Large amplitude vibration of buckled beams and rectangular plates.
Large amplitude forced vibrations of buckled beams and rectangular plates about static buckled positions
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Results for “structural buckling”
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On the postbuckling behavior of imperfection- sensitive structures in the plastic range
Axisymmetric plastic deformation of imperfection sensitive spherical shell after elastic buckling, considering load carrying capacity
Hutchinson, J. W.↗
Noncollinear antiferromagnetic order in the buckled honeycomb lattice of magnetoelectric Co 4 Ta 2 O 9 determined by single-crystal neutron diffraction
Co 4 Ta 2 O 9 exhibits a three-dimensional magnetic lattice based on the buckled honeycomb motif. It shows unusual magnetoelectric effects, including the sign change and nonlinearity. These effects cannot be understood without the detailed knowledge of the magnetic structure. Herein, we report neutron diffraction and direction-dependent magnetic susceptibility measurements on Co 4 Ta 2 O 9 single crystals. In this work, below 20.3 K, we find a long-range antiferromagnetic order in the alternating buckled and flat honeycomb layers of Co 2+ ions stacked along the c axis. Within experimental accuracy, the magnetic moments lie in the ab plane. They form a canted antiferromagnetic structure with a tilt angle of ~14° at 15 K in the buckled layers, while the magnetic moments in each flat layer are collinear. This is directly evidenced by a finite (0, 0, 3) magnetic Bragg peak intensity, which would be absent in the collinear magnetic order. The magnetic space group is C2/c'. It is different from the previously reported C2/c' group, also found in the isostructural Co 4 Nb 2 O 9 . The revised magnetic structure successfully explains the major features of the magnetoelectric tensor of Co 4 Ta 2 O 9 within the framework of the spin-flop model.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Methods for structural design at elevated temperatures
A procedure which can be used to design elevated temperature structures is discussed. The desired goal is to have the same confidence in the structural integrity at elevated temperature as the factor of safety gives on mechanical loads at room temperature. Methods of design and analysis for creep, creep rupture, and creep buckling are presented. Example problems are included to illustrate the analytical methods. Creep data for some common structural materials are presented. Appendix B is description, user's manual, and listing for the creep analysis program. The program predicts time to a given creep or to creep rupture for a material subjected to a specified stress-temperature-time spectrum. Fatigue at elevated temperature is discussed. Methods of analysis for high stress-low cycle fatigue, fatigue below the creep range, and fatigue in the creep range are included. The interaction of thermal fatigue and mechanical loads is considered, and a detailed approach to fatigue analysis is given for structures operating below the creep range.
Ellison, A. M.↗
Design and Analysis of a Stiffened Composite Fuselage Panel
A stiffened composite panel has been designed that is representative of the fuselage structure of existing wide bodied aircraft. The panel is a minimum weight design, based on the current level of technology and realistic loads and criteria. Several different stiffener configurations were investigated in the optimization process. The final configuration is an all graphite epoxy J-stiffened design in which the skin between adjacent stiffeners is permitted to buckle under design loads. Fail-safe concepts typically employed in metallic fuselage structure have been incorporated in the design. A conservative approach has been used with regard to structural details such as skin frame and stringer frame attachments and other areas where sufficient design data was not available.
Dickson, J. N.↗
TPSAS-NF1676L-26160-DND
The structural performance of two advanced composite tow-steered shells is assessed using experiments and analyses. The fiber angles vary continuously around the shell circumference, and one shell has all 24 tows applied during fabrication, while the second shell uses the fiber placement systems tow drop/add capability to achieve a uniform wall thickness. The shells are tested in compression, and their axial stiffnesses and buckling loads are estimated using linear finite element analyses. Scaled passenger and cargo door cutouts are machined into one side of each shell. Axial stiffnesses and buckling loads of the shells with cutouts are computed using linear finite element analyses. The retested shells carry over 90 percent of the axial stiffness, and 85 percent of the buckling loads, of the shells without cutouts. These small reductions demonstrate the potential of tow steering to mitigate adverse effects of cutouts on the structural performance. The good correlation between experimental buckling loads and linear buckling analyses noted here may result from their circumferential stiffness variation, reducing geometric imperfection sensitivity. Analysis models of both shells were evaluated without and with measured geometric imperfections superposed in different longitudinal orientations. Small variations in prebuckling stiffness and buckling load of the shells are observed.
K C Wu↗
Development of an integrated aeroservoelastic analysis program and correlation with test data
The details and results are presented of the general-purpose finite element STructural Analysis RoutineS (STARS) to perform a complete linear aeroelastic and aeroservoelastic analysis. The earlier version of the STARS computer program enabled effective finite element modeling as well as static, vibration, buckling, and dynamic response of damped and undamped systems, including those with pre-stressed and spinning structures. Additions to the STARS program include aeroelastic modeling for flutter and divergence solutions, and hybrid control system augmentation for aeroservoelastic analysis. Numerical results of the X-29A aircraft pertaining to vibration, flutter-divergence, and open- and closed-loop aeroservoelastic controls analysis are compared to ground vibration, wind-tunnel, and flight-test results. The open- and closed-loop aeroservoelastic control analyses are based on a hybrid formulation representing the interaction of structural, aerodynamic, and flight-control dynamics.
Gupta, K. K.↗
Structural synthesis of integrally stiffened cylinders.
Structural design of stiffened cylindrical shells, discussing minimum weight, prevention of buckling modes, etc
Kicher, T. P.↗
Adhesive for cryogenic temperature applications
Adhesive, which bonds a metal liner to a filament wound composite structure used for cryogenic pressure vessels, prevents the metal liner from buckling under depressurization. The adhesive consists of adducts of urethane and epoxy resins.
Doyle, H. M.↗
A finite element procedure for nonlinear prebuckling and initial postbuckling analysis
A procedure cast in a form appropriate to the finite element method is presented for geometrically nonlinear prebuckling and postbuckling structural analysis, including the identification of snap-through type of buckling. The principal features of this procedure are the use of direct iteration for solution of the nonlinear algebraic equations in the prebuckling range, an interpolation scheme for determination of the initial bifurcation point, a perturbation method in definition of the load-displacement behavior through the postbuckling regime, and extrapolation in determination of the limit point for snap-through buckling. Three numerical examples are presented in illustration of the procedure and in comparison with alternative approaches.
Mau, S. T.↗
Minimum-weight designs for hat-stiffened composite panels under uniaxial compression
Optimum hat-stiffened compression panel designs are determined by a structural synthesis technique. The effects of simplifying assumptions made in the buckling analysis for the optimization program are investigated by a linked plate element program. Optimization results for hat-stiffened graphite-epoxy panels show a 50-percent weight savings over optimized aluminum panels. Composite panels are shown to possess a variety of proportions at nearly constant weight.
Agarwal, B.↗
Some comments on global-local analyses
The main theme concerns methods that may be classified as global (approximate) and local (exact). Some specific applications of these methods are found in: fracture and fatigue analysis of structures with 3-D surface flaws; large-deformation, post-buckling analysis of large space trusses and space frames, and their control; and stresses around holes in composite laminates.
Atluri, Satya N.↗
Charts for the minimum-weight design of 24s-t aluminum-alloy flat compression panels with longitudinal z-section stiffeners
Design charts are developed for 24s-t aluminum-alloy flat compression panels with longitudinal z-section stiffeners. These charts make possible the design of the lightest panels of this type for a wide range of design requirements. Examples of the use of the charts are given and it is pointed out on the basis of these examples that, over a wide range of design conditions, the maintenance of buckle-free surfaces does not conflict with the achievement of high structural efficiency. The achievement of the maximum possible structural efficiency with 24s-t aluminum-alloy panels, however, requires closer stiffener spacings than those now in common use.
Schuette, Evan H↗
Reliability, Risk and Cost Trade-Offs for Composite Designs
Risk and cost trade-offs have been simulated using a probabilistic method. The probabilistic method accounts for all naturally-occurring uncertainties including those in constituent material properties, fabrication variables, structure geometry and loading conditions. The probability density function of first buckling load for a set of uncertain variables is computed. The probabilistic sensitivity factors of uncertain variables to the first buckling load is calculated. The reliability-based cost for a composite fuselage panel is defined and minimized with respect to requisite design parameters. The optimization is achieved by solving a system of nonlinear algebraic equations whose coefficients are functions of probabilistic sensitivity factors. With optimum design parameters such as the mean and coefficient of variation (representing range of scatter) of uncertain variables, the most efficient and economical manufacturing procedure can be selected. In this paper, optimum values of the requisite design parameters for a predetermined cost due to failure occurrence are computationally determined. The results for the fuselage panel analysis show that the higher the cost due to failure occurrence, the smaller the optimum coefficient of variation of fiber modulus (design parameter) in longitudinal direction.
Shiao, Michael C.↗
Engineering Overview of a Multidisciplinary HSCT Design Framework Using Medium-Fidelity Analysis Codes
An objective of the HPCC Program at NASA Langley has been to promote the use of advanced computing techniques to more rapidly solve the problem of multidisciplinary optimization of a supersonic transport configuration. As a result, a software system has been designed and is being implemented to integrate a set of existing discipline analysis codes, some of them CPU-intensive, into a distributed computational framework for the design of a High Speed Civil Transport (HSCT) configuration. The proposed paper will describe the engineering aspects of integrating these analysis codes and additional interface codes into an automated design system. The objective of the design problem is to optimize the aircraft weight for given mission conditions, range, and payload requirements, subject to aerodynamic, structural, and performance constraints. The design variables include both thicknesses of structural elements and geometric parameters that define the external aircraft shape. An optimization model has been adopted that uses the multidisciplinary analysis results and the derivatives of the solution with respect to the design variables to formulate a linearized model that provides input to the CONMIN optimization code, which outputs new values for the design variables. The analysis process begins by deriving the updated geometries and grids from the baseline geometries and grids using the new values for the design variables. This free-form deformation approach provides internal FEM (finite element method) grids that are consistent with aerodynamic surface grids. The next step involves using the derived FEM and section properties in a weights process to calculate detailed weights and the center of gravity location for specified flight conditions. The weights process computes the as-built weight, weight distribution, and weight sensitivities for given aircraft configurations at various mass cases. Currently, two mass cases are considered: cruise and gross take-off weight (GTOW). Weights information is obtained from correlations of data from three sources: 1) as-built initial structural and non-structural weights from an existing database, 2) theoretical FEM structural weights and sensitivities from Genesis, and 3) empirical as-built weight increments, non-structural weights, and weight sensitivities from FLOPS. For the aeroelastic analysis, a variable-fidelity aerodynamic analysis has been adopted. This approach uses infrequent CPU-intensive non-linear CFD to calculate a non-linear correction relative to a linear aero calculation for the same aerodynamic surface at an angle of attack that results in the same configuration lift. For efficiency, this nonlinear correction is applied after each subsequent linear aero solution during the iterations between the aerodynamic and structural analyses. Convergence is achieved when the vehicle shape being used for the aerodynamic calculations is consistent with the structural deformations caused by the aerodynamic loads. To make the structural analyses more efficient, a linearized structural deformation model has been adopted, in which a single stiffness matrix can be used to solve for the deformations under all the load conditions. Using the converged aerodynamic loads, a final set of structural analyses are performed to determine the stress distributions and the buckling conditions for constraint calculation. Performance constraints are obtained by running FLOPS using drag polars that are computed using results from non-linear corrections to the linear aero code plus several codes to provide drag increments due to skin friction, wave drag, and other miscellaneous drag contributions. The status of the integration effort will be presented in the proposed paper, and results will be provided that illustrate the degree of accuracy in the linearizations that have been employed.
Weston, R. P.↗
Aeroelastic Sizing for High-Speed Research (HSR) Longitudinal Control Alternatives Project (LCAP)
The Longitudinal Control Alternatives Project (LCAP) compared three high-speed civil transport configurations to determine potential advantages of the three associated longitudinal control concepts. The three aircraft configurations included a conventional configuration with a layout having a horizontal aft tail, a configuration with a forward canard in addition to a horizontal aft tail, and a configuration with only a forward canard. The three configurations were aeroelastically sized and were compared on the basis of operational empty weight (OEW) and longitudinal control characteristics. The sized structure consisted of composite honeycomb sandwich panels on both the wing and the fuselage. Design variables were the core depth of the sandwich and the thicknesses of the composite material which made up the face sheets of the sandwich. Each configuration was sized for minimum structural weight under linear and nonlinear aeroelastic loads subject to strain, buckling, ply-mixture, and subsonic and supersonic flutter constraints. This report describes the methods that were used and the results that were generated for the aeroelastic sizing of the three configurations.
Walsh, Joanne L.↗
Ares I-X Upper Stage Simulator Structural Analyses Supporting the NESC Critical Initial Flaw Size Assessment
The structural analyses described in the present report were performed in support of the NASA Engineering and Safety Center (NESC) Critical Initial Flaw Size (CIFS) assessment for the ARES I-X Upper Stage Simulator (USS) common shell segment. The structural analysis effort for the NESC assessment had three thrusts: shell buckling analyses, detailed stress analyses of the single-bolt joint test; and stress analyses of two-segment 10 degree-wedge models for the peak axial tensile running load. Elasto-plastic, large-deformation simulations were performed. Stress analysis results indicated that the stress levels were well below the material yield stress for the bounding axial tensile design load. This report also summarizes the analyses and results from parametric studies on modeling the shell-to-gusset weld, flange-surface mismatch, bolt preload, and washer-bearing-surface modeling. These analyses models were used to generate the stress levels specified for the fatigue crack growth assessment using the design load with a factor of safety.
Knight, Norman F., Jr.↗
Fabric geometry distortion during composites processing
Waviness and tow misalignment are often cited as possible causes of data scatter and lower compression stiffness and strength in textile composites. Strength differences of as much as 40 percent have been seen in composites that appear to have the same basic material and structural properties -- i.e., yarn orientation, yarn size, interlacing geometry. Fabric geometry distortion has been suggested as a possible reason for this discrepancy, but little quantitative data or substantial evidence exists. The focus of this research is to contribute to the present understanding of the causes and effects of geometric distortion in textile composites. The initial part of the study was an attempt to gather qualitative information on a variety of textile structures. Existing and new samples confirmed that structures with a significant direction presence would be more susceptible to distortion due to the compaction process. Thus, uniweaves (fiber vol frac: 54-72 percent) biaxial braids (vf: 34-58 percent) demonstrated very little fabric geometry distortion. In stitched panels, only slight buckling of z-direction stitches was observed, primarily near the surface. In contrast, for structures with high compaction ratios -- e.g., large cylindrical yarns (2.5:1) orpowder towpreg (4:1) -- there were visible distortions where previously smooth and periodic undulations were transformed to abrupt changes in direction. A controlled study of the effect of forming pressure on distortion was conducted on type 162 glass plain weave fabrics. Panels (6 x 6 in) were produced via a resin infusion type setup, but with an EPON 815 epoxy resin. Pressures ranging from hand layup to 200 psi were used (vf: 34-54 percent). Photomicrographs indicated that at pressures up to 50 psi, large changes in thickness were due primarily to resin squeeze out. At higher pressures, when intimate contact was made between the layers, there was some tow flattening and in-plane shifting to optimize nesting. However, even at 200 psi the period and amplitude of the tow undulation remained constant, suggesting that for this relatively fine fabric, distortions from compaction were not a problem. Because of the interest in using larger tows (to reduce cost) and more complex structures, tests were also run on 2D triaxial glass braid (113 yd/lb at 0, 225 yd/lb at +/- 45). Forming pressures of 20, 50, 200, and 500 psi were used, and short block compression tests were run. The 500 psi specimen had a 10 percent decrease in modulus and an almost 50 percent decrease in strength (vs. 20 psi). Because the total fiber wgt/panel was kept constant, the thickness varied from 0.32 to 0.22 in (49-70 percent vf). Yet, the strength value is clearly below what would be expected, even with the decrease in thickness. Photomicrographs of these samples will be taken to determine if more fabric distortion exists in the 500 psi specimens. Finally, because the ultimate goal is to be able to predict and control distortion in a variety of textile structures, a model compaction test was developed to directly measure the deformation of the tows during compaction. Layers of dry glass fabric were placed in a mold with a clear plexiglass window. The yarn amplitude and period was then calculated using image analysis of the videotaped deformation. Preliminary tests demonstrated the feasibility of this technique for simple fabrics with large tows.
Chen, Julie↗