Richard D. Young

NONLINEAR LOCAL BENDING RESPONSE AND BULGING FACTORS FOR LONGITUDINAL CRACKS IN PRESSURIZED CYLINDRICAL SHELLS

Results of a geometrically nonlinear finite element parametric study to determine curvature correction factors or “bulging factors” that account for increased stresses due to curvature for longitudinal cracks in unstiffened pressurized cylindrical shells are presented. Geometric parameters varied in the study include the shell radius, the shell wall thickness, and the crack length. The major results are presented in graphs of the bulging factor as a function of the applied load and as a function of geometric parameters that include the shell radius, the shell thickness and the crack length, The computed bulging factors are compared with solutions based on linear shallow shell theory, and with semi-empirical solutions that approximately account for the nonlinear deformation in the vicinity of the crack. The effect of biaxial loads on the computed bulging factors is also discussed.

Effects of Initial Geometric Imperfections On the Non-Linear Response of the Space Shuttle Superlightweight Liquid-Oxygen Tank

Abstract The results of an analytical study of the elastic buckling and non-linear behavior of the liquid-oxygen tank for the new Space Shuttle superlightweight external fuel tank are presented. Selected results that illustrate three distinctly different types of non-linear response phenomena for thin-walled shells which are subjected to combined mechanical and thermal loads are presented. These response phenomena consist of a bifurcation-type buckling response, a short-wavelength non-linear bending response, and a non-linear collapse or “snap-through” response associated with a limit point. The effects of initial geometric imperfections on the response characteristics are emphasized. The results illustrate that the buckling and non-linear response of a geometrically imperfect shell structure subjected to complex loading conditions may not be adequately characterized by an elastic linear bifurcation buckling analysis, and that the traditional industry practice of applying a buckling-load knock-down factor can result in an ultra-conservative design. Results are also presented that show that a fluid-filled shell can be highly sensitive to initial geometric imperfections, and that the use a buckling-load knock-down factor is needed for this case.

Nonlinear Behavior of Space Shuttle Superlightweight Liquid-Oxygen Tank Under Prelaunch Loads

The new Space Shuttle superlightweight external fuel tank e ew for the e rst time on 2 June 1998 (Space Transportation System-mission 91 ). We present results of elastic linear-bifurcation buckling and nonlinear analyses of one of its major components; that is, the liquid-oxygen tank. The contents include an overview of the structure and a brief description of the e nite element code that was used to conduct the analyses. Results are presented that illustrate three distinctly different types of nonlinearresponsephenomena for thin-walled shells that aresubjected to combined mechanical and thermal loads that launch-vehicle shell designers may encounter. A procedure is demonstrated that can beused by structural analysts and designers to obtain reasonable, conservative estimates of linear-bifurcation, buckling-load knockdown factors for shells that are subjected to complex loading conditions or to characterize the effects of initial geometric imperfections on nonlinear shell response phenomena. Results are also presented that show that the superlightweight liquid-oxygen tank can carry loads in excess of twice the values of the operational prelaunch loads considered and that a e uid-e lled launch-vehicle shell can be highly sensitive to initial geometric imperfections. Presentedherearee vepapersonlarge-scaleanalysesofacomplexshellstructure.Thee rst,longerpaper,“ NonlinearBehaviorofSpaceShuttleSuperlightweight Liquid-OxygenTankUnderPrelaunchLoads,” coversthestructure,theanalysistechnique,someloading cases,andexperimentalverie cationonthemethod.Itis followed by a companion paper, “ Modeling and NonlinearStructural Analysis of a Large-ScaleLaunch Vehicle,” which goes into greaterdepth on themethods, and then by three shorter papers, “ Effects of Welding-Induced Imperfections on Behavior of Space Shuttle Superlightweight Tank,” “ Nonlinear Behavior of Space Shuttle Superlightweight Tank Under Booster Ascent Loads,” and “ Nonlinear Behavior of Space Shuttle Superlightweight Tank Under End-of-Flight Loads,” covering interesting behaviorunder differing load cases. Thesepapersare intended to stand ontheir own (and hencehavesomeredundant introductory material) but are complementary to one another, and so they are presented here together.

Nonlinear Behavior of Space Shuttle Superlightweight Tank Under End-of-Flight Loads

Results of elastic, linear-bifurcation buckling and nonlinear analyses of the new Space Shuttle superlightweight external liquid-oxygen tank are presented for an important end-of-e ight loading condition. These results illustrate an important type of response mode for thin-walled shells subjected to combined mechanical and thermal loads that may be encountered in the design of other liquid-fuel launch vehicles. Linear-bifurcation buckling analyses are presented that predict several nearly equal eigenvalues that correspond to local buckling modes in the aft dome of the liquid-oxygen tank. In contrast, the nonlinear response phenomenon is shown to consist of a shortwavelength bending deformation in the aft elliptical dome of the liquid-oxygen tank that grows in amplitude in a stable manner with increasing load. Imperfection sensitivity analyses are presented that show that the presence of several nearly equal eigenvalues does not lead to a premature general instability mode for the aft dome. For the linear-bifurcation and nonlinear analyses, the results show that accurate predictions of the response of the shell generally require a large-scale, high-e delity, e nite element model, and that a design based on a linear-bifurcation buckling analysis and a buckling-load knockdown factor is overly conservative. Results are also presented that showthatthesuperlightweightliquid-oxygentankcansupportloadsin excessofapproximately1.9 timesthevalues of the operational loads considered.

Modeling and Nonlinear Structural Analysis of a Large-Scale Launch Vehicle

Advanced modeling and analysiscapabilitiesof a state-of-the-art general purposee niteelementcode, developed fornonlinearstructuralanalysisoflaunchvehicles,aredescribed.Inparticular,theapplicationofthesecapabilities to nonlinearanalyses of thenewSpaceShuttlesuperlightweight external liquid-oxygen tank arepresented thatcan beused asa guidefor conducting similar analyses on future launch vehicles. A typical prelaunch loading condition withcombinedthermalandmechanicalloadsisconsidered,andapplicationsoftheadvancedmodelingandanalysis capabilities to linear bifurcation buckling and nonlinear staticanalysesare presented. Theresults forthis problem illustrate a localized short-wavelength bending response, and that a high-e delity model is required to represent accurately the behavior. A mesh ree nement strategy is presented that is based on the linear bifurcation buckling analyses and does not require respecie cation of the shell wall properties and loads. Specie cally, mesh ree nement is simplie ed byusing user-writtensubroutinestodescribethespatialdistributionofcomplexshellwallpropertiesand loading conditions.In addition,a procedureforassessing thesensitivity to initialshellwallgeometricimperfections is presented. For the prelaunch load condition considered, the deformations from a nonlinear analysis using these capabilities are found to be similar in shape to the linear bifurcation buckling mode shape and insensitive to initial geometric imperfections. Recommended solution procedures for large-scale nonlinear analysis include using an arc-length projection method, and a combination of modie ed and true Newton refactoring schemes to balance computational efe ciency and robustness, with careful monitoring of the stability of the obtained solutions.

Effects of Welding-Induced Imperfections on Behavior of Space Shuttle Superlightweight Tank

Results of linear-bifurcation buckling and nonlinear analyses of the Space Shuttle superlightweight external liquid-oxygen tank are presented for an important prelaunch loading condition. These results show the effects of actual, measured welding-induced initial geometric imperfections on an important response mode for thin-walled shellsthataresubjectedtocombinedmechanicalandthermalloads.Thistypeofinitialgeometricimperfectionmay be encountered in the design of other liquid-fuel launch vehicles. Results are presented that show that the liquidoxygen tank will buckle in the barrel section, but at load levels nearly four times the magnitude of the operational load level, and will exhibit stable postbuckling behavior. The actual measured imperfections are located in this sectionofthetank. Resultsofimperfection sensitivity analysesarepresented thatshowthat thelargestdegradation in the apparent membrane stiffnesses of the liquid-oxygen tank barrel section is caused by an imperfection shape that is in the form of the linear-bifurcation buckling mode with a relatively small amplitude. These results also show that the effect of the relatively large-amplitude measured imperfection is benign.

Nonlinear Behavior of Space Shuttle Superlightweight Tank Under Booster Ascent Loads

Results of linear-bifurcation and nonlinear analyses of the Space Shuttle superlightweight (SLWT) external liquid-oxygen (LO2) tank for an important early booster ascent loading condition are presented. These results for thin-walled linear elastic shells that are subjected to combined mechanical and thermal loads illustrate an important type of response mode that may be encountered in the design of other liquid-fuel launch vehicles. Linear-bifurcation analyses are presented that predict several nearly equal eigenvalues that correspond to local buckling modes in the forward ogive section of the LO 2 tank. In contrast, the nonlinear response phenomenon is shown to consist of short-wavelength bending deformations in the forward-ogive and barrel sections of the LO2 tank that grow in amplitude in a stable manner with increasing load. Imperfection sensitivity analyses are presented that show that the presence of several nearly equal eigenvalues does not lead to a premature general instability mode for the forward-ogive section. For the linear-bifurcation and nonlinear analyses, the results show that accurate predictions of the response of the shell generally require a large-scale, high-e delity, e nite element model, and that a design based on a linear-bifurcation buckling analysis and a buckling-load knockdown factor is overly conservative. Results are presented that show that the SLWT LO 2 tank can support loads in excess of approximately 2.6 timesthevaluesof theoperationalloads considered. In addition, results are presented that show that local bending deformations may cause failure of the thermal protection system (TPS) at load levels less than the load level corresponding to structural collapse. Results are presented that can be used to estimate the load level at which TPS failure is likely to occur.

Structural Stability of a Stiffened Aluminum Fuselage Panel Subjected to Combined Mechanical and Internal Pressure Loads

Results from an experimental and analytical study of a curved stiffened aluminum panel subjected to combined mechanical and internal pressure loads are presented. The panel loading conditions were simulated using a D-box test fixture. Analytical buckling load results calculated from a finite element analysis are presented and compared to experimental results. Buckling results presented indicate that the buckling load of the fuselage panel is significantly influenced by internal pressure loading. The experimental results suggest that the stress distribution is uniform in the panel prior to buckling. Nonlinear finite element analysis results correlates well with experimental results up to buckling.

Prebuckling and Postbuckling Response of Tailored Composite Stiffened Panels with Axial-Shear Coupling

Results of a numerical parametric study of the prebuckling and postbuckling response of tailored composite stiffened panels with axial-shear coupling are presented. In the stiffened panels, axial-shear stiffness coupling is created by rotating the stiffener orientation and tailoring the skin laminate anisotropy. The panels are loaded in axial compression and the effects of stiffener orientation and skin anisotropy on the panel stiffness, buckling parameters, and axial-shear coupling response are described. Results are obtained from a nonlinear general shell finite element analysis computer code. The prebuckling and postbuckling responses can be affected by both the stiffener orientation and skin laminate anisotropy, and the effects are different and load dependent. The results help identify different mechanisms for axial-shear coupling, and show that a load-dependent structural response can be controlled by selecting appropriate stiffener and skin parameters.

Nonlinear Analysis of the Space Shuttle Superlightweight LO2 Tank. Part 1; Bahavior Under Booster Ascent Loads

NONLINEAR ANALYSIS OF THE SPACE SHUTTLE SUPERLIGHTWEIGHTLO 2 TANK: PART I - BEHAVIOR UNDER BOOSTER ASCENT LOADSRichard D. Young, Michael P. Nemeth, Timothy J. Collins, and James. H. Starnes, Jr.NASA Langley Research CenterHampton, Virginia 23681-0001Presented at the 39th AIAA/ASME/ASCE/AHS/ASC Structures,Structural Dynamics, and Material ConferenceAIAA Paper No. 98-1838Long Beach, CahforniaApril 20-23, 1998