Launch vehicles and payload adapters are mainly composed of thin-walled cylindrical shells and conical shells, where conical shells are necessary when transitioning from a larger to a small diameter. These thin-walled shell structures are constructed with metallic or composite materials. Mass is a critical factor in the design and operation of launch vehicles, so it is desirable to save as much mass as possible on primary (core stage, interstage) and secondary structures (payload adapters). This objective can be achieved by maximizing the radius-to-thickness ratio in conical and cylindrical shell structures. However, structures with high radius-to-thickness ratios are usually more susceptible to buckling failure. Traditionally, conical and cylindrical shells are designed and analyzed as independent structures. State-of-the-art manufacturing and numerical methods also allow designers to consider novel shapes and joints to save mass and increase volume, for example, combining the conical and cylindrical shells in a single integrated structure. By combining these two sections with a seamless toroidal transition, designers can remove the heavy, stiff interface ring that often connects the two independent structures, which potentially saves mass. An example of this type of integrated structure is the NASA Universal Stage Adapter.

Demonstrating the ability to successfully predict the buckling behavior of integrated conical-cylindrical shells is a critical step in the development of buckling design guidelines for this class of structures. Although there are numerous papers documenting the test and analysis correlation of conical and cylindrical shells separately, there is a limited number of research papers specifically related to the test and analysis of an integrated conical-cylindrical shell under axial compression. Furthermore, a modeling methodology has yet to be proven to predict the buckling behavior of these integrated shell structures.

To address this need, a buckling analysis methodology was developed which successfully predicted the buckling behavior of a composite cylindrical shell with a nontraditional composite layup. The methodology was further applied to an integrated conical-cylindrical composite shell. The finite element model included as-built geometric imperfections and thickness variations, and a geometrically nonlinear analysis was used to predict the buckling behavior for both the cylindrical and the conical-cylindrical shells. A composite conical-cylindrical shell was designed, built, and tested until buckling. The observed buckling behavior was in good agreement with the predicted behavior. Since the test specimen buckled elastically, it could be reused for further testing. The specimen was modified with additional composite plies that were added to the transition region. The same finite element modeling approach was also used to successfully predict the buckling of the composite conical-cylindrical shell with the modified design. This additional test provided further validation of the modeling methodology.

After validation, the modeling methodology was used to investigate whether the current buckling design methodology for conical and cylindrical shells can be applied to integrated conical-cylindrical shells. This begins with comparing the buckling response of conical and cylindrical shells, and how they compare with the buckling response of an integrated conical-cylindrical shell using an eigenvalue analysis (buckling equation) and a geometrically nonlinear analysis (implicit quasi-static analysis).

The buckling behavior and imperfection sensitivity of the conical-cylindrical shell was used to assess
the traditional buckling design methodology. It was determined that the traditionally
recommended knockdown factors may not be conservative for conical-cylindrical shells
in some cases. It was also discovered that the effects of geometrical nonlinearity may be
more influential than imperfections for conical-cylindrical shells, which is contrary to the
case of the individual components.

To help quantify the relative importance of various design parameters, a Polynomial Chaos Expansion was employed to express the critical buckling load of a conical-cylindrical
shell as a function of the shell thicknesses, cone angles, transition geometry and axial stiffness. Polynomial Chaos Expansion was also used to highlight differences in the predicted buckling loads obtained from a buckling eigenvalue analysis and a geometrically nonlinear implicit dynamics analysis. Isotropic and composite shells were considered separately. Due to its capacity to successfully predict the buckling load of a conical-cylindrical shell, the Polynomial Chaos Expansion of the buckling load may be a useful design tool during launch vehicle sizing studies, as it may limit the number of finite element analyses required, particularly in the early design stages.

This research aimed to present the fundamental buckling behavior of conical-cylindrical shells through numerical and experimental means. This led to the conclusion that the traditional buckling design approach for cone and cylinders is not appropriate for conical-cylindrical shells. Additionally, it may be more mass efficient to design a conical-cylindrical shell that has a lower buckling capability because it is less sensitive to imperfections. The recommendations provided are based on experimentally validated data and observations, which provides credibility to the conclusions and recommendations. ... Read more

Traditionally, launch vehicles are constructed with a series of buckling-prone thin-walled cylindrical and conical shells, in which the buckling behavior of these shells has been well studied and buckling design guidance exists. Conical-cylindrical shell geometry is now being utilized for launch-vehicle stage adapters and payload adapters due to advances in manufacturing and numerical techniques, but there is no available buckling design guidance for this nontraditional combined geometry. In order to provide design recommendations, the buckling behavior and imperfection sensitivity of conical-cylindrical shells and how it differs from the conical and cylindrical components needs to be better understood. From this premise, it is possible to investigate whether or not the buckling knockdown factor guidelines for conical and cylindrical shells outlined in NASA SP-8019 and NASA SP-8007, respectively, are still applicable. The results in this paper will show that the current recommendations are not appropriate in some cases. In addition, it was observed that the large rotations and displacements near the transition between the cone and cylinder can have a larger effect on the buckling load than the presence of radial imperfections for conical-cylindrical shells, which is different than for conical or cylindrical shells. More interesting is the fact that design modifications to increase the buckling capability of a conical-cylindrical shell such as adding reinforcement, which may add mass, will make the shell more sensitive to imperfections. The increased imperfection sensitivity may negate the increase in buckling capability that was thought to be achievable. In the end, it may be more beneficial to design a conical-cylindrical shell in which the buckling behavior is dominated by the more predictable geometric nonlinearity, which may lead to an overall lower buckling load, but a lower knockdown factor may be possible since it will not be as sensitive to the lessknown radial imperfections. ... Read more

Launch vehicle structures, such as payload adapters and interstages, are increasingly designed and constructed using composite materials due to their high stiffness- and strength-to-weight ratios. Therefore, it is important to develop a validated finite element modeling methodology for designing and analyzing composite launch-vehicle shell structures. This can be achieved, in part, by correlating high-fidelity numerical models with test data. Buckling is often an important failure mode for cylindrical shells, and the buckling response of such structures is also often quite sensitive to imperfections in geometry and loading. Hence, it is crucial to understand the model parameters and details required to accurately predict the buckling load and behavior of composite cylindrical shells, especially if the shell is buckling critical. The inclusion of as-built features, such as radial imperfections, thickness variations, and loading imperfections can help improve the correlation between test and analysis. To demonstrate such an approach, a validated modeling methodology that was used to predict the buckling behavior of a scaled component for a launch-vehicle-like structure is presented, and results from the model are compared with experimental results. The modeling approach presented herein was used to successfully predict the buckling behavior. ... Read more

Conical shells are commonly used as structural components for launch vehicles. The axial compression experienced during launch is one of the sizing load cases, because it can lead to loss of structural stability. Because experimentally testing these full-scale structures is cumbersome and expensive, it is expedient to understand how reduced-scale shells can be designed such that their buckling behavior is representative of the full-scale shell behavior. An analytical, sequential scaling methodology is developed based on the nondimensional governing equations for composite conical shells with a symmetric, balanced layup and negligible flexural anisotropy. Linear and nonlinear finite element analyses characterizing the buckling behavior of the different size shells yielded comparable results in terms of buckling load, meridional displacement, and buckling mode. The inclusion of geometric imperfections affects the prediction accuracy, but not to the extent that the methodology is no longer valid. ... Read more