machined into one side of each shell. The prebuckling axial stiffnesses and bifurcation buckling loads of the shells with cutouts are also computed using linear finite element structural analyses for initial comparisons with test data. When retested, large deflections were observed around the cutouts, but the shells carried an average of 92 percent of the axial stiffness, and 86 percent of the buckling loads, of the shells without cutouts. These relatively small reductions in performance demonstrate the potential for using tow steering to mitigate the adverse effects of typical design features on the overall structural performance.

Wu, K. Chauncey↗

GENERAL INSTABILITY OF ORTHOGONALLY STIFFENED CYLINDRICAL SHELLS

Earlier research at the National Aeronautics Research Institute (N.L.R.), Amsterdam, which forms the basis of recent work is reviewed. This early work refers to 2 schemes: the orthotropic shell and, in view of buckling modes where the half wave length is of the order of the ring distance, the shell with continuously distributed stringers and discrete rings. Linear theory is considered to be adequate for these structures, where the imperfections are small in comparison to the height of the ring sections. Recent developments account for pressure difference in addition to axial compression, for the correct stiffness matrix of skin panels in the post-buckling stage and for stringer bending due to hoop stresses in the skin, which are of importance as has been shown by the investigation of the post-buckling behaviour. Numerical data for the stiffness matrix of skin panels have been established. Numerical evaluation of the stability equation has not been performed as yet.

SHELL STABILITY↗

Future Directions and Challenges in Shell Stability Analysis

An answer is sought to the question how comes that today, in 1997, after so many years of concentrated research effort, when it comes to designing buckling critical thin walled shells, one cannot do any better than using the rather conservative Lower Bound Design Philosophy of the sixties. It will be shown that with the establishment of Initial Imperfection Data Banks and the introduction of Probabilistic Design Procedures one has, what appears to be, a viable alternative that when used judiciously may lead step by step to improved shell design recommendations.

Arbocz, Johann↗

Summary of Research Report

Ten papers, published in various publications, on buckling, and the effects of imperfections on various structures are presented. These papers are: (1) Buckling mode localization in elastic plates due to misplacement in the stiffner location; (2) On vibrational imperfection sensitivity on Augusti's model structure in the vicinity of a non-linear static state; (3) Imperfection sensitivity due to elastic moduli in the Roorda Koiter frame; (4) Buckling mode localization in a multi-span periodic structure with a disorder in a single span; (5) Prediction of natural frequency and buckling load variability due to uncertainty in material properties by convex modeling; (6) Derivation of multi-dimensional ellipsoidal convex model for experimental data; (7) Passive control of buckling deformation via Anderson localization phenomenon; (8)Effect of the thickness and initial im perfection on buckling on composite cylindrical shells: asymptotic analysis and numerical results by BOSOR4 and PANDA2; (9) Worst case estimation of homology design by convex analysis; (10) Buckling of structures with uncertain imperfections - Personal perspective.

Elishakoff, Isaac↗