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NASA NTRS1993

Finite element study of plate buckling induced by spatial temperature gradients

Finite element analyses of thermal buckling of thin metallic plates with prescribed spatial temperature distributions are described. Thermally induced compressive membrane stresses and transverse plate displacement imperfections initiate plates buckling. A finite element formulation based on von Karman plate theory is presented. The resulting nonlinear equations are solved for incremental temperature increases by Newton-Raphson iteration. The computational method is used to investigate the buckling response of rectangular plates with steady and unsteady spatially varying temperature distributions. The role of initial plate imperfections and temperature distributions on the nonlinear response of plate displacements and stresses is described. The relatively high levels of stress induced by spatial temperature gradients should be considered carefully in the postbuckling design of panels for aerospace vehicles subjected to combined mechanical and thermal loads.

Thornton, Earl A.↗

NASA NTRS1994

Effects of Tangential Edge Constraints on the Postbuckling Behavior of Flat and Curved Panels Subjected to Thermal and Mechanical Loads

A parametric study of the effects of tangential edge constraints on the postbuckling response of flat and shallow curved panels subjected to thermal and mechanical loads is presented. The mechanical loads investigated are uniform compressive edge loads and transverse lateral pressure. The temperature fields considered are associated with spatially nonuniform heating over the panels, and a linear through-the-thickness temperature gradient. The structural model is based on a higher-order transverse-shear-deformation theory of shallow shells that incorporates the effects of geometric nonlinearities, initial geometric imperfections, and tangential edge motion constraints. Results are presented for three-layer sandwich panels made from transversely isotropic materials. Simply supported panels are considered in which the tangential motion of the unloaded edges is either unrestrained, partially restrained, or fully restrained. These results focus on the effects of the tangential edge restraint on the postbuckling response. The results of this study indicate that tangentially restraining the edges of a curved panel can make the panel insensitive to initial geometric imperfections in some cases.

Lin, W.↗

NASA NTRS1996

A Comparison of Tension and Compression Creep in a Polymeric Composite and the Effects of Physical Aging on Creep Behavior

Experimental and analytical methods were used to investigate the similarities and differences of the effects of physical aging on creep compliance of IM7/K3B composite loaded in tension and compression. Two matrix dominated loading modes, shear and transverse, were investigated for two load cases, tension and compression. The tests, run over a range of sub-glass transition temperatures, provided material constants, material master curves and aging related parameters. Comparing results from the short-term data indicated that although trends in the data with respect to aging time and aging temperature are similar, differences exist due to load direction and mode. The analytical model used for predicting long-term behavior using short-term data as input worked equally as well for the tension or compression loaded cases. Comparison of the loading modes indicated that the predictive model provided more accurate long term predictions for the shear mode as compared to the transverse mode. Parametric studies showed the usefulness of the predictive model as a tool for investigating long-term performance and compliance acceleration due to temperature.

Gates, Thomas S.↗

NASA NTRS1988

An analytical study of the effects of transverse shear deformation and anisotropy on natural vibration frequencies of laminated cylinders

Natural vibration frequencies of orthotropic and anisotropic simply supported right circular cylinders are predicted using a higher-order transverse-shear deformation theory. A comparison of natural vibration frequencies predicted by first-order transverse-shear deformation theory and the higher-order theory shows that an additional allowance for transverse shear deformation has a negligible effect on the lowest predicted natural vibration frequencies of laminated cylinders but significantly reduces the higher natural vibration frequencies. A parametric study of the effects of ply orientation on the natural vibration frequencies of laminated cylinders indicates that while stacking sequence affects natural vibration frequencies, cylinder geometry is more important in predicting transverse-shear deformation effects. Interaction curves for cylinders subjected to axial compressive loadings and low natural vibration frequencies indicate that transverse shearing effects are less important in predicting low natural vibration frequencies than in predicting axial compressive buckling loads. The effects of anisotropy are more important than the effects of transverse shear deformation for most strongly anisotropic laminated cylinders in predicting natural vibration frequencies. However, transverse-shear deformation effects are important in predicting high natural vibration frequencies of thick-walled laminated cylinders. Neglecting either anisotropic effects or transverse-shear deformation effects leads to non-conservative errors in predicted natural vibration frequencies.

Jegley, Dawn C.↗

NASA NTRS1989

An analytical study of the effects of transverse shear deformation and anisotropy on natural vibation frequencies of laminated cylinders

Jegley, Dawn C.↗

NASA NTRS1942

Tensile and pack compressive tests of some sheets of aluminum alloy, 1025 carbon steel, and chromium-nickel steel

Tensile and compressive stress-strain curves, stress-deviation curves, and secant modulus-stress curves are given for longitudinal and transverse specimens of 17S-T, 24S-T, and 24S-RT aluminum-alloy sheet in thicknesses from 0.032 to 0.081 inch, 1025 carbon steel sheet in thicknesses of 0.054 and 0.120 inch, and chromium-nickel steel sheet in thicknesses form 0.020 to 0.0275 inch. Significant differences were found between the tensile and the compressive stress-strain curves, and also the corresponding corollary curves; similarly, differences were found between the curves for the longitudinal and transverse directions. These differences are of particular importance in considering the compressive strength of aircraft structures made of thin sheet. They are explored further for the case of compression by giving tangent modulus-stress curves in longitudinal and transverse compression and dimensionless curves of the ratio of tangent modulus to Young's modulus and of the ratio of reduced modulus for a rectangular section to Young's modulus, both plotted against the ratio of stress to secant yield strength.

Atchison, C S↗

NASA NTRS1989

Recent results concerning the stability of viscoelastic shear deformable plates under compressive edge loading

Some recent results obtained by the authors are summarized concerning the stability of transversely isotropic flat panels whose materials exhibit a viscoelastic behavior and whose edges are subjected to in-plane biaxial compressive loads. Two transversely isotropic type materials, largely used in advanced technology, are considered: (1) the pyrolytic-graphite type, used in the thermal protection of aerospace vehicles, and (2) the type corresponding to unidirectional fiber-reinforced composites. In the former case, the planes of isotropy are parallel at each point to the midplane of the plate. In the latter case, they are normal to the fiber directions. The micromechanical relations developed by Aboudi (1984, 1986, 1987) are considered in conjunction with the correspondence principle of linear viscoelastic theory in order to predict the macroscopic viscoelastic properties of a material composed of uniaxial elastic fibers embedded in a linear viscoelastic matrix.

Librescu, L.↗

NASA NTRS1979

Recent development in the design, testing and impact-damage tolerance of stiffened composite panels

Structural technology of laminated filamentary-composite stiffened-panel structures under combined inplane and lateral loadings is discussed. Attention is focused on: (1) methods for analyzing the behavior of these structures under load and for determining appropriate structural proportions for weight-efficient configurations; and (2) effects of impact damage and geometric imperfections on structural performance. Recent improvements in buckling analysis involving combined inplane compression and shear loadings and transverse shear deformations are presented. A computer code is described for proportioning or sizing laminate layers and cross-sectional dimensions, and the code is used to develop structural efficiency data for a variety of configurations, loading conditions, and constraint conditions. Experimental data on buckling of panels under inplane compression is presented. Mechanisms of impact damage initiation and propagation are described.

Williams, J. G.↗

NASA NTRS1994

Post-impact fatigue of cross-plied, through-the-thickness reinforced carbon/epoxy composites

An experimental investigation of the post-impact fatigue response of integrally woven carbon/epoxy composites was conducted. Five different through-the-thickness (TTT) reinforcing fibers were used in an experimental textile process that produced an integrally woven (0/90/0/90/0/90/0/90/0)(sub T) ply layup with 21K AS4 carbon tow fiber. The resin was Hercules 3501-6, and the five TTT reinforcing fibers were Kevlar, Toray carbon, AS4 carbon, glass, and IM6 carbon. The purpose of this investigation was to study the post-impact fatigue response of these material systems and to identify the optimum TTT fiber. Samples were impacted with one half inch diameter aluminum balls with an average velocity of 543 ft/sec. Post-impact static compression and constant amplitude tension-compression fatigue tests were conducted. Fatigue tests were conducted with a loading ratio of R=-5, and frequency of 4 Hz. Damage growth was monitored using x-radiographic and sectioning techniques and by examining the stress-strain response (across the impact site) throughout the fatigue tests. The static compressive stress versus far-field strain response was nearly linear for all material groups. All the samples had a transverse shear failure mode. The average compressive modulus (from far-field strain) was about 10 Msi. The average post-impact static compressive strength was about 35.5 Ksi. The IM6 carbon sample had a strength of over 40 Ksi, more than 16 percent stronger than average. There was considerable scatter in the S-N data. However, the IM6 carbon samples clearly had the best fatigue response. The response of the other materials, while worse than IM6 carbon, could not be ranked definitively. The initial damage zones caused by the impact loading and damage growth from fatigue loading were similar for all five TTT reinforcing materials. The initial damage zones were circular and consisted of delaminations, matrix cracks and ply cracks. Post-impact fatigue loading caused delamination growth, ply cracking and fiber bundle failures, typically 45 deg from impact load direction. During the initial 97 percent of fatigue life, delaminations, ply cracks and fiber bundle failures primarily grew at and near the impact site. During the final 3 percent of life, damage grew rapidly transverse to the loading direction as a through-the-thickness transverse shear failure. The stress-strain response was typically linear during the initial 50 percent of life, and stiffness dropped about 20 percent during this period. During the next 47 percent of life, stiffness dropped about 34 percent, and the stress-strain response was no longer linear. The stiffness decreased about 23 percent during the final 3 percent of life. These trends were typical of all the materials tested. Therefore, by monitoring stiffness loss, fatigue failure could be accurately anticipated.

Serdinak, Thomas E.↗

NASA NTRS1991

Transverse injection into Mach 2 flow behind a rearward-facing step - A 3-D, compressible flow test case for hypersonic combustor CFD validation

A spatially-complete data set of the important primitive flow variables is presented for the complex, nonreacting, 3D unit combustor flow field employing transverse injection into a Mach 2 flow behind a rearward-facing step. A unique wind tunnel facility providing the capability for iodine seeding was built specifically for these measurements. Two optical techniques based on laser-induced-iodine fluorescence were developed and utilized for nonintrusive, in situ flow field measurements. LDA provided both mean and fluctuating velocity component measurements. A thermographic phosphor wall temperature measurement technique was developed and employed. Data from the 2D flow over a rearward-facing step and the complex 3D mixing flow with injection are reported.

Mcdaniel, James C.↗

NASA NTRS1981

Effect of load introduction on graphite epoxy compression specimens

Compression testing of modern composite materials is affected by the manner in which the compressive load is introduced. Two such effects are investigated: (1) the constrained edge effect which prevents transverse expansion and is common to all compression testing in which the specimen is gripped in the fixture; and (2) nonuniform gripping which induces bending into the specimen. An analytical model capable of quantifying these foregoing effects was developed which is based upon the principle of minimum complementary energy. For pure compression, the stresses are approximated by Fourier series. For pure bending, the stresses are approximated by Legendre polynomials.

Reiss, R.↗

NASA NTRS1984

Anomalous transport by magnetohydrodynamic Kelvin-Helmholtz instabilities in the solar wind-magnetosphere interaction

The high latitude, or downstream flank, and dayside low latitude magnetospheric boundaries are modeled in an MHD simulation of Kelvin-Helmholtz instablities in a compressible plasma for parallel and transverse configurations. Detailed attention is given to the nonlinear consequences of the instabilities for several different Alfven and sound Mach numbers in both configurations. Emphasis is given to the anomalous transport of momentum and energy by the Kelvin-Helmholtz instabilities across the magnetospheric boundary, which is crucial in evaluating the instabilities' contribution to magnetospheric convection. It is concluded that the anomalous tangential stress at the magnetospheric boundary caused by the instability may be of the order of 1 percent of the magnetosheath flow momentum adjacent to the boundary, and gives a contribution to the convection potential drop over the polar cap of 10-30 kV.

Miura, A.↗

NASA NTRS1924

Micarta propellers I : materials

Here, values for tension, compression edgewise of laminations, and transverse flatwise of laminations are given for Micarta made with various kinds of sheet material. The corresponding values for white oak are given for comparison. It was found by destructive and service tests that Micarta made with a good grade of cotton duck will give satisfactory service with most designs. In propellers having detachable blades, it is desirable that the root of the blade be of a small cross section to decrease the weight of the metal hub. Here the use of the special fabric or wood veneer offers advantages due to greater tensile strength. These materials, especially the wood veneer, produce stiffer blades than duck. This is also a value in controllable and reversible pitch designs where it is desirable that the plan form of the blades be symmetrical.

Caldwell, F W↗

NASA NTRS1998

Analysis and Design of Variable Stiffness Composite Cylinders

An investigation of the possible performance improvements of thin circular cylindrical shells through the use of the variable stiffness concept is presented. The variable stiffness concept implies that the stiffness parameters change spatially throughout the structure. This situation is achieved mainly through the use of curvilinear fibers within a fiber-reinforced composite laminate, though the possibility of thickness variations and discrete stiffening elements is also allowed. These three mechanisms are incorporated into the constitutive laws for thin shells through the use of Classical Lamination Theory. The existence of stiffness variation within the structure warrants a formulation of the static equilibrium equations from the most basic principles. The governing equations include sufficient detail to correctly model several types of nonlinearity, including the formation of a nonlinear shell boundary layer as well as the Brazier effect due to nonlinear bending of long cylinders. Stress analysis and initial buckling estimates are formulated for a general variable stiffness cylinder. Results and comparisons for several simplifications of these highly complex governing equations are presented so that the ensuing numerical solutions are considered reliable and efficient enough for in-depth optimization studies. Four distinct cases of loading and stiffness variation are chosen to investigate possible areas of improvement that the variable stiffness concept may offer over traditional constant stiffness and/or stiffened structures. The initial investigation deals with the simplest solution for cylindrical shells in which all quantities are constant around the circumference of the cylinder. This axisymmetric case includes a stiffness variation exclusively in the axial direction, and the only pertinent loading scenarios include constant loads of axial compression, pressure, and torsion. The results for these cases indicate that little improvement over traditional laminates exists through the use of curvilinear fibers, mainly due to the presence of a weak link area within the stiffness variation that limits the ultimate load that the structure can withstand. Rigorous optimization studies reveal that even though slight increases in the critical loads can be produced for designs with an arbitrary variation of the fiber orientation angle, the improvements are not significant when compared to traditional design techniques that utilize ring stiffeners and frames. The second problem that is studied involves arbitrary loading of a cylinder with a stiffness variation that changes only in the circumferential direction. The end effects of the cylinder are ignored, so that the problem takes the form of an analysis of a cross-section for a short cylinder segment. Various load cases including axial compression, pressure, torsion, bending, and transverse shear forces are investigated. It is found that the most significant improvements in load-carrying capability exist for cases which involve loads that also vary around the circumference of the shell, namely bending and shear forces. The stiffness variation of the optimal designs contribute to the increased performance in two ways: lowering the stresses in the critical areas through redistribution of the stresses; and providing a relatively stiff region that alters the buckling behavior of the structure. These results lead to an in-depth optimization study involving weight optimization of a fuselage structure subjected to typical design constraints. Comparisons of the curvilinear fiber format to traditional stiffened structures constructed of isotropic and composite materials are included. It is found that standard variable stiffness designs are quite comparable in terms of weight and load-carrying capability yet offer the added advantage of tailorability of distinct regions of the structure that experience drastically different loading conditions. The last two problems presented in this work involve the nonlinear phenomenon of long tubes under bending. Though this scenario is not as applicable to fuselage structures as the previous problems, the mechanisms that produce the nonlinear effect are ideally suited to be controlled by the variable stiffness concept. This is due to the fact that the dominating influence for long cylinders under bending is the ovalization of the cross-section, which is governed mainly by the stiffness parameters of the cylindrical shell. Possible improvement of the critical buckling moments for these structures is investigated using either a circumferential or axial stiffness variation. For the circumferential case involving infinite length cylinders, it is found that slight improvements can be observed by designing structures that resist the cross-sectional deformation yet do not detract from the buckling resistance at the critical location. The results also indicate that buckling behavior is extremely dependent on cylinder length. This effect is most easily seen in the solution of finite length cylinders under bending that contain an axial stiffness variation. For these structures, the only mechanism that exhibits improved response are those that effectively shorten the length of the cylinder, thus reducing the cross-sectional deformation due to the forced restraint at the ends. It was found that the use of curvilinear fibers was not able to achieve this effect in sufficient degree to resist the deformation, but that ring stiffeners produced the desired response admirably. Thus, it is shown that the variable stiffness concept is most effective at improving the bending response of long cylinders through the use of a circumferential stiffness variation.

Tatting, Brian F.↗

NASA NTRS1997

Application of High Resolution Topography and Remote Sensing: Imagery to the Kinematics of Fold-and-Thrust Belts

This report summarizes one year of funding for NASA contract NAGW-3691, Application of High Resolution Topography and Remote Sensing: Imagery to the Kinematics of Fold-and-Thrust Belts. I never received year three from NASA. The funds were to support on going tectonic and topographic studies along the front of the central Transverse Ranges and expand the topographic studies to the north. Below are results from the first two years of actual funds that I received from NASA (see attached Federal Cash Transaction Reports). The main focus of this contract was to define and understand the major tectonic processes affecting the formation and evolution of the topography in convergent tectonic settings. The results will be used to test ongoing space-based geodetic measurements and will be compared with present-day seismicity in the central Transverse Ranges and adjacent basins. Two major factors that controls topography in active regions are (1) tectonic uplift due to fault-normal compression and (2) subsequent erosion. The central Transverse and Temblor Ranges are excellent regions for these focused topographic studies. The tectonic processes leading to the mountain building are relatively straightforward and thus are easy to model. Available evidence suggests that the topography in this region is relatively young, - 3.5 Ma or less. In addition,, erosional processes may be relatively easier to model compared to larger and more ancient mountain belts. For example, in larger mountain belts, topographic relief may cause significant orographic effects and high elevation may result in part of the topography located above snowline. Both factors complicate interpretation of erosional processes that may be controlled by elevation. Mountain ranges that are significantly older may have experienced a much wider variety of erosional or climatic conditions over their lifetime. While erosion rates have certainly not been consistent in the Transverse or Temblor ranges over its 3.5 Ma lifetime, we are sure that the region was spared the Pleistocene glaciation that affected parts of the Sierra Nevada Range.

Rubin, Charles↗

NASA NTRS2016

Multiscale Static Analysis of Notched and Unnotched Laminates Using the Generalized Method of Cells

The generalized method of cells (GMC) is demonstrated to be a viable micromechanics tool for predicting the deformation and failure response of laminated composites, with and without notches, subjected to tensile and compressive static loading. Given the axial [0], transverse [90], and shear [+45/-45] response of a carbon/epoxy (IM7/977-3) system, the unnotched and notched behavior of three multidirectional layups (Layup 1: [0,45,90,-45](sub 2S), Layup 2: [0,60,0](sub 3S), and Layup 3: [30,60,90,-30, -60](sub 2S)) are predicted under both tensile and compressive static loading. Matrix nonlinearity is modeled in two ways. The first assumes all nonlinearity is due to anisotropic progressive damage of the matrix only, which is modeled, using the multiaxial mixed-mode continuum damage model (MMCDM) within GMC. The second utilizes matrix plasticity coupled with brittle final failure based on the maximum principle strain criteria to account for matrix nonlinearity and failure within the Finite Element Analysis--Micromechanics Analysis Code (FEAMAC) software multiscale framework. Both MMCDM and plasticity models incorporate brittle strain- and stress-based failure criteria for the fiber. Upon satisfaction of these criteria, the fiber properties are immediately reduced to a nominal value. The constitutive response for each constituent (fiber and matrix) is characterized using a combination of vendor data and the axial, transverse, and shear responses of unnotched laminates. Then, the capability of the multiscale methodology is assessed by performing blind predictions of the mentioned notched and unnotched composite laminates response under tensile and compressive loading. Tabulated data along with the detailed results (i.e., stress-strain curves as well as damage evolution states at various ratios of strain to failure) for all laminates are presented.

GMC↗

NASA NTRS1987

Effects of transverse shear deformation on buckling of laminated cylinders as a function of thickness and ply orientation

Buckling loads of thick-walled, orthotropic, simply-supported right circular cylinders are predicted using a new higher-order transverse shear deformation theory. The higher-order theory shows that, by more accurately accounting for transverse shear deformation effects, the predicted buckling load may be reduced by as much as 80 percent compared to predictions based on conventional transverse shear deformation theory. A parametric study of the effect of ply orientation on the buckling load of axially compressed cylinders indicates that laminates containing 0 deg plies are the most sensitive to transverse shear deformation effects. Interaction curves for buckling of cylinders with axial compressive and external pressure loadings indicate that buckling loads due to external pressure loadings are much less sensitive to transverse shear deformation effects than those due to axial compressive loadings.

Jegley, Dawn C.↗

NASA NTRS1973

BUCLASP 2: A computer program for instability analysis of biaxially loaded composite stiffened panels and other structures

The use of the computer program BUCLASP2 is described. The program is intended for linear instability analyses of structures such as unidirectionally stiffened panels. Any structure that has a constant cross section in one direction, that may be idealized as an assemblage of beam elements and laminated flat and curved plant strip elements can be analyzed. The loadings considered are combinations of axial compressive loads and in-plane transverse loads. The two parallel ends of the panel must be simply supported and arbitrary elastic boundary conditions may be imposed along any one or both external longitudinal side. This manual consists of instructions for use of the program with sample problems, including input and output information. The theoretical basis of BUCLASP2 and correlations of calculated results with known solutions, are presented.

Tripp, L. L.↗