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Orthotropic cylindrical shell buckling under axial compression - structural dynamics
Simple formulas for the buckling stress of homogeneous, specially orthotropic, laminated-composite cylinders are presented. The formulas are obtained by using nondimensional parameters and equations that facilitate general validation, and are validated against the exact solution for a wide range of cylinder geometries and laminate constructions. Results are presented that establish the ranges of the nondimensional parameters and coefficients used. General results, given in terms of the nondimensional parameters, are presented that encompass a wide range of geometries and laminate constructions. These general results also illustrate a wide spectrum of behavioral trends. Design-oriented results are also presented that provide a simple, clear indication of laminate composition on critical stress, critical strain, and axial stiffness. An example is provided to demonstrate the application of these results to thin-walled column designs.
With increasing use of ceramic materials in high temperature structural applications such as advanced heat engine components, the need arises to accurately predict thermomechanical behavior. This paper, which is the first of two in a series, will focus on inelastic deformation behavior associated with these service conditions by providing an overview of a viscoplastic constitutive model that accounts for time-dependent hereditary material deformation (e.g., creep, stress relaxation, etc.) in monolithic structural ceramics. Early work in the field of metal plasticity indicated that inelastic deformations are essentially unaffected by hydrostatic stress. This is not the case, however, for ceramic-based material systems, unless the ceramic is fully dense. The theory presented here allows for fully dense material behavior as a limiting case. In addition, ceramic materials exhibit different time-dependent behavior in tension and compression. Thus, inelastic deformation models for ceramics must be constructed in a fashion that admits both sensitivity to hydrostatic stress and differing behavior in tension and compression. A number of constitutive theories for materials that exhibit sensitivity to the hydrostatic component of stress have been proposed that characterize deformation using time-independent classical plasticity as a foundation. However, none of these theories allow different behavior in tension and compression. In addition, these theories are somewhat lacking in that they are unable to capture creep, relaxation, and rate-sensitive phenomena exhibited by ceramic materials at high temperature. When subjected to elevated service temperatures, ceramic materials exhibit complex thermomechanical behavior that is inherently time-dependent, and hereditary in the sense that current behavior depends not only on current conditions, but also on thermo-mechanical history. The objective of this work is to present the formulation of a macroscopic continuum theory that captures these time-dependent phenomena. Specifically, the overview contained in this paper focuses on the multiaxial derivation of the constitutive model, and examines the scalar threshold function and its attending geometrical implications.
Experiments on graphite-epoxy laminated plates containing unloaded small holes show that these laminates are notch insensitive. That is, the uniaxial strength of these laminates with small holes exceeds the strength predicted by a point stress criterion using the stress concentration factor for the in-plane stress field. Laminates containing large holes exhibit notch sensitive behavior and consequently their strength is reasonably well predicted by the stress concentration effect. This hole size effect is manifested both in tension and in compression. Apparently, some mechanism must cause in-plane stress relief for laminates containing small holes. The purpose of this research was to study the influence of geometric nonlinearity on the micromechanical response of a filamentary composite material in the presence of a strain gradient caused by a discontinuity such as a hole. A mathematical model was developed at the micromechanical level to investigate this geometrically nonlinear effect.
A total of 183 panel specimens of 24ST aluminum alloy with nominal thickness of 0.020, and 0.040 inch with extruded bulb-angle sections of 12 shapes spaced 4 and 5 inches as stiffeners were tested to obtain the buckling stress and the amplitude of the maximum wave when buckled. Bulb angles from 3 to 27 1/2 inches long were tested as pin-end columns. The experimental data are presented as stress-strain and column curves and in tabular form. Some comparisons with theoretical results are presented. Analytical methods are developed that make it possible for the designer to predict with reasonable accuracy the buckling stress and the maximum-wave amplitude of the sheet in stiffened-panel combinations. The scope of the tests was insufficient to formulate general design criteria but the results are presented as a guide for design and an indication of the type of theoretical and experimental work that is needed.
A numerical study was performed to investigate the unsteady, multidimensional flow inside the combustion chambers of an idealized, two-dimensional, rotary engine under motored conditions. The numerical study was based on the time-dependent, two-dimensional, density-weighted, ensemble-averaged conservation equations of mass, species, momentum, and total energy valid for two-component ideal gas mixtures. The ensemble-averaged conservation equations were closed by a K-epsilon model of turbulence. This K-epsilon model of turbulence was modified to account for some of the effects of compressibility, streamline curvature, low-Reynolds number, and preferential stress dissipation. Numerical solutions to the conservation equations were obtained by the highly efficient implicit-factored method of Beam and Warming. The grid system needed to obtain solutions were generated by an algebraic grid generation technique based on transfinite interpolation. Results of the numerical study are presented in graphical form illustrating the flow patterns during intake, compression, gaseous fuel injection, expansion, and exhaust.
A numerical study was performed to investigate the unsteady, multidimensional flow inside the combustion chambers of an idealized, two-dimensional, rotary engine under motored conditions. The numerical study was based on the time-dependent, two-dimensional, density-weighted, ensemble-averaged conservation equations of mass, species, momentum, and total energy valid for two-component ideal gas mixtures. The ensemble-averaged conservation equations were closed by a K-epsilon model of turbulence. This K-epsilon model of turbulence was modified to account for some of the effects of compressibility, streamline curvature, low-Reynolds number, and preferential stress dissipation. Numerical solutions to the conservation equations were obtained by the highly efficient implicit-factored method of Beam and Warming. The grid system needed to obtain solutions were generated by an algebraic grid generation technique based on transfinite interpolation. Results of the numerical study are presented in graphical form illustrating the flow patterns during intake, compression, gaseous fuel injection, expansion, and exhaust.
The present paper presents a numerical procedure to calculate supersonic and hypersonic flows using the compressible law of the wall. The turbulence models under consideration include the Launder-Reece-Rodi-Gibson Reynolds-stress model and the k-epsilon model. The models coupled with the proposed wall function technique have been tested in both separated and unseparated flows. The flows include (1) an insulated flat plate flow over a range of Mach numbers, (2) a Mach 5 flat plate flow with cold wall conditions, (3) a two dimensional supersonic compression corner flow, (4) a hypersonic flow over an axisymmetric flare, and (5) a hypersonic flow over a 2-D compression corner. Results indicate that the wall function technique gives improved predictions of skin friction and heat transfer in separated flows compared with models using wall dampers. Predictions of the extent of separation are not improved over the wall damper models except with the Reynolds-stress model for the supersonic compression corner flow case.
A preliminary study of structural concepts for noncircular fuselage configurations is presented. For an unconventional flying-wing type aircraft, in which the fuselage is inside the wing, multiple fuselage bays with non-circular sections need to be considered. In a conventional circular fuselage section, internal pressure is carried efficiently by a thin skin via hoop tension. If the section is non-circular, internal pressure loads also induce large bending stresses. The structure must also withstand additional bending and compression loads from aerodynamic and gravitational forces. Flat and vaulted shell structural configurations for such an unconventional, non-circular pressurized fuselage of a large flying-wing were studied. A deep honeycomb sandwich-shell and a ribbed double-wall shell construction were considered. Combinations of these structural concepts were analyzed using both analytical and simple finite element models of isolated sections for a comparative conceptual study. Weight, stress, and deflection results were compared to identify a suitable configuration for detailed analyses. The flat sandwich-shell concept was found preferable to the vaulted shell concept due to its superior buckling stiffness. Vaulted double-skin ribbed shell configurations were found to be superior due to their weight savings, load diffusion, and fail-safe features. The vaulted double-skin ribbed shell structure concept was also analyzed for an integrated wing-fuselage finite element model. Additional problem areas such as wing-fuselage junction and pressure-bearing spar were identified.
Shear stress and eddy viscosity distribution in Mach 20 compressible turbulent boundary layer, using mixing length flow theory
The effect of varying planetary crustal strength and surface gravity on the depth of impact craters is investigated, by coupling the results of compressible flow, finite difference calculations carried out to stress levels below the compressional dynamic yield point, in keeping with the incompressible fluid flow model of Maxwell (1973). The fundamental assumption in this description is that the amplitude of the particle velocity field decreases with time as kinetic energy is converted into heat and gravitational potential energy. By using a Mohr-Coulomb yield criterion, the effect of varying strength on transient crater depth and on crater formation time in the gravity field of the moon is investigated for the case of 5 km/sec impactors having radii in the 10 to 10 to the 7th cm range.
The aluminide intermetallic compounds are considered potential structural materials for aerospace applications. The B2 binary aluminide FeAl has a melting point in excess of 1500 K, is of simple cubic structure, exits over a wide range of composition with solubility for third elements and is potentially self-protecting in extreme environments. The B2 FeAl compound has been alloyed with 1 to 5 at % ternary additions of Si, Ti, Zr, Hf, Cr, Ni, Co, Nb, Ta, Mo, W, and Re. The alloys were prepared by blending a third elemental powder with prealloyed binary FeAl powder. Consolidation was by hot extrusion at 1250 K. Annealing studies on the extruded rods showed that the third element addition can be classified into three categories based upon the amount of homogenization and the extent of solid solutioning. Constant strain rate compression tests were performed to determine the flow stress as a function of temperature and composition. The mechanical strength behavior was dependent upon the third element homogenization classification.
The aluminide intermetallic compounds are considered potential structural materials for aerospace applications. The B2 binary aluminide FeAl has a melting point in excess of 1500 K, is of simple cubic structure, exists over a wide range of composition with solubility for third elements and is potentially self-protecting in extreme environments. The B2 FeAl compound has been alloyed with 1 to 5 at. pct ternary additions of Si, Ti, Zr, Hf, Cr, Ni, Co, Nb, Ta, Mo, W, and Re. The alloys were prepared by blending a third elemental powder with pre-alloyed binary FeAl powder. Consolidation was by hot extrusion at 1250 K. Annealing studies on the extruded rods showed that the third element addition can be classified into three categories based upon the amount of homogenization and the extent of solid solutioning. Constant strain rate compression tests were performed to determine the flow stress as a function of temperature and composition. The mechanical strength behavior was dependent upon the third element homogenization classification.
This paper presents (1) a brief overview of mathematical models used in the numerical study of turbulent flows; (2) a k-epsilon model of turbulence; and (3) extensions of the k-epsilon model. These account for some of the effects of compressibility, low Reynolds number, streamline curvature, and preferential stress dissipation.
The microstructural evolution of a commercial single crystal superalloy, NASAIR 100, is analyzed using the existing high-temperature lattice mismatch data and high-temperature moduli obtained from tests on single crystals of gamma and gamma prime. A multiparticle analysis of the microstructural evolution is performed using a novel microstructural lattice simulation technique, MCFET. Under a uniaxial stress, a regular array of gamma prime particles in the simulated microstructure is predicted to coalesce and form a plate morphology, with the broad faces of the plates and stress axis perpendicular in tension but parallel in compression. These results are consistent with changes in gamma prime shape observed in NASAIR 100 following creep testing at 1000 C.
The potential gain in buckling resistance is explored by using the curvilinear format with a plate containing a centrally located circular hole and subjected to a uniaxial compressive load. The buckling loads for a uniform stress loading and simple support boundary conditions were examined. The method of analysis is outlined for the buckling improvement study. Several designs that represent an improvement over a baseline quasi-isotropic design (a design that is quite good for buckling resistance) are discussed. The tensile load of these designs is examined. A recommended design is presented that not only shows an improved buckling capacity, but also shows improved tensile performance. Follow-on activities are also discussed.
The invention is a method and apparatus for characterizing residual uniaxial stress in a ferromagnetic test member by distinguishing between residual stresses resulting from positive (tension) forces and negative (compression) forces by using the distinct and known magnetoacoustic (MAC) and a magnetoacoustic emission (MAE) measurement circuit means. A switch permits the selective operation of the respective circuit means.
Baldwin-Lomax and kappa-epsilon turbulence models were modified for use in Navier-Stokes numerical computations of Mach 2.9 supersonic turbulent boundary layer flows along compression ramps. The computational results of Reynolds shear stress profiles were compared with experimental data. The Baldwin-Lomax model was modified to account for the Reynolds shear stress amplification within the flow field. A hybrid kappa-epsilon model with viscous sublayer turbulence treatment was constructed to predict the Reynolds shear stress profiles within the entire flow field. These modified turbulence models were effective for the computations of the surface pressure and the skin friction factor variations along an 8 deg ramp surface. The hybrid kappa-epsilon model could improve the predictions of the Reynolds shear stress profile and the skin friction factor near the corner of a 16 deg ramp.