Search NASA⌕ Search

SEARCH · Search NASA

Results for “bending stiffness”

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.

At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1931

Flat sheet metal girders with very thin metal web. Part I : general theories and assumptions

The object of this report was to develop the structural method of sheet metal girders and should for that reason be considered solely from this standpoint. The ensuing methods were based on the assumption of the infinitely low stiffness in bending of the metal web. This simplifies the basis of calculations to such an extent that many questions of great practical importance can be examined which otherwise cannot be included in any analysis of the bending stiffness of the buckled plate. This report refers to such points as the safety in buckling of uprights to the effect of bending flexibility of spars, to spars not set parallel, etc.

Wagner, Herbert↗
NASA NTRS1980

The behavior of bonded doubler splices for composite sandwich panels

The results of an investigation into the behavior of adhesively bonded doubler splices of two composite material sandwich panels are presented. The splices are studied from three approaches: analytical; numerical (finite elements); and experimental. Several parameters that characterize the splice are developed to determine their influence upon joint strength. These parameters are: doubler overlap length; core stiffness; laminate bending stiffness; the size of the gap between the spliced sandwich panels; and room and elevated temperatures. Similarities and contrasts between these splices and the physically similar single and double lap joints are discussed. The results of this investigation suggest several possible approaches to improving the strength of the sandwich splices.

Zeller, T. A.↗
NASA NTRS1989

Enhanced element-specific modal formulations for flexible multibody dynamics

The accuracy of current flexible multibody formalisms based on assumed modes is examined in the context of standard spacecraft motions involving structural components undergoing both slow and fast overall translational and rotational motions as well as small deformations. Limitations of current techniques in treating: (1) element-specific coupling behavior of large motion and small deformation, and (2) motion-induced structural stiffness variations, are noted. The roles of nonlinear and linear elastic structural theories in accurately predicting transient large-displacement dynamic behavior of flexible multibody systems are examined in detail. Coupling effects between deformation and overall motion are carefully scrutinized in the context of assumed-mode discretization techniques. Consistently linearized beam, plate, and shell formulations involving in-plane stretch variables are proposed and shown to yield very accurate simulation results and extremely fast modal convergence for most motions involving small strains. In some particular cases, however, in which membrane stiffness dominates bending stiffness, a nonlinear strain formulation is required in order to capture proper coupling between deformation and overall motion.

Ryan, Robert R.↗
NASA NTRS1991

Structural behavior of scientific balloons - Finite element simulation and verification

An off-the-shelf nonlinear finite element code was used to analyze fully inflated scientific balloons. The thin balloon film was modeled by shell bending elements. Numerical difficulties caused by insignificant bending stiffness terms were overcome by introducing some artificial bending stiffness. This approximation is justified by the fact that in thin shells with nonzero Gaussian curvature the membrane solution component is essentially independent of the bending solution component. Perturbation of the coveraged solution by increasing the bending stiffness by a full decade verified this assertion. This analytical approach was experimentally verified. As a result of this verification process it was discovered that the generally accepted linearly visco-elastic model for polyethylene film is inappropriate for a significant planar (as opposed to uniaxial) stress state. A linear elastic model presents a good approximation for planar stress states.

Schur, Willi W.↗
NASA NTRS1986

An experiment for determining the Euler load by direct computation

A direct algorithm is presented for computing the Euler load of a column from experimental data. The method is based on exact inextensional theory for imperfect columns, which predicts two distinct deflected shapes at loads near the Euler load. The bending stiffness of the column appears in the expression for the Euler load along with the column length, therefore the experimental data allows a direct computation of bending stiffness. Experiments on graphite-epoxy columns of rectangular cross-section are reported in the paper. The bending stiffness of each composite column computed from experiment is compared with predictions from laminated plate theory.

Thurston, Gaylen A.↗
NASA NTRS2004

Analysis of a Circular Composite Disk Subjected to Edge Rotations and Hydrostatic Pressure

The structural analysis results for a graphite/epoxy quasi-isotropic circular plate subjected to a forced rotation at the boundary and pressure is presented. The analysis is to support a specialized material characterization test for composite cryogenic tanks. Finite element models were used to ensure panel integrity and determine the pressure necessary to achieve a predetermined equal biaxial strain value. The displacement results due to the forced rotation at the boundary led to a detailed study of the bending stiffness matrix [D]. The variation of the bending stiffness terms as a function of angular position is presented graphically, as well as, an illustrative technique of considering the laminate as an I-beam.

Oliver, Stanley T.↗
NASA NTRS2018

A Simple Test Method for Large Deformation Bending of Thin High Strain Composite Flexures

A simple test method for large deformation bending of thin composite laminates is investigated using image processing and full-field strain measurements. The assumptions and kinematic equations that represent the test are used to calculate numerically the laminate bending stiffness and strength as well as the curvature and strains at failure. In order to validate the test methodology, a comparison is performed between analytical model predictions and empirical data in terms of computed surface strains versus digital image correlation data and calculated rotation angles of the fixture arms throughout the test versus measured ones. The new test method is then used to calculate the bending stiffness in the D11 and D22 directions as well as failure strains for various thin-ply laminates of interest. These parameters are ultimately compared with predicted values using micromechanics and classical lamination theory analysis. In general, bending stiffness and strain test results and predictions for 0 degree orientation coupons have a maximum difference of 10% and 35%.

Fernandez, Juan M.↗
NASA NTRS1984

Skin-stiffener interface stresses in composite stiffened panels

A model and solution method for determining the normal and shear stresses in the interface between the skin and the stiffener attached flange were developed. An efficient, analytical solution procedure was developed and incorporated in a sizing code for stiffened panels. The analysis procedure described provides a means to study the effects of material and geometric design parameters on the interface stresses. These stresses include the normal stress, and the shear stresses in both the longitudinal and the transverse directions. The tendency toward skin/stiffener separation may therefore be minimized by choosing appropriate values for the design variables. The most important design variables include the relative bending stiffnesses of the skin and stiffener attached flange, the bending stiffness of the stiffener web, and the flange width. The longitudinal compressive loads in the flange and skin have significant effects on the interface stresses.

Wang, J. T. S.↗
NASA NTRS2013

Method for Estimating Operational Loads on Aerospace Structures Using Span-Wisely Distributed Surface Strains

This report presents a new method for estimating operational loads (bending moments, shear loads, and torques) acting on slender aerospace structures using distributed surface strains (unidirectional strains). The surface strain-sensing stations are to be evenly distributed along each span-wise strain-sensing line. A depth-wise cross section of the structure along each strain-sensing line can then be considered as an imaginary embedded beam. The embedded beam was first evenly divided into multiple small domains with domain junctures matching the strain-sensing stations. The new method is comprised of two steps. The first step is to determine the structure stiffness (bending or torsion) using surface strains obtained from a simple bending (or torsion) loading case, for which the applied bending moment (or torque) is known. The second step is to use the strain-determined structural stiffness (bending or torsion), and a new set of surface strains induced by any other loading case to calculate the associated operational loads (bending moments, shear loads, or torques). Performance of the new method for estimating operational loads was studied in light of finite-element analyses of several example structures subjected to different loading conditions. The new method for estimating operational loads was found to be fairly accurate, and is very promising for applications to the flight load monitoring of flying vehicles with slender wings.

Ko, William L.↗
NASA NTRS2002

The Use of Doublers in Delamination Toughness Testing

In this paper, the data reduction equations for common delamination toughness tests are rederived for use with specimens which have bonded doublers. The common toughness tests considered here are the double cantilever beam (DCB) for mode I toughness; the end notch flexure (3ENF) and 4 point ENF (4ENF) for mode II toughness; and the mixed mode bending (MMB) test for testing under combined mode I and mode II loading. Because the addition of the doublers changes the bending stiffness of the specimens, these data reduction equations may need to be corrected. Doublers were added to the delamination test specimens to solve a premature failure problem. Delamination toughness is normally tested using a beam with an imbedded insert so that one end of the specimen is split into two arms. If the specimen is too thin, or if the toughness of the material is too high, an arm of the specimen may fail in bending before the delamination grows. When this occurs, the toughness of the material cannot be determined. To delay the bending failure so that delamination growth occurs, doubler plates were bonded to both top and bottom surfaces of the specimen. A doubler parameter, beta, which describes how much the use of doubler plates changed the ratio of full thickness to delaminated bending stiffnesses, was defined. When changes to the data reduction equations were required, the changes were minor when written in terms of the beta parameter. The doubler plate technique was demonstrated by measuring the mixed-mode fracture toughness of a carbon-carbon composite using test specimens which would otherwise have failed before delamination growth occurred. The doubler plate technique may solve several problems that can be encountered when testing delamination fracture toughness.

Reeder, James R.↗
NASA NTRS1977

Flutter of an elastic plate under tension

The problem of flutter of a tensioned elastic plate is reconsidered on a model of two-dimensional aerodynamic flow over a one-dimensional, infinitely wide plate. The purpose is to clarify the effect of variations in plate bending stiffness on the flutter of a plate under a given tension, and vice versa. On the basis that the flutter mode for the one-dimensional infinitely wide plate is essentially the first plate natural mode for subsonic and low supersonic Mach numbers, and that the dynamic pressure required for flutter is proportional to the square of the first natural mode frequency, it is shown that the membrane paradox disappears for Mach numbers 0 and 1.3, so that reduced bending stiffness reduces the dynamic pressure required for flutter.

Dowell, E. H.↗
NASA NTRS1988

Stability sensitivity analysis for the aeroelastic optimization of a helicopter rotor

A sensitivity study of blade stability in forward flight for a hingeless rotor with respect to structural design variables is carried out using a direct analytical method. Structural design variables include nonstructural mass distribution (spanwise and chordwise), chordwise offset of center of gravity, and blade bending stiffnesses (flap, lag and torsion). The formulation for blade steady response is based on a finite element method in space and time. The vehicle trim and blade steady response are calculated iteratively as one coupled solution using a modified Newton method. Eigenvalues corresponding to different blade modes are calculated using Floquet transition matrix theory. The formulation for derivatives of the eigenvalues with respect to design variables is implemented using a direct analytical approach (chain rule differentiation), and constitutes an integral part of the regular stability analysis. The stability sensitivity derivatives were obtained at a fraction of computation time compared to the frequently adopted finite difference method. A parametric study showed that nonstructural mass and chordwise cg offset of outboarad elements, and lag bending stiffness of inboard elements, have powerful influence on blade stability.

Lim, Joon W.↗
NASA NTRS1962

ON THE INSTABILITY OF ORTHOTROPIC CYLINDERS

Preliminary results from experimental investigations on the buckling strength of rlng-and-strlnger stiffened aluminum cylinders and filament-wound glass-epoxy cylinders are compared with instability calculations based on small-deflection orthotropic cylinder theory. Correlation between experiment and calculation was reasonably good for the glass-epoxy cylinders; however, correlation for the ring-and-stringer stiffened cylinders cam be achieved only when some of the basic wall stlffnesses for stiffened cylinders with buckled skin can be better defined. In particular, the wall shear stiffness and the wall bending stiffness in the circumferential direction need better definition.

ORTHOTROPIC CYLINDER↗
NASA NTRS1985

Investigation of composite materials property requirements for sonic fatigue research

Experimental techniques for determining the extensional and bending stiffness characteristics for symmetric laminates are presented. Vibrational test techniques for determining the dynamic modulus and material damping are also discussed. Partial extensional stiffness results intially indicate that the laminate theory used for predicting stiffness is accurate. It is clearly shown that the laminate theory can only be as accurate as the physical characteristics describing the lamina, which may vary significantly. It is recommended that all of the stiffness characteristics in both extension and bending be experimentally determined to fully verify the laminate theory. Dynamic modulus should be experimentally evaluated to determine if static data adequately predicts dynamic behavior. Material damping should also be ascertained because laminate damping is an order of magnitude greater than found in common metals and can significantly effect the displacement response of composite panels.

Patrick, H. V. L.↗
NASA NTRS2021

Experimental and Analytical Characterization of Fluted-Core Sandwich Composite Structures

As composite materials continue to gain wider acceptance for aerospace primary structures, experimental characterization and analysis methods must evolve, especially if new or underutilized composite structural concepts are to be successfully implemented. One such potentially underutilized concept is the fluted-core sandwich composite, which consists of facesheets separated by angled web members, and has a number of potential advantages over traditional-core (honeycomb, foam, etc.) sandwich composites. However, fluted-core sandwich composites also exhibit a behaviors not seen with traditional-core sandwich composites. For example, stable local buckling that can lead to material failure can occur in the facesheets between webs or in the webs themselves. Additionally, in the direction perpendicular to the webs, the effective transverse-shear stiffness is largely determined by the bending stiffnesses of the facesheets and the webs and is generally much lower than in the direction parallel to the webs. These local buckling and transverse-shear behaviors can have a large influence on material failure and global buckling, respectively. Thus, it is important to accurately characterize and model these behaviors. In this report, a series of experiments designed to elicit some of these fluted-core sandwich composite structural responses is discussed and the results are compared with results from a previously developed finite element analysis approach; qualitative and quantitative agreement between the experiment and analysis is shown.

Marc R. Schultz↗
NASA NTRS1984

The effects of thermal cycling on matrix cracking and stiffness changes in composite tubes

The study investigated the accumulation of transverse matrix cracks and the resultant loss of torsional, extensional, and bending stiffnesses in 8 layer 0.5 in. diameter crossply tubes subjected to thermal cycling. The tubes were graphite-epoxy and the temperature range during cycling was -250 to 200 F. The effect of fiber and matrix properties was investigated through the use of T300 and P75S fibers and 934 and CE339 resins. The study considered 0, 10, 50, 100, 300, and 500 thermal cycles. Photomicrographs, X-rays, and edge replication were used to evaluate cracking. Special loading fixtures were used to measure stiffness changes. An important finding was that for the tubes studied, even with extensive cracking, the bending and extensional stiffnesses were not affected. The torsional stiffness, however, was strongly affected.

Cohen, D.↗
NASA NTRS1989

Structurally-Tailorable, Nonlinear, Snap-Through Spring

Abrupt change in load/deflection response controllable and predictable. Structurally-tailorable, nonlinear, snap-through spring (STNSTS) exhibits controllable and predictable abrupt change in load/deflection response and based upon known phenomenon of snap-through structural response. Composed of pin-connected two-bar linkage which depicts combined tension/compression springs. As load applied to STNSTS, stiffness is function of internal spring and bending stiffness of pin-connected bars. As load increases, bars deform laterally until they collapse and snap through. Has application in passively-tailored rotor-blade flap, pitch, and lag response, to improve aerodynamic performance and stability characteristics of rotors; in aerodynamically- and aeroelastically-tailored wing spars and ribs, to produce tailored deformation state for improved effectiveness in maneuvering, aerodynamic performance, and stability characteristics; and in energy absorbers for automobile bumpers and aircraft land

Starnes, James H., Jr.↗