Mark W. Hilburger

Effects of Imperfections on the Buckling Response of Compression-Loaded Composite Shells

The results of an experimental and analytical study of the effects of initial imperfections on the buckling and postbuckling response of three unstiffened thin-walled compression-loaded graphite-epoxy cylindrical shells with different orthotropic and quasi-isotropic shell-wall laminates are presented. The results identify the effects of traditional and non-traditional initial imperfections on the non-linear response and buckling loads of the shells. The traditional imperfections include the geometric shell-wall mid-surface imperfections that are commonly discussed in the literature on thin shell buckling. The non-traditional imperfections include shell-wall thickness variations, local shell-wall ply-gaps associated with the fabrication process, shell-end geometric imperfections, non-uniform applied end loads, and variations in the boundary conditions including the effects of elastic boundary conditions. A high-fidelity non-linear shell analysis procedure that accurately accounts for the effects of these traditional and non-traditional imperfections on the non-linear responses and buckling loads of the shells is described. The analysis procedure includes a non-linear static analysis that predicts stable response characteristics of the shells and a non-linear transient analysis that predicts unstable response characteristics.

Shell Buckling Design Criteria Based on Manufacturing Imperfection Signatures

An analysis-based approach for developing shell-buckling design criteria for laminated-composite cylindrical shells that accurately account for the effects of initial geometric imperfections is presented. With this approach, measured initial geometric imperfection data from six graphite-epoxy shells are used to determine a manufacturing-process-specific imperfection signature for these shells. This imperfection signature is then used as input into nonlinear finite element analyses. The imperfection signature represents a first-approximation mean imperfection shape that is suitable for developing preliminary-design data. Comparisons of test data and analytical results obtained by using several different imperfection shapes are presented for selected shells. These shapes include the actual measured imperfection shape of the test specimens, a first-approximation mean imperfection shape, with and without plus or minus one standard deviation, and the linear-bifurcation-mode imperfection shape. In addition, buckling interaction curves for composite shells subjected to combined axial compression and torsion loading are presented that were obtained by using the various imperfection shapes in the analyses. A discussion of the nonlinear finite element analyses is also presented. Overall, the results indicate that the analysis-based approach presented for developing reliable preliminary-design criteria has the potential to provide improved, less conservative buckling-load estimates and to reduce the weight and cost of developing buckling-resistant shell structures.

Progressive failure analyses of compression-loaded composite curved panels with and without cutouts

Progressive failure analyses results are presented for composite curved panels with and without a circular cutout and subjected to axial compression loading well into their postbuckling regime. Ply damage modes such as matrix cracking, fiber-matrix shear, and fiber failure are modeled by degrading the material properties. Results from finite element analyses are compared with experimental data. Good agreement between experimental data and numerical results are observed for most part of the loading range for the structural configurations considered. Modeling of initial geometric imperfections may be required to obtain accurate analysis results depending on the ratio of the cutout width to panel width.

Progressive Failure Studies of Stiffened Panels Subjected to Shear Loading

Abstract Experimental and analytical results are presented for progressive failure of stiffened composite panels with and without a notch and subjected to in-plane shear loading well into the postbuckling regime. Initial geometric imperfections are included in the finite element models. Ply damage modes such as matrix cracking, fiber-matrix shear, and fiber failure are modeled by degrading the material properties. Experimental results from the test include strain full-field data from a video image correlation system in addition to other strain and displacement measurements. Results from nonlinear finite element analyses are compared with experimental data. Good agreement between experimental data and numerical results is observed for the stitched stiffened composite panels studied.

Comparison of Methods to Predict Lower Bound Buckling Loads of Cylinders Under Axial Compression

Results from a numerical study of the buckling response of two different orthogrid stiffened circular cylindrical shells with initial imperfections and subjected to axial compression are used to compare three different lower bound buckling load prediction techniques. These lower bound prediction techniques assume different imperfection types and include an imperfection based on a mode shape from an eigenvalue analysis, an imperfection caused by a lateral perturbation load, and an imperfection in the shape of a single stress-free dimple. The STAGS finite element code is used for the analyses. Responses of the cylinders for ranges of imperfection amplitudes are considered, and the effect of each imperfection is compared to the response of a geometrically perfect cylinder. Similar behavior was observed for shells that include a lateral perturbation load and a single dimple imperfection, and the results indicate that the predicted lower bounds are much less conservative than the corresponding results for the cylinders with the mode shape imperfection considered herein. In addition, the lateral perturbation technique and the single dimple imperfection produce response characteristics that are physically meaningful and can be validated via testing.

Validation of Lower-Bound Estimates for Compression-Loaded Cylindrical Shells

The traditional approach used in the design of stability critical thin-walled circular cylinders, is to reduce unconservative buckling load predictions with an empirical knockdown factor. An alternative analysis-based approach to determine a lower bound buckling load for cylinders subjected to an axial compressive load is to use a lateral perturbation load to create an initial geometric imperfection and determine the buckling load while that perturbation load is applied. This paper describes a preliminary eort to develop a test capability to verify this analysis-based lower bound approach. Results from tests of three aluminum alloy cylinders are described and compared to nite element predictions.

Response of Composite Shells with Cutouts to Internal Pressure and Compression Loads

Results from a numerical study of the response of composite shells with cutouts and subjected to internal pressure and axial compression are presented. The numerical results are obtained using a geometrically nonlinear finite element code. Results for axial compression and combined internal pressure and axial compression are presented. The effects of varying internal pressure and cutout size on the prebuckling, buckling, and postbuckling responses of the shell are described. Results indicate that the nonlinear interaction between destabilizing in-plane compressive resultant stresses and out-of-plane dispiacements near the cutout can cause a local buckling response to occur near the cutout. The local load distributions and displacements near the cutout can be affected by the size of the cutout and by the internal pressure load. Numerical results indicate that the buckling load decreases as the size of the cutout is increased. In addition, the results indicate that the buckling load increases as the internal pressure is increased.

PROGRESSIVE FAILURE STUDIES OF COMPOSITE PANELS WITH AND WITHOUT CUTOUTS

Progressive failure analyses results are presented for composite panels with and without a cutout and are subjected to in-plane shear loading and compression loading well into their postbuckling regime. Ply damage modes such as matrix cracking, fiber-matrix shear, and fiber failure are modeled by degrading the material properties. Results from finite element analyses are compared with experimental data. Good agreement between experimental data and numerical results are observed for most structural configurations when initial geometric imperfections are appropriately modeled.

The Effects of Geometric and Loading Imperfections on the Response and Lower-Bound Buckling Load of a Compression-Loaded Cylindrical Shell

Results from a numerical study of the buckling response of a thin-walled compression- loaded isotropic circular cylindrical shell with initial geometric and loading imperfections are used to determine a lower bound buckling load estimate suitable for preliminary design. The lower bound prediction techniques presented herein include an imperfection caused by a lateral perturbation load, an imperfection in the shape of a single stress-free dimple (similar to the lateral pertubation imperfection), and a distributed load imperfection that induces a nonuniform load in the shell. The ABAQUS finite element code is used for the analyses. Responses of the cylinders for selected imperfection amplitudes and imperfection types are considered, and the effect of each imperfection is compared to the response of a geometrically perfect cylinder. The results indicate that compression-loaded shells subjected to a lateral perturbation load or a single dimple imperfection, and a nonuniform load imperfection, exhibit similar buckling behavior and lower bound trends and the predicted lower bounds are much less conservative than the corresponding design recommendation NASA SP-8007 for the design of buckling-critical shells. In addition, the lateral perturbation technique and the distributed load imperfection produce response characteristics that are physically meaningful and can be validated via laboratory testing.

Design and Analysis of Subscale and Full-Scale Buckling-Critical Cylinders for Launch Vehicle Technology Development

NASA s Shell Buckling Knockdown Factor (SBKF) project has the goal of developing new analysis-based shell buckling design factors (knockdown factors) and design and analysis technologies for launch vehicle structures. Preliminary design studies indicate that implementation of these new knockdown factors can enable significant reductions in mass and mass-growth in these vehicles. However, in order to validate any new analysis-based design data or methods, a series of carefully designed and executed structural tests are required at both the subscale and full-scale levels. This paper describes the design and analysis of three different orthogrid-stiffeNed metallic cylindrical-shell test articles. Two of the test articles are 8-ft-diameter, 6-ft-long test articles, and one test article is a 27.5-ft-diameter, 20-ft-long Space Shuttle External Tank-derived test article.