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NASA NTRS1949

Some New Problems on Shells and Thin Structures

Cylindrical shells of arbitrary section, reinforced by longitudinal and transverse members (stringers and ribs) are considered by us, for a sufficiently close spacing of the ribs, as in our previously published papers (references 1 end 2), as thin-walled orthotropic spatial systems at the cross-sections of which only axial (normal and shearing) forces can arise. The longitudinal bending and twisting moments, due to their weak effect on the stress state of the shell, are taken equal to zero. Along the longitudinal sections of the shell there may arise transverse forces in addition to the normal ~d shearing forces. Under the so-called static assumptions there is taken for the computation model of the shell a thin-walled spatial system consisting along its length (along a generator) of an infinite number of elementary strips capable of bending. Each of these strips is likened to a curved rod operating in each of its sections not only in tension (compression)but also in transverse bending and shear. The interaction between two adjoining transverse strips in the shell expresses itself in the transmission from one strip to the other of only the normal and shearing stresses. The static structure of the computation model here described is shown in figure 1, where the connections through which the normal and shearing stresses transmitted from one transverse strip to smother are indicated schematically by the rods located in the middle surface of the shell. In addition to the static hypothesis we introduce also geometric hypotheses. According to the latter the elongational deformations of the shell along lines parallel to the generator of its middle surface and the shear deformations in the middle surface, as ma+gitudes having . little effect on the state of the fundamental internal forces of the shell, are taken equal to zero. The deformations of the shell in our computational model are such that in the first place the lines of this surface perpendicular to the generator are inextensible at each point end in the second place the angles between the lines of principal curvature (the coordinate lines) which are straight before the deformation remain straight after the deformation.

Vlasov, V. S.↗

NASA NTRS1991

Fluid-structure interaction forces at pump-impeller-shroud surfaces for axial vibration analysis

The axial forces developed on a pump impeller shroud surfaces are analyzed using a bulk-flow model of the leakage path between the impeller and the housing. Shear stresses at the impeller and the housing surfaces are modeled according to Hirs's turbulent lubrication model. The calculated results yield predictions of resonance peaks of the fluid within the annulus formed by the impeller shroud and housing. Numerical results are presented for a double-suction single-stage pump, showing that the direct stiffness of the perturbed impeller shroud forces is negligible; the forces become important only for pumps with very low axial natural frequencies in comparison to the running speed.

Childs, D. W.↗

NASA NTRS1993

Analytical stress intensity solution for the Stable Poisson Loaded specimen

An analytical calibration of the Stable Poisson Loaded (SPL) specimen is presented. The specimen configuration is similar to the ASTM E-561 compact-tension specimen with displacement controlled wedge loading used for R-curve determination. The crack mouth opening displacements (CMODs) are produced by the diametral expansion of an axially compressed cylindrical pin located in the wake of a machined notch. Due to the unusual loading configuration, a three-dimensional finite element analysis was performed with gap elements simulating the contact between the pin and specimen. In this report, stress intensity factors, CMODs, and crack displacement profiles, are reported for different crack lengths and different contacting conditions. It was concluded that the computed stress intensity factor decreases sharply with increasing crack length thus making the SPL specimen configuration attractive for fracture testing of brittle, high modulus materials.

Ghosn, Louis J.↗

NASA NTRS1981

Application of the line-spring model to a cylindrical shell containing a circumferential or axial part-through crack

An approximate solution was obtained for a cylindrical shell containing a part-through surface crack. It was assumed that the shell contains a circumferential or axial semi-elliptic internal or external surface crack and was subjected to a uniform membrane loading or a uniform bending moment away from the crack region. A Reissner type theory was used to account for the effects of the transverse shear deformations. The stress intensity factor at the deepest penetration point of the crack was tabulated for bending and membrane loading by varying three dimensionless length parameters of the problem formed from the shell radius, the shell thickness, the crack length, and the crack depth. The upper bounds of the stress intensity factors are provided by the results of the elasticity solution obtained from the axisymmetric crack problem for the circumferential crack, and that found from the plane strain problem for a circular ring having a radial crack for the axial crack. The line-spring model gives the expected results in comparison with the elasticity solutions. Results also compare well with the existing finite element solution of the pressurized cylinder containing an internal semi-elliptic surface crack.

Delale, F.↗

NASA NTRS1977

Biaxial fatigue loading of notched composites

Thin walled, 2.54-cm (1-in.) diameter tubular specimens of T300/934 graphite/epoxy were fabricated and fatigue cycled in combinations of axial, torsional, and internal pressure loading. Two different four-ply layup configurations were tested: (0/90)S and (+ or - 45)S; all tubes contained a 0.48-cm (3/16-in.) diameter circular hole penetrating one wall midway along the tube length. S-N curves were developed to characterize fatigue behavior under pure axial, torsional, or internal pressure loading, as well as combined loading fatigue. A theory was developed based on the Hill plane stress model which enabled the S-N curve for combined stress states to be predicted from the S-N data for the uniaxial loading modes. Correlation of the theory with the experimental data proved to be remarkably good.

Francis, P. H.↗

NASA NTRS1981

Edge delamination in angle-ply composite laminates

Edge delamination has caused severe concern in the design and analysis of advanced composite materials and structures. Due to its complex nature, very limited knowledge for the problem is currently available. It involves not only geometric and material discontinuities but also inherently coupled mode I, II and III fracture in the layered anisotropic system. Based on complex-variable stress potentials in the anisotropic elasticity theory and eigenfunction expansion, exact orders of the crack-tip stress singularity and complete field solutions are obtained. Results are given for edge delaminated, angle-ply composites subjected to uniform axial extension for illustrative purposes. Effects of geometric, lamination, and crack variables are determined.

Wang, S. S.↗

NASA NTRS1983

A turbulence model for three dimensional turbulent shear flows over curved rotating bodies

There exists currently considerable interest in the development of numerical procedures for solving the equations governing three-dimensional fluid flows. In particular, improved calculations of viscous flows on rotating bodies such a turbomachinery rotors are of great importance. The present investigation is mainly concerned with the analysis of the effect of rotation on the dissipation rate equation and the Reynolds stress equations. Attention is given to governing equations and modelling, algebraic Reynolds stress equations, a procedure for implementing the turbulence closure scheme, results for a model representative of centrifugal turbomachinery, and results for axial turbomachinery. The proposed turbulence model is valid for three-dimensional, rotating, and curved flows. The model has all the essential physics of turbulence, mean flow, rotation, and the curvature.

Galmes, J. M.↗

NASA NTRS1987

Effect of dropped plies on the strength of graphite-epoxy laminates

The reduction in the compressive and tensile strengths of graphite-epoxy laminates with thickness discontinuities due to dropped plies was studied by experiment and analysis. The specimens were fabricated with all the dropped plies lumped together in the center of a sixteen-ply quasi-isotropic layup, such that one surface was flat and the slope of the opposite surface changed abruptly at the dropped ply location to accommodate the thickness change. Even though the thick and thin sections are symmetrically laminated, there exists bending-extension coupling due to the geometric eccentricity of the middle planes of the thick and thin sections. Experiments were conducted on fifty-four specimens that differed in the configuration of the dropped plies only. The strength of a laminate with dropped plies is less than the strength of its thin section, and the compressive strength of a laminate with dropped plies is less than its tensile strength. The reduction in strength is directly related to the axial stiffness change between the thick and thin sections. To examine the mechanism of failure, the three-dimensional state of stress in the dropped ply region was evaluated by the finite element method. A tensile interlaminar criterion predicted the correct location of failure, but underestimated the failure load.

Curry, James M.↗

NASA NTRS1997

Turbulence Measurements in the Near Field of a Wingtip Vortex

The roll-up of a wingtip vortex, at Reynolds number based on chord of 4.6 million was studied with an emphasis on suction side and near wake measurements. The research was conducted in a 32 in. x 48 in. low-speed wind tunnel. The half-wing model had a semi-span of 36 in. a chord of 48 in. and a rounded tip. Seven-hole pressure probe measurements of the velocity field surrounding the wingtip showed that a large axial velocity of up to 1.77 U(sub infinity) developed in the vortex core. This level of axial velocity has not been previously measured. Triple-wire probes have been used to measure all components of the Reynolds stress tensor. It was determined from correlation measurements that meandering of the vortex was small and did not appreciably contribute to the turbulence measurements. The flow was found to be turbulent in the near-field (as high as 24 percent RMS w - velocity on the edge of the core) and the turbulence decayed quickly with streamwise distance because of the nearly solid body rotation of the vortex core mean flow. A streamwise variation of the location of peak levels of turbulence, relative to the core centerline, was also found. Close to the trailing edge of the wing, the peak shear stress levels were found at the edge of the vortex core, whereas in the most downstream wake planes they occurred at a radius roughly equal to one-third of the vortex core radius. The Reynolds shear stresses were not aligned with the mean strain rate, indicating that an isotropic-eddy-viscosity based prediction method cannot accurately model the turbulence in the cortex. In cylindrical coordinates, with the origin at the vortex centerline, the radial normal stress was found to be larger than the circumferential.

Chow, Jim↗

NASA NTRS2001

Theoretical Investigation of Thermo-Mechanical Behavior of Carbon Nanotube-Based Composites Using the Integral Transform Method

This project uses the integral transform technique to model the problem of nanotube behavior as an axially symmetric system of shells. Assuming that the nanotube behavior can be described by the equations of elasticity, we seek a stress function x which satisfies the biharmonic equation: del(exp 4) chi = [partial deriv(r(exp 2)) + partial deriv(r) + partial deriv(z(exp 2))] chi = 0. The method of integral transformations is used to transform the differential equation. The symmetry with respect to the z-axis indicates that we only need to consider the sine transform of the stress function: X(bar)(r,zeta) = integral(from 0 to infinity) chi(r,z)sin(zeta,z) dz.

Pawloski, Janice S.↗

NASA NTRS2002

High-Fidelity Generalization Method of Cells for Inelastic Periodic Multiphase Materials

An extension of a recently-developed linear thermoelastic theory for multiphase periodic materials is presented which admits inelastic behavior of the constituent phases. The extended theory is capable of accurately estimating both the effective inelastic response of a periodic multiphase composite and the local stress and strain fields in the individual phases. The model is presently limited to materials characterized by constituent phases that are continuous in one direction, but arbitrarily distributed within the repeating unit cell which characterizes the material's periodic microstructure. The model's analytical framework is based on the homogenization technique for periodic media, but the method of solution for the local displacement and stress fields borrows concepts previously employed by the authors in constructing the higher-order theory for functionally graded materials, in contrast with the standard finite-element solution method typically used in conjunction with the homogenization technique. The present approach produces a closed-form macroscopic constitutive equation for a periodic multiphase material valid for both uniaxial and multiaxial loading. The model's predictive accuracy in generating both the effective inelastic stress-strain response and the local stress said inelastic strain fields is demonstrated by comparison with the results of an analytical inelastic solution for the axisymmetric and axial shear response of a unidirectional composite based on the concentric cylinder model, and with finite-element results for transverse loading.

Aboudi, Jacob↗

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 NTRS2012

Evaluation of Brazed Joints Using Failure Assessment Diagram

Fitness-for service approach was used to perform structural analysis of the brazed joints consisting of several base metal / filler metal combinations. Failure Assessment Diagrams (FADs) based on tensile and shear stress ratios were constructed and experimentally validated. It was shown that such FADs can provide a conservative estimate of safe combinations of stresses in the brazed joints. Based on this approach, Margins of Safety (MS) of the brazed joints subjected to multi-axial loading conditions can be evaluated..

Flom, Yury↗

NASA NTRS2022

Calculating Factors of Safety and Margins of Safety from Interaction Equations for Preloaded Bolts

This report presents the derivation of the factored interaction equations for preloaded bolts in two- or three-dimensional space. This is an extension of the previous work of the first author which covered factored interaction equations consisting of load or stress-ratios which were either solely constant or solely varying quantities. The factored interaction equations for preloaded bolts consist of an axial load-ratio that is a combination of a constant quantity, preload and thermal load at preload, and a varying quantity, tensile and bending loads, and was not covered under the previous work. Two forms of the factored interaction equations for preloaded bolts, arising from two perspectives, are presented and compared. Closed form solutions for the tensile, shear, and bending loads as functions of the other concurrent loads that produces zero margin of safety are presented.

interaction equations↗

NASA NTRS1999

Turbomachinery Design Quality Checks to Avoid Friction Induced Structural Failure

A unique configuration of the P&W SSME Alternate Fuel Turbopump turbine disk/blade assembly, combined with a severe thermal environment, resulted in several structural anomalies that were driven by frictional contact forces. Understanding the mechanics of these problems provides new quality checks for future turbo machinery designs. During development testing in 1997 of the SSME alternate fuel turbopump at Stennis Space Center, several potentially serious problems surfaced with the turbine disk/blade assembly that had not been experienced in extensive earlier testing. Changes to the operational thermal environment were noted based on analytical prediction of modifications that affected performance and on stationary thermal measurements adjacent to the rotor assembly. A detailed structural investigation was required to reveal the mechanism of distress induced by the change. The turbine disk experienced cracking in several locations due to increased thermal gradient induced stress during start and shutdown transients. This was easily predictable using standard analysis procedures and expected once the thermal environment was characterized. What was not expected was the curling of a piston ring used for blade axial retention in the disk, indentation of the axial face of the blade attachment by a spacer separating the first and second stage blades, and most significantly, galling and cracking of the blade root attachment that could have resulted in blade release. Past experience, in gas turbine environments, set a precedent of never relying on friction for help and to evaluate it only in specific instances where it was obvious that it would degrade capability. In each of the three cases above, friction proved to be a determining factor that pushed the components into an unsatisfactory mode of operation. The higher than expected temperatures and rapid thermal transients combined with friction to move beyond past experience. The turbine disk/blade assembly configuration contributed to the potential for these problems to occur by limiting the radial deflection from thermals and centrifugal loading. The cooled solid bore configuration was chosen to improve rotordynamic stability by limiting the length of rotor overhang while still protecting the roller bearing by maintaining zero slope under the inner race. During a start transient, the rim area of the disk heats rapidly and expands axially and circumferentially and requires corresponding radial and axial growth of the disk to maintain relative positioning of the disk, blades, spacers and retainer rings. The stiffness, large thermal mass, and bore cooling flow combine to severely limit the disk rim radial growth which results in the potential for relative movement between these parts. Friction then becomes a player in the determination of component stress.

Moore, Jerry H.↗

NASA NTRS1959

Analysis of Turbulent Flow and Heat Transfer in Noncircular Passages

Previous work on turbulent heat transfer and flow in tubes was generalized and applied to flow in non-circular passages of equilateral triangular and square cross section. Expressions for eddy diffusivity that had been verified for flow and heat transfer in tubes were assumed to apply in general along lines normal to a wall. Velocity distributions, wall shear-stress distributions, and friction factors, as well as wall heat-transfer distributions, wall temperature distributions, and average heat-transfer coefficients were calculated. In addition, results from a previous analysis for axial flow between rods were compared with new experimental data. For calculating wall temperature distributions, uniform heat generation in the passage wall and uniform heat transfer at the outer surface were assumed. The application of the results is restricted to moderately small peripheral wall temperature variations. Calculations were made for Reynolds numbers from 20,000 to 900,000 and Prandtl numbers from 0.73 to 300. Results show that velocities, shear stresses, and heat transfer in the region near the corner were lower than average values and were zero at the corner. Friction factors and average Nusselt numbers were lower than in a tube.

Taylor, Maynard F.↗

NASA NTRS1976

Nonlinear analysis of laminated fibrous composites

A computerized analysis of the nonlinear behavior of fibrous composite laminates including axial loading, thermal loading, temperature dependent properties, and edge effects is presented. Ramberg-Osgood approximations are used to represent lamina stress-strain behavior and percent retention curves are employed to model the variation of properties with temperature. Balanced, symmetric laminates comprised of either boron/epoxy, graphite/epoxy, or borsic-aluminum are analyzed using a quasi-three-dimensional finite element analysis. Results are presented for the interlaminar stress distributions in cross-ply, angle-ply, and more complex laminates. Nonlinear stress-strain curves for a variety of composite laminates in tension and compression are obtained and compared to other existing theories and experimental results.

Renieri, G. D.↗

NASA NTRS1990

The University of Minnesota oscillating flow experiments

Hot-wire anemometry techniques used to document laminar-to-turbulent transition in oscillating flow are discussed, and two transition mechanisms proposed by Seume (1988) are reviewed. Reliable near-wall data, and the convergence of ensemble-averaged velocities and rms velocity fluctuations will aid in evaluating wall shear stresses and calculating various boundary-layer parameters. Special consideration was given to a detailed measurement program which documents transition at different axial positions for the space power research engine (SPRE) operating point. Future work on the effect of entry geometry and measurements of heat transfer are outlined. In order to better simulate flow conditions in actual Stirling engine heat exchangers, the effects of various inflow geometries are investigated. Once the hydrodynamic conditions in the test section are documented, a measurement program to assess the effect of flow oscillation on heat transfer will commence.

Friedman, G. T.↗