HEXAGONAL CELL STRUCTURES UNDER POST-BUCKLING AXIAL LOAD
Determining the approximate crushing stress of hexagonal cell structures subject to axial loading
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Development and verification of global/local analysis techniques for laminated composites
A two-dimensional to three-dimensional global/local finite element approach was developed, verified, and applied to a laminated composite plate of finite width and length containing a central circular hole. The resulting stress fields for axial compression loads were examined for several symmetric stacking sequences and hole sizes. Verification was based on comparison of the displacements and the stress fields with those accepted trends from previous free edge investigations and a complete three-dimensional finite element solution of the plate. The laminates in the compression study included symmetric cross-ply, angle-ply and quasi-isotropic stacking sequences. The entire plate was selected as the global model and analyzed with two-dimensional finite elements. Displacements along a region identified as the global/local interface were applied in a kinematically consistent fashion to independent three-dimensional local models. Local areas of interest in the plate included a portion of the straight free edge near the hole, and the immediate area around the hole. Interlaminar stress results obtained from the global/local analyses compares well with previously reported trends, and some new conclusions about interlaminar stress fields in plates with different laminate orientations and hole sizes are presented for compressive loading. The effectiveness of the global/local procedure in reducing the computational effort required to solve these problems is clearly demonstrated through examination of the computer time required to formulate and solve the linear, static system of equations which result for the global and local analyses to those required for a complete three-dimensional formulation for a cross-ply laminate. Specific processors used during the analyses are described in general terms. The application of this global/local technique is not limited software system, and was developed and described in as general a manner as possible.
Thompson, Danniella Muheim↗
The stresses in stiffener openings
The present study treats as a typical example a ring the center line of which is produced by the intersection of two circular cylinders of different diameter. Three load cases are analyzed: (1) Axial and circumferential stresses in both cylinders, the cylinder stresses themselves to be in the ratio conformal to the cylinders loaded under internal pressure. (2) Pure longitudinal tension in the large cylinder. (3) Pure shear (torsion) in the large cylinder. To simplify the calculation, it is assumed that the ring, compared to the shell, is very strong, so that its deformations have no perceptible effect on the stress condition in the shell. This provides an upper limit for the ring stresses actually produced in a shell design, for, according to the theory of stressed skin statics the shells, by elastic flexibility of the ring, regroup the forces deposited on it in such a manner that the ring is relieved.
Marguerre, K↗
Residual stress in high modulus carbon fibers
The modulus and residual strain in carbon fibers are measured by successively electrochemically milling away the fiber surface. Electrochemical etching is found to remove the carbon fiber surface very uniformly, in contrast to air and wet oxidation. The precision of fiber diameter measurements is improved by using a laser diffraction technique instead of optical methods. More precise diameter measurements reveal that past correlations of diameter and fiber modulus are largely measurement artifact. The moduli of most carbon fibers decrease after the outer layers of the fibers are removed. Owing to experimental difficulties, the moduli and strengths of the fibers at their centers are not determined, and moduli are estimated on the basis of microstructure. The calculated residual stresses are found to be insensitive to these moduli estimates as well as the exact form of regression equation used to describe the moduli and residual strain distributions. Axial compressive residual stresses are found to be very high for some higher modulus carbon fibers. It is pointed out that the compressive stress makes the fibers insensitive to surface flaws when loaded in tension but it may initiate failure by buckling when loaded in compression.
Chen, K. J.↗
Analytical study of graphite-epoxy tube response to thermal loads
The thermally-induced stresses and deformations in graphite-epoxy tubes with aluminum foil bonded to both inner and outer surfaces, and to the outer surface only are computed. Tubes fabricated from three material systems, T300/934, P75s/934, and P75s/BP907, and having a 1 inch inner radius and a lamination sequence of (+15/0 + or - 10/0)sub s are studied. Radial, axial, and circumferential stresses in the various layers of the tube, in the foil, and in the adhesive bonding the foil to the tubes are computed using an elasticity solution. The results indicate that the coatings have no detrimental effect on the stress state in the tube, particularly those stresses that lead to microcracking. The addition of the aluminum foil does, however, significantly influence the axial expansion of the T300/934 tube, the tube with the softer graphite fibers. The addition of foil can change the sign of the axial coefficient of thermal expansion. Twist tendencies of the tubes are only slightly affected by the addition of the coatings, but are of second order compared to the axial response.
Knott, Tamara W.↗
Analysis of bonded joints
A refined elastic analysis of bonded joints which accounts for transverse shear deformation and transverse normal stress was developed to obtain the stresses and displacements in the adherends and in the bond. The displacements were expanded in terms of polynomials in the thicknesswise coordinate; the coefficients of these polynomials were functions of the axial coordinate. The stress distribution was obtained in terms of these coefficients by using strain-displacement and stress-strain relations. The governing differential equations were obtained by integrating the equations of equilibrium, and were solved. The boundary conditions (interface or support) were satisfied to complete the analysis. Single-lap, flush, and double-lap joints were analyzed, along with the effects of adhesive properties, plate thicknesses, material properties, and plate taper on maximum peel and shear stresses in the bond. The results obtained by using the thin-beam analysis available in the literature were compared with the results obtained by using the refined analysis. In general, thin-beam analysis yielded reasonably accurate results, but in certain cases the errors were high. Numerical investigations showed that the maximum peel and shear stresses in the bond can be reduced by (1) using a combination of flexible and stiff bonds, (2) using stiffer lap plates, and (3) tapering the plates.
Srinivas, S.↗
Analysis of pressurized and axially loaded orthotropic multicell tanks
Nondimensional stress resultants and displacements for multicell tanks of orthotropic construction loaded by internal pressure and axial compression
ORTHOTROPIC CYLINDER↗
Stresses and deformations in cross-ply composite tubes subjected to a uniform temperature change: Elasticity and Approximate Solutions
The effects of a uniform temperature change on the stresses and deformations of composite tubes are investigated. The accuracy of an approximate solution based on the principle of complementary virtual work is determined. Interest centers on tube response away from the ends and so a planar elasticity approach is used. For the approximate solution a piecewise linear variation of stresses with the radial coordinate is assumed. The results from the approximate solution are compared with the elasticity solution. The stress predictions agree well, particularly peak interlaminar stresses. Surprisingly, the axial deformations also agree well. This, despite the fact that the deformations predicted by the approximate solution do not satisfy the interface displacement continuity conditions required by the elasticity solution. The study shows that the axial thermal expansion coefficient of tubes with a specific number of axial and circumferential layers depends on the stacking sequence. This is in contrast to classical lamination theory which predicts the expansion to be independent of the stacking arrangement. As expected, the sign and magnitude of the peak interlaminar stresses depends on stacking sequence.
Hyer, M. W.↗
Micromechanical predictions of crack propagation and fracture energy in a single fiber boron/aluminum model composite
The axisymmetric finite element model and associated computer program developed for the analysis of crack propagation in a composite consisting of a single broken fiber in an annular sheath of matrix material was extended to include a constant displacement boundary condition during an increment of crack propagation. The constant displacement condition permits the growth of a stable crack, as opposed to the catastropic failure in an earlier version. The finite element model was refined to respond more accurately to the high stresses and steep stress gradients near the broken fiber end. The accuracy and effectiveness of the conventional constant strain axisymmetric element for crack problems was established by solving the classical problem of a penny-shaped crack in a thick cylindrical rod under axial tension. The stress intensity factors predicted by the present finite element model are compared with existing continuum results.
Adams, D. F.↗
Use of wire lacing to reduce blade vibration in an axial-flow compressor rotor
Stress analysis and wear tests in use of lacing wire as vibration damper on turbocompressor blades
Hager, R. D.↗
Phase average measurements of the coherent structure in a Mach number 0.6 jet
Phase averaged measurements of the axial mass velocity, radial velocity, and the product of the two have been made in an artificially excited cold air jet. The radial velocity fluctuations had a lower amplitude for both the full wave and phase averaged fluctuations compared to the axial mass velocity fluctuations. The Reynolds stress tended to decay faster in amplitude than the axial mass velocity and radial velocity fluctuations for both the full wave and phase averaged components. The radial velocity fluctuations possessed higher levels of coherence than the axial mass velocity fluctuation and the Reynolds stress. When the jet was excited at the frequency of St = 0.474, a high amplitude component at that frequency dominated the entire phase averaged flowfield from X/D = 1 to 10. This fundamental frequency was accompanied by several relatively high amplitude harmonics. These harmonics were more pronounced in the radial velocity fluctuations than for the axial fluctuations or the Reynolds stress.
Emami, S.↗
Influence of discontinuity stresses on main propellant tankage of a space shuttle orbiter.
Derivation of a general closed-form solution for the calculation of local stresses in cylindrical axial load-carrying pressure vessels which are heavily stiffened in the axial direction and circumferentially restrained by closely spaced ring stiffeners. The ring stiffeners are treated as discrete stiffeners and are allowed to have a temperature variation throughout the radial extension of the stiffener and different material properties compared with those of the vessel.
Meyer, H.-R.↗
Roller bearing geometry design
A theory of kinematic stabilization of rolling cylinders is extended and applied to the design of cylindrical roller bearings. The kinematic stabilization mechanism puts a reverse skew into the rolling elements by changing the roller taper. Twelve basic bearing modification designs are identified amd modeled. Four have single transverse convex curvature in their rollers while eight have rollers which have compound transverse curvature made up of a central cylindrical band surrounded by symmetric bands with slope and transverse curvature. The bearing designs are modeled for restoring torque per unit axial displacement, contact stress capacity, and contact area including dynamic loading, misalignment sensitivity and roller proportion. Design programs are available which size the single transverse curvature roller designs for a series of roller slopes and load separations and which design the compound roller bearings for a series of slopes and transverse radii of curvature. The compound rollers are proportioned to have equal contact stresses and minimum size. Design examples are also given.
Savage, M.↗
Buckling of angle-ply laminated circular cylindrical shells
This note presents closed-form solutions for axisymmetrical and axially unsymmetrical buckling of angle-ply laminated circular cylindrical shells under axial compression. The axisymmetrical and axially unsymmetrical buckling stress are found to be different from each other, and the best lamination angles which give the highest buckling stress are obtained.
Hirano, Y.↗
Elastic-plastic analysis using a triangular ring element in NASTRAN
An elastic plastic triangular ring element is implemented in NASTRAN computer program. The plane strain problem of partially plastic thick walled cylinder under internal pressure is solved and compared with the earlier finite difference solution. A very good agreement has been reached. In order to demonstrate its application to more general problems, an overloaded thread problem for the British Standard Buttress is examined. The maximum axial and principal stresses are located and their values are determined as functions of loadings.
Chen, P. C. T.↗
Advanced reinforcement systems for intermetallic applications
A 2-D axisymmetric model was employed to determine the magnitude of the radial, axial, and hoop stresses caused by the thermal expansion difference between fiber and matrix and which result from the fabrication temperature cycle. Finite element analysis was conducted for single fiber model systems based on SCS-6/Ti3Al+Nb and Al2O3/NiAl. The stress distribution due to the imposition of a graded intermediate layer for each system was determined and included variables of layer thickness and gradation in interlayer chemistry in order to vary the expansion gradient between fiber and matrix. Thermal cycling tests were conducted on sputter coated SCS-6 fibers selectively coated with Ti3Al+Nb, with and without an intermediate layer. Cracking of the Ti3Al+Nb layers was prevented by an interlayer based on Ti-TiN-Ti. The interlayer thickness appeared critical to its efficiency. Similarly, for the case of Al2O3/NiAl, an intermediate layer consisting of a Ni bond coat on the sapphire fiber followed by a graded Al2O3-NiAl layer did not crack when given a thermal excursion to 1100 C and then cooled to room temperature. Acoustic emission tests on single fiber specimens were unsuccessful in detecting load drops associated with the successive fracture of the fiber. For the SCS-6/Ti3Al system this was the result of several factors which included the matrix/fiber ratio and poor bonding of the matrix and fiber. In the case of the Al2O3/NiAl system brittle failure of the NiAl matrix precluded fiber breakdown during tensile loading.
Merrick, Howard F.↗
Supersonic shock wave/vortex interaction
Although shock wave/vortex interaction is a basic and important fluid dynamics problem, very little research has been conducted on this topic. Therefore, a detailed experimental study of the interaction between a supersonic streamwise turbulent vortex and a shock wave was carried out at the Penn State Gas Dynamics Laboratory. A vortex is produced by replaceable swirl vanes located upstream of the throat of various converging-diverging nozzles. The supersonic vortex is then injected into either a coflowing supersonic stream or ambient air. The structure of the isolated vortex is investigated in a supersonic wind tunnel using miniature, fast-response, five-hole and total temperature probes and in a free jet using laser Doppler velocimetry. The cases tested have unit Reynolds numbers in excess of 25 million per meter, axial Mach numbers ranging from 2.5 to 4.0, and peak tangential Mach numbers from 0 (i.e., a pure jet) to about 0.7. The results show that the typical supersonic wake-like vortex consists of a non-isentropic, rotational core, where the reduced circulation distribution is self similar, and an outer isentropic, irrotational region. The vortex core is also a region of significant turbulent fluctuations. Radial profiles of turbulent kinetic energy and axial-tangential Reynolds stress are presented. The interactions between the vortex and both oblique and normal shock waves are investigated using nonintrusive optical diagnostics (i.e. schlieren, planar laser scattering, and laser Doppler velocimetry). Of the various types, two Mach 2.5 overexpanded-nozzle Mach disc interactions are examined in detail. Below a certain vortex strength, a 'weak' interaction exists in which the normal shock is perturbed locally into an unsteady 'bubble' shock near the vortex axis, but vortex breakdown (i.e., a stagnation point) does not occur. For stronger vortices, a random unsteady 'strong' interaction results that causes vortex breakdown. The vortex core reforms downstream of the rear stagnation point, and the reduced circulation distribution once again becomes self-similar in this region. A-new model of this interaction is proposed. Finally, a curve defining the approximate limits of supersonic vortex breakdown is presented.
Settles, G. S.↗
Nonlinear Visco-Elastic Response of Composites via Micro-Mechanical Models
Micro-mechanical models for a study of nonlinear visco-elastic response of composite laminae are developed and their performance compared. A single integral constitutive law proposed by Schapery and subsequently generalized to multi-axial states of stress is utilized in the study for the matrix material. This is used in conjunction with a computationally facile scheme in which hereditary strains are computed using a recursive relation suggested by Henriksen. Composite response is studied using two competing micro-models, viz. a simplified Square Cell Model (SSCM) and a Finite Element based self-consistent Cylindrical Model (FECM). The algorithm is developed assuming that the material response computations are carried out in a module attached to a general purpose finite element program used for composite structural analysis. It is shown that the SSCM as used in investigations of material nonlinearity can involve significant errors in the prediction of transverse Young's modulus and shear modulus. The errors in the elastic strains thus predicted are of the same order of magnitude as the creep strains accruing due to visco-elasticity. The FECM on the other hand does appear to perform better both in the prediction of elastic constants and the study of creep response.
Gates, Thomas S.↗