Notes on the Lagrangian multiplier method in elastic-stability analysis
Explore the source record for details and available documents.
EQUATIONS - MOTION - LAGRANGE↗
SEARCH · Search NASA
Results for “buckling (C)”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Probabilistic assessment of uncertain adaptive hybrid composites
Adaptive composite structures using actuation materials, such as piezoelectric fibers, were assessed probabilistically utilizing intraply hybrid composite mechanics in conjunction with probabilistic composite structural analysis. Uncertainties associated with the actuation material as well as the uncertainties in the regular (traditional) composite material properties were quantified and considered in the assessment. Static and buckling analyses were performed for rectangular panels with various boundary conditions and different control arrangements. The probability density functions of the structural behavior, such as maximum displacement and critical buckling load, were computationally simulated. The results of the assessment indicate that improved design and reliability can be achieved with actuation material.
Shiao, Michael C.↗
Compression behavior of delaminated composite plates
The response of delaminated composite plates to compressive in-plane loads was investigated. The delaminated region may be either circular or elliptical, and may be located between any two plies of the laminate. For elliptical delaminations, the axes of the ellipse may be arbitrarily oriented with respect to the applied loads. A model was developed that describes the stresses, strains, and deformation of the sublaminate created by the delamination. The mathematical model is based on a two dimensional nonlinear plate theory that includes the effects of transverse shear deformation. The model takes into account thermal and moisture induced strains, transverse pressures acting on the sublaminate, and contact between the sublaminate and plate. The solution technique used is the Ritz method. A computationally efficient computer implementation of the model was developed. The code can be used to predict the nonlinear-load-strain behavior of the sublaminate including the buckling load, postbuckling behavior, and the onset of delamination growth. The accuracy of the code was evaluated by comparing the model results to benchmark analytical solutions. A series of experiments was conducted on Fiberite T300/976 graphite/epoxy laminates bonded to an aluminum honeycomb core forming a sandwich panel. Either circles or ellipses made from Teflon film were embedded in the laminates, simulating the presence of a delamination. Each specimen was loaded in compression and the strain history of the sublaminate was recorded far into the postbuckling regime. The extent of delamination growth was evaluated by C-scan examination of each specimen. The experimental data were compared to code predictions. The code was found to describe the data with reasonable accuracy. A sensitivity study examined the relative importance of various material properties, the delamination dimensions, the contact model, the transverse pressure differential, the critical strain energy release rate, and the relative growth direction on the buckling load, the postbuckling behavior, and the growth load of the sublaminate.
Peck, Scott O.↗
Sintering inhibition enables hierarchical porosity with extreme resistance to degradation during redox cycling of Fe-Mo foams
High-temperature (800 ºC) steam-hydrogen redox cycling, relevant to grid-scale energy storage, is studied for iron-based freeze-cast lamellar foams. In contrast to previously studied Fe, Fe-Ni, and Fe-Co foams that rapidly degrade, Fe-25Mo foams feature a much-enhanced structural damage resistance. Utilizing in-situ x-ray diffraction, microscopy, and x-ray tomography, strong sintering inhibition is observed in Fe-Mo foams, creating a hierarchically porous lamellar structure. This leads to (i) wide channels between lamellae, enabling high macroscopic porosity (~78%) which can accommodate gas flow as well as volumetric expansion without lamellar contact, and (ii) microporosity within lamellae, providing additional free volume to accommodate expansion during oxidation, limiting both swelling of the lamellae and the formation of Kirkendall pores. Finally, these combined effects enable a near-complete reversibility of the microstructure during cycling, preventing damage produced via internal lamellar buckling, cracking, contacting and sintering, with a remarkably high porosity (65%) remaining after 50 consecutive redox cycles.
36 MATERIALS SCIENCE↗
Curved Caps Raise Corrugation Strength
Construction concept increases strength-to-weight ratio of corrugated panels. Flat caps are replaced by curved caps in new concept for constructing corrugated panels. Geometry utilizes curved cap for wider cap/web attachment. Beading web prevents local buckling in web while allowing maximum separation between cap strips. Geometry offers significant weight saving over conventional geometry for wide range of loading.
Davis, R. C.↗
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.↗
Nonlinear analysis of damaged stiffened fuselage shells subjected to combined loads
The results of an analytical study of the nonlinear response of stiffened fuselage shells with long cracks are presented. The shells are modeled with a hierarchical modeling strategy that accounts for global and local response phenomena accurately. Results are presented for internal pressure and mechanical bending loads. The effects of crack location and orientation on shell response are described. The effects of mechanical fasteners on the response of a lap joint and the effects of elastic and elastic-plastic material properties on the buckling response of tension-loaded flat panels with cracks are also addressed.
Starnes, James H., Jr.↗
Structural Efficiency of Stitched Composite Panels with Stiffener Crippling
The structural efficiency of blade-stiffened stitched specimens is compared to determine their weight saving potential if blades were allowed to buckle at less than or equal to design ultimate load. Analytical and experimental results from four configurations of crippling specimens are presented. Specimen skin and blades were held together with through-the-thickness stitches prior to curing. No mechanical fasteners were used for the assembly. Tests were conducted with and without low-speed impact damage. Failure modes are discussed. Finite element and experimental results agree for the response of the structures. For some specimen configurations, improved structural efficiency can be obtained by allowing stiffeners to buckle at design limit load rather than requiring that buckling not occur prior to design ultimate load. A parametric study is presented herein which describes the possible weight savings with this approach.
Jegley, Dawn C.↗
New design criteria for predicting buckling of cylindrical shells under axial compression
Design criteria for buckling prediction of elliptical and circular cylindrical shells under axial compression from asymmetric and axisymmetric shape imperfections distribution
Caswell, R. D.↗
Design Optimization and Analysis of a Composite Honeycomb Intertank
Intertanks, the structure between tanks of launch vehicles, are prime candidates for weight reduction of rockets. This paper discusses the optimization and detailed analysis of a 96 in (2.44 m) diameter, 77 in (1.85 m) tall intertank. The structure has composite face sheets and an aluminum honeycomb core. The ends taper to a thick built up laminate for a double lap bolted shear joint. It is made in 8 full length panels joined with bonded double lap joints. The nominal load is 4000 lb/in (7 x 10(exp 5) N/m). Optimization is by Genetic Algorithm and minimizes weight by varying C, core thickness, number and orientation of acreage and buildup plies, and the size, number and spacing of bolts. A variety of cases were run with populations up to 2000 and chromosomes as long as 150 bits. Constraints were buckling, face stresses (normal, shear, wrinkling and dimpling, bolt stress, and bolt hole stresses (bearing, net tension, wedge splitting, shear out and tension/shear out). Analysis is by a combination of theoretical solutions and empirical data. After optimization, a series of coupon tests were performed in conjunction with a rigorous analysis involving a variety of finite element models. The analysis and test resulted in several small changes to the optimized design. The intertank has undergone a 250,000 lb (1.1 x 10(exp 6) N) limit load test and been mated with a composite liquid hydrogen tank. The tank/intertank unit is being installed in a test stand where it will see 200 thermal/load cycles. Afterwards the intertank will be demated and loaded in compression to failure.
Finckenor, Jeffrey↗
Residual Strength Analyses of Riveted Lap-Splice Joints
The objective of this paper was to analyze the crack-linkup behavior in riveted-stiffened lap-splice joint panels with small multiple-site damage (MSD) cracks at several adjacent rivet holes. Analyses are based on the STAGS (STructural Analysis of General Shells) code with the critical crack-tip-opening angle (CTOA) fracture criterion. To account for high constraint around a crack front, the "plane strain core" option in STAGS was used. The importance of modeling rivet flexibility with fastener elements that accurately model load transfer across the joint is discussed. Fastener holes are not modeled but rivet connectivity is accounted for by attaching rivets to the sheet on one side of the cracks that simulated both the rivet diameter and MSD cracks. Residual strength analyses made on 2024-T3 alloy (1.6-mm thick) riveted-lap-splice joints with a lead crack and various size MSD cracks were compared with test data from Boeing Airplane Company. Analyses were conducted for both restrained and unrestrained buckling conditions. Comparison of results from these analyses and results from lap-splice-joint test panels, which were partially restrained against buckling indicate that the test results were bounded by the failure loads predicted by the analyses with restrained and unrestrained conditions.
Seshadri, B. R.↗
Buckling Testing and Analysis of Honeycomb Sandwich Panel Arc Segments of a Full-Scale Fairing Barrel: 8-ply Out-of-Autoclave Facesheets - Part 3
Four honeycomb sandwich panels, representing 1/16th arc segments of a 10 m diameter barrel section of the heavy lift launch vehicle, were manufactured under the NASA Composites for Exploration program and the NASA Constellation Ares V program. Two configurations were chosen for the panels: 6-ply facesheets with 1.125 in. honeycomb core and 8-ply facesheets with 1.000 in. honeycomb core. Additionally, two separate carbon fiber/epoxy material systems were chosen for the facesheets: inautoclave IM7/977-3 and out-of-autoclave T40-800B/5320-1. Smaller 3- by 5-ft panels were cut from the 1/16th barrel sections. These panels were tested under compressive loading at the NASA Langley Research Center. Furthermore, linear eigenvalue and geometrically nonlinear finite element analyses were performed to predict the compressive response of the 3- by 5-ft panels. This manuscript summarizes the experimental and analytical modeling efforts pertaining to the panel composed of 8-ply, T40-800B/5320-1 facesheets (referred to as Panel C). To improve the robustness of the geometrically nonlinear finite element model, measured surface imperfections were included in the geometry of the model. Both the linear and nonlinear, two-dimensional (2-D) and three-dimensional (3-D), models yield good qualitative and quantitative predictions. Additionally, it was predicted correctly that the panel would fail in buckling prior to failing in strength.
heavy lift launch vehicles↗
A probabilistic method for the buckling assessment of stiffened composite shells
A method is described to computationally simulate probabilistic buckling behavior of multilayered composite shells. The simulation accounts for all naturally-occurring uncertainties including those in constituent (fiber/matrix) material properties, fabrication variables, and structure geometry. The method is demonstrated for probabilistically assessing the buckling survivability of a specific case of a stiffened composite cylindrical shell with and without cutouts. The sensitivities of various uncertain variables on the buckling survivability are evaluated at specified reliability. The results show that the buckling survivability for a shell without cutouts depends primarily on shell skin related uncertainties. However, stringer related uncertainties become important for a shell with cutouts.
Shiao, Michael C.↗
Experimental investigation of graphite/polyimide sandwich panels in edgewise compression
The local and general buckling of graphite/polyimide sandwich panels simply supported along all four edges and loaded in uniaxial edgewise compression is investigated. Material properties of sandwich panel constituents (adhesive and facings) were determined from flatwise tension and sandwich beam flexure tests. An adhesive bond study resulted in the selection of a suitable cure cycle for FM 34 polyimide film adhesive and, a bonding technique using a liquid cell edge version of that adhesive resulted in considerable mass savings. Tensile and compressive material properties of the facings, quasiisotropic, symmetric, laminates (0, +45,90,-45)s of Celion/PMR-15, were determined at 116, R.T., and 589 K (-250, R.T., and 600 F) usng the sandwich beam flexure test method. Results indicate the Gr/PI is a usable structural material for short term use at temperatures as high as 589 K (600 F). Buckling specimens were 1006.5 sq cm. 156 sq in., had quasiisotropic symmetric facings (0, + or - 45,90)s and a glass/polyimide honeycomb core (HRH-327-3/8-4).
Camarda, C. J.↗
Critical combinations of shear and transverse direct stress for an infinitely long flat plate with edges elastically restrained against rotation
An exact solution and a closely concurring approximate energy solution are given for the buckling of an infinitely long flat plate under combined shear and transverse direct stress with edges elastically restrained against rotation. It was found that an appreciable fraction of the critical stress in pure shear may be applied to the plate without any reduction in the transverse compressive stress necessary to produce buckling. An interaction formula in general use was shown to be decidedly conservative for the range in which it is supposed to apply.
Batdorf, S B↗
Assuring Life in Composite Systems
A computational simulation method is presented to assure life in composite systems by using dynamic buckling of smart composite shells as an example. The combined use of composite mechanics, finite element computer codes, and probabilistic analysis enable the effective assessment of the dynamic buckling load of smart composite shells. A universal plot is generated to estimate the dynamic buckling load of composite shells at various load rates and probabilities. The shell structure is also evaluated with smart fibers embedded in the plies right below the outer plies. The results show that, on the average, the use of smart fibers improved the shell buckling resistance by about 9% at different probabilities and delayed the buckling occurrence time. The probabilistic sensitivities results indicate that uncertainties in the fiber volume ratio and ply thickness have major effects on the buckling load. The uncertainties in the electric field strength and smart material volume fraction have moderate effects and thereby in the assured life of the shell.
Chamis, Christos c.↗
Hidden anomalies in topological t – PtBi 2 – x probed by second harmonic generation
The noncentrosymmetric Weyl semimetal PtBi 2–x (t-PtBi 2–x ) exhibits various interesting technologically important physical properties. We report the experimental investigation of PtBi 1.6 via second harmonic generation (SHG), single-crystal x-ray diffraction, magnetic susceptibility, and electrical resistivity measurements. While bulk structural, magnetic, and electrical properties show no phase transitions below room temperature, the temperature dependence of the SHG intensity reveals two anomalies: one at T* ~ 60 K and another at T x ~ 200 K. Quantitative analysis indicates that the SHG signal results from both the buckled Bi1 surface termination with the 3m symmetry and flat Bi2 surface termination with the m symmetry. However, the anomalies are mainly driven by Bi1 on the surface: (1) T* marks the onset of surface states which is also manifested in the c-axis resistivity drop and (2) T x corresponds to the lowest thermal contraction of the structure and enhanced magnetic susceptibility. Furthermore, this study demonstrates that SHG is a powerful technique for probing surface properties even for noncentrosymmetric materials.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Analytical prediction of reverse buckling pressure for thin shells
Analytical technique is developed for prediction of reverse buckling in thin curved shells. Test data indicate technique predicts actual reverse buckling pressure within 10 percent, and should be useful for analytical prediction of reversed condition failure for problems such as explosive decomposition through vacuum failure.
Martindale, D. L.↗