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NASA NTRS2008

Improved Design Formulae for Buckling of Orthotropic Plates under Combined Loading

Simple, accurate buckling interaction formulae are presented for long orthotropic plates with either simply supported or clamped longitudinal edges and under combined loading that are suitable for design studies. The loads include 1) combined uniaxial compression (or tension) and shear, 2) combined pure inplane bending and 3) shear and combined uniaxial compression (or tension) and pure inplane bending. The interaction formulae are the results of detailed regression analysis of buckling data obtained from a very accurate Rayleigh-Ritz method.

Weaver, Paul M.↗

NASA NTRS2004

Combined Loads Test Fixture for Thermal-Structural Testing Aerospace Vehicle Panel Concepts

A structural test requirement of the National Aero-Space Plane (NASP) program has resulted in the design, fabrication, and implementation of a combined loads test fixture. Principal requirements for the fixture are testing a 4- by 4-ft hat-stiffened panel with combined axial (either tension or compression) and shear load at temperatures ranging from room temperature to 915 F, keeping the test panel stresses caused by the mechanical loads uniform, and thermal stresses caused by non-uniform panel temperatures minimized. The panel represents the side fuselage skin of an experimental aerospace vehicle, and was produced for the NASP program. A comprehensive mechanical loads test program using the new test fixture has been conducted on this panel from room temperature to 500 F. Measured data have been compared with finite-element analyses predictions, verifying that uniform load distributions were achieved by the fixture. The overall correlation of test data with analysis is excellent. The panel stress distributions and temperature distributions are very uniform and fulfill program requirements. This report provides details of an analytical and experimental validation of the combined loads test fixture. Because of its simple design, this unique test fixture can accommodate panels from a variety of aerospace vehicle designs.

Fields, Roger A.↗

NASA NTRS1972

Combined loading criterial influence on structural performance

An investigation was conducted to determine the influence of combined loading criteria on the space shuttle structural performance. The study consisted of four primary phases: Phase (1) The determination of the sensitivity of structural weight to various loading parameters associated with the space shuttle. Phase (2) The determination of the sensitivity of structural weight to various levels of loading parameter variability and probability. Phase (3) The determination of shuttle mission loading parameters variability and probability as a function of design evolution and the identification of those loading parameters where inadequate data exists. Phase (4) The determination of rational methods of combining both deterministic time varying and probabilistic loading parameters to provide realistic design criteria. The study results are presented.

Kuchta, B. J.↗

NASA NTRS2000

Loads Combination Research at Marshall Space Flight Center

This is the result of a study conducted by the Structural Dynamics Division of the Marshall Space Flight Center concerning the combination of low- and high-frequency dynamic loads for spacecraft design. Low-frequency transient loads are combined with high frequency acoustically induced loads to arrive at a limit load, for design purposes. Different methods are used for combining the loads which can lead to considerable variation in limit loads, depending on which NASA Center did the calculation. This study investigates several different combination methods and compares the combination methods with Spacelab 1 flight data. In addition, the relative timing of low- and high-frequency loads is examined.

Ferebee, R.↗

NASA NTRS2000

Loads Combination Research at Marshall Space Flight Center

Ferebee, R.↗

NASA NTRS1991

Combined-load buckling behavior of metal-matrix composite sandwich panels under different thermal environments

Combined compressive and shear buckling analysis was conducted on flat rectangular sandwich panels with the consideration of transverse shear effects of the core. The sandwich panel is fabricated with titanium honeycomb core and laminated metal matrix composite face sheets. The results show that the square panel has the highest combined load buckling strength, and that the buckling strength decreases sharply with the increases of both temperature and panel aspect ratio. The effect of layup (fiber orientation) on the buckling strength of the panels was studied in detail. The metal matrix composite sandwich panel was much more efficient than the sandwich panel with nonreinforced face sheets and had the same specific weight.

Ko, William L.↗

NASA NTRS1972

Thermal-structural combined loads design criteria study

A study was conducted to determine methodology for combining thermal structural loads and assessing the effects of the combined loads on the design of a thermal protection system and a hot structure of a high cross range delta wing space shuttle orbiter vehicle. The study presents guidelines for establishing a basis for predicting thermal and pressure environments and for determining limit and ultimate design loads on the vehicle during reentry. Limit trajectories were determined by using dispersions on a representative nominal mission and system parameters expected during the life of the vehicle. Nine chosen locations on the vehicle surface having TPS or hot structures were examined, and weight sensitivity analyses were performed for each location.

Deriugin, V.↗

NASA NTRS2001

The Nonlinear Response of Cracked Aluminum Shells Subjected to Combined Loads

The results of a numerical study of the nonlinear response of thin unstiffened aluminum cylindrical shells with a longitudinal crack are presented. The shells are analyzed with a nonlinear shelf analysis code that accurately accounts for global and structural response phenomena. The effects of initial crack length on the prebuckling, buckling and postbuckling responses of a typical shell subjected to axial compression loads, and subjected to combined internal pressure and axial compression loads are described. Both elastic and elastic-plastic analyses are conducted. Numerical results for a fixed initial crack length indicate that the buckling load decreases as the crack length increases for a given pressure load, and that the buckling load increases as the internal pressure load increases for a given crack length. Furthermore, results indicate that predictions from an elastic analysis for the initial buckling load of a cracked shell subjected to combined axial compression and internal pressure loads can be unconservative. In addition, the effect of crack extension on the initial buckling load is presented.

Rose, Cheryl A.↗

NASA NTRS1998

On the Buckling of Imperfect Anisotropic Shells with Elastic Edge Supports Under Combined Loading Part I:: Theory and Numerical Analysis - Pt. 1

A rigorous solution is presented for the case of stiffened anisotropic cylindrical shells with general imperfections under combined loading, where the edge supports are provided by symmetrical or unsymmetrical elastic rings. The circumferential dependence is eliminated by a truncated Fourier series. The resulting nonlinear 2-point boundary value problem is solved numerically via the "Parallel Shooting Method". The changing deformation patterns resulting from the different degrees of interaction between the given initial imperfections and the specified end rings are displayed. Recommendations are made as to the minimum ring stiffnesses required for optimal load carrying configurations.

Arbocz, Johann↗

NASA NTRS2000

Nonlinear Bulging Factors for Longitudinal and Circumferential Cracks in Cylindrical Shells Subjected to Combined Loads

Results of a geometrically nonlinear finite element parametric study to determine curvature correction factors or bulging factors that account for increased crack-tip stresses due to curvature for longitudinal and circumferential cracks in unstiffened cylindrical shells subjected to combined loads are presented. Nondimensional parameters varied in the study include the shell curvature parameter, l , which is a function of the shell radius, the shell wall thickness, and the crack length; a pressure loading parameter, h , which is a function of the shell geometry, material properties and the applied internal pressure; and a biaxial loading parameter, c , which is the ratio of the farfield axial stress to the farfield circumferential stress. The major results are presented in the form of contour plots of the bulging factor as a function of these three nondimensional parameters. These plots identify the ranges of the shell curvature and loading parameters for which the effects of geometric nonlinearity are significant, and show the effect of the biaxial loads on the value of the bulging factor. Simple empirical expressions for the bulging factor are then derived from the numerical results and are shown to predict accurately the nonlinear response of shells with longitudinal and circumferential cracks.

Young, Richard D.↗

NASA NTRS1993

Optimal design of imperfect, anisotropic, ring-stiffened cylinders under combined loads

Development of an algorithm to perform the optimal sizing of buckling resistant, imperfect, anisotropic ring-stiffened cylinders subjected to axial compression, torsion, and internal pressure is presented. The enforcement of stability constraints is treated in a way that does not require any eigenvalue analysis. Assumption of criticality of these stability constraints during the optimal sizing of the cylinders produced designs that nevertheless satisfied all of the stress constraints as well as the stability constraints. Case studies performed using a combination of penalty function and feasible direction optimization methods indicate that the presence of the axisymmetric initial imperfection in the cylinder wall can significantly affect the optimal designs. Weight savings associated with the addition of two rings to the unstiffened cylinder and/or the addition of internal pressure is substantial when torsion makes up a significant fraction of the combined load state.

Ley, Robert P.↗

NASA NTRS1999

Combined Loads, Vibration, and Modal Testing of QuickSCAT Spacecraft

Combining the quasi-static loads, workmanship verification, and model validation tests of aerospace hardware into a single vibration test sequence can considerably reduce schedule and cost.

QuickScat Spacecraft vibration testing force↗

NASA NTRS1977

Minimum-mass design of filamentary composite panels under combined loads: Design procedure based on a rigorous buckling analysis

A procedure is presented for designing uniaxially stiffened panels made of composite material and subjected to combined inplane loads. The procedure uses a rigorous buckling analysis and nonlinear mathematical programing techniques. Design studies carried out with the procedure consider hat-stiffened and corrugated panels made of graphite-epoxy material. Combined longitudinal compression and shear and combined longitudinal and transverse compression are the loadings used in the studies. The capability to tailor the buckling response of a panel is also explored. Finally, the adequacy of another, simpler, analysis-design procedure is examined.

Stroud, W. J.↗

NASA NTRS1962

ELASTIC INSTABILITY OF CONICAL SHELLS UNDER COMBINED LOADING

1. Criteria are presented for the elastic instability of thin single and multilayer conical and cylindrical shells under combined axial load and external pressure. These criteria, used in design analysis, are based on theoretical results and the correlation of these results with readily available experimental data. 2. A summary is included of the studies at Avco RAD of shells under static or dynamic loads.

ELASTIC SHELL↗

NASA NTRS1996

Effects of Combined Loads on the Nonlinear Response and Residual Strength of Damaged Stiffened Shells

Starnes, James H., Jr.↗

NASA NTRS1989

Experimental/analytical characterization of composite tubes under combined loading

The paper outlines the results of an investigation performed to characterize the response of P75/934 graphite/epoxy tubes with a stacking sequence of (15/0/+,-10/0/-15)s under pure torsion and combined axial/torsion loading. The experimentally observed nonlinear response and path-dependent failure are discussed in terms of material nonlinearites at the ply level and first ply failure loads with the help of an analytical model.

Derstine, Mark S.↗

NASA NTRS1974

Effects of proof loads and combined mode loadings on fracture and flaw growth characteristics of aerospace alloys

This experimental program was undertaken to determine the effects of (1) combined tensile and bending loadings, (2) combined tensile and shear loadings, and (3) proof overloads on fracture and flaw growth characteristics of aerospace alloys. Tests were performed on four alloys: 2219-T87 aluminum, 5Al-2.5Sn (ELl) titanium, 6Al-4V beta STA titanium and high strength 4340 steel. Tests were conducted in room air, gaseous nitrogen at -200F (144K), liquid nitrogen and liquid hydrogen. Flat center cracked and surface flawed specimens, cracked tube specimens, circumferentially notched round bar and surface flawed cylindrical specimens were tested. The three-dimensional photoelastic technique of stress freezing and slicing was used to determine stress intensity factors for surface flawed cylindrical specimens subjected to tension or torsion. Results showed that proof load/temperature histories used in the tests have a small beneficial effect or no effect on subsequent fracture strength and flaw growth rates.

Shah, R. C.↗

NASA NTRS1996

Nonlinear Response and Residual Strength of Damaged Stiffened Shells Subjected to Combined Loads

The results of an analytical study of the nonlinear response of stiffened fuselage shells with long cracks are presented. The shells are modeled with a hierarchical modeling strategy and analyzed with a nonlinear shell analysis code that maintains the shell in a nonlinear equilibrium state while the crack is grown. The analysis accurately accounts for global and local structural response phenomena. Fuselage skins, frames stringers and failsafe straps are included in the models. Results are presented for various combinations of internal pressure and mechanical bending, vertical shear and torsion loads, and the effects of crack orientation and location on the shell response are described. These results indicate that the nonlinear interaction between the in-plane stress resultants and the out-of-plane displacements near a crack can significantly affect the structural response of the shell, and the stress-intensity factors associated with a crack that are used to predict residual strength. The effects of representative combined loading conditions on the stress-intensity factors associated with a crack are presented. The effects of varying structural parameters on the stress-intensity factors associated with a crack, and on self-similar and non-self-similar crack-growth are also presented.

Starnes, James H., Jr.↗