Bending Stiffness in Prepreg Composites
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Automated Fiber Placement↗
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Investigation of the Effect of Blade Sweep on Rotor Vibratory Loads
The effect of helicopter rotor blade planform sweep on rotor vibratory hub, blade, and control system loads has been analytically investigated. The importance of sweep angle, sweep initiation radius, flap bending stiffness and torsion bending stiffness is discussed. The mechanism by which sweep influences the vibratory hub loads is investigated.
Tarzanin, F. J., Jr.↗
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↗
An experiment-informed discrete element modelling study of knife milling for flexural biomass feedstocks
A discrete element method (DEM) based approach is used to study the relationships between material attributes (MAs), processing parameters (PPs), and quality attributes (QAs) for the knife milling of maize stalks. An approximate DEM shape model was conceptualized based on real maize stalks and calibrated based on experimental bending test data for flexural properties (elastic bending stiffness, elastic bending angle limit, elastoplastic ratio, etc.). DEM simulations of maize stalk comminution in a Jordan Reduction Solutions (“JRS”) knife mill were performed to investigate the relationships between the MAs (maize stalk size and breakage stress limit), PPs (impeller rotational speed), and QAs (mass throughput and output particle size distribution (PSD)). The DEM results suggest that stalk length has little influence on mass throughput and PSD, whilst stalks with larger cross sections tend to generate larger sizes of milled particles given the same breakage stress limit. Both the DEM and experimental results show that faster impeller rotation (or higher power) does not necessarily generate higher throughput or smaller output PSD, especially for maize stalks of higher breakage stress limit. The correlations between these MAs, PPs and QAs are found highly stochastic, though breakage stress limit dictates mass throughput, regardless of stalk size. The DEM-predicted output particle size tended to match the experimental data with coarse PSDs based on sieve size but showed weakened fidelity with finer material, indicating the potential for further model improvement.
09 BIOMASS FUELS↗
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.↗
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.↗
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.↗
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.↗
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.↗
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.↗
Heterogeneous flexibility can contribute to chromatin segregation in the cell nucleus
The highly and slightly condensed forms of chromatin, heterochromatin and euchromatin, respectively, segregate in the cell nucleus. Heterochromatin is more abundant in the nucleus periphery. Here, in this work, we study the mechanism of heterochromatin segregation by modeling interphase chromosomes as diblock ring copolymers confined in a rigid spherical shell using molecular dynamics simulations. In our model, heterochromatin and euchromatin are distinguished by their bending stiffnesses only, while an interaction potential between the spherical shell and chromatin is used to model lamin-associated proteins. Our simulations indicate that in the absence of attractive interactions between the nuclear shell and the chromatin, most heterochromatin segregates towards the nuclear interior due to the depletion of less flexible heterochromatin segments from the nuclear periphery. This inverted chromatin distribution, which is opposite to the conventional case with heterochromatin dominating at the periphery, is in accord with experimental observations in rod cells. This “inversion” is also found to be independent of the heterochromatin concentration and chromosome number. The chromatin distribution at the periphery found in vivo can be recovered by further increasing the bending stiffness of heterochromatin segments or by turning on attractive interactions between the nuclear shell and heterochromatin. Our results indicate that the bending stiffness of chromatin could be a contributor to chromosome organization along with differential effects of HP 1𝛼-driven phase segregation and of loop extruders and interactions with the nuclear envelope and topological constraints.
biomolecular & subcellular processes↗
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.↗
Modeling of surface mechanical behaviors of soft elastic solids: theory and examples
Surfaces of soft solids can have significant surface stress, extensional modulus and bending stiffness. Previous theoretical studies have usually examined cases in which both the surface stress and bending stiffness are constant, assuming small deformation. In this work we consider a general formulation in which the surface can support large deformation and carry both surface stresses and surface bending moments. We show that the large deformation theory can be reduced to the classical linear theory (Shuttleworth equation). We obtain exact solutions for problems of an inflated cylindrical shell and bending of a plate with a finite thickness. Our analysis illustrates the different manners in which surface stiffening and surface bending stabilize these structures. We discuss how the complex surface constitutive behaviors affect the stress field of the bulk. Our calculation provides insights into effects of strain-dependent surface stress and surface bending in the large deformation regime, and can be used as a model to implement surface finite elements to study large deformation of complex structures.
36 MATERIALS SCIENCE↗
Loads analysis and testing of flight configuration solid rocket motor outer boot ring segments
The loads testing on in-house-fabricated flight configuration Solid Rocket Motor (SRM) outer boot ring segments. The tests determined the bending strength and bending stiffness of these beams and showed that they compared well with the hand analysis. The bending stiffness test results compared very well with the finite element data.
Ahmed, Rafiq↗
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.↗
Waveguides for neurostimulation in the cochlea
Introduction Optical stimulation has been suggested for neural stimulation to improve cochlear implants. Light allows for more spatially selective activation of neuron populations than electrical current, offering more independent frequency bands along the spiral ganglion. These bands are available to encode acoustic information with anticipated better frequency resolution, improving cochlear implant user performance in noisy listening environments, tonal languages, and music perception. Methods Optical cochlear implants (oCIs) can deliver light either directly via small emitters within the cochlea or via waveguides from external optical sources. We investigated three waveguide designs made from OrmoComp ® , a polymer that cures through ultraviolet (UV) radiation. Waveguides were fabricated via injection molding and coated using dip-coating or thermal reflow, or through aspiration of OrmoComp ® into polyimide tubing that served as the cladding of the waveguide. The choice of fabrication technique directly determined the waveguides' total diameter: thermal reflow yielded ≈940 μm, dip-coating produced ≈306 μm, and aspiration resulted in ≈132 μm core diameter waveguides. Given the human cochlea's small size, we focused on analyzing the 306-μm and 132-μm waveguides, evaluating their optical performance (propagation and bending losses) and mechanical properties (bending stiffness and insertion forces). Furthermore, we evaluated some of these designs in in-vivo guinea pigs experiments. Results For the 100-μm core diameter waveguides, the propagation losses were 12.34 ± 1.26, 1.18 ± 0.88, 1.49 ± 0.58, and 3.43 ± 0.68 dB/cm at 534, 1,375, 1,460, and 1,550 nm, respectively. The respective bending losses at a 2 mm radius of curvature were 5.50 ± 1.32, 0.56 ± 0.26, 0.79 ± 0.18, and 0.64 ± 0.23 dB, and at 1 mm 8.54 ± 1.30, 2.05 ± 0.84, 2.11 ± 0.50, and 1.44 ± 0.37 dB. The bending stiffness of a 1 mm segment of the 100-μm-diameter waveguides was 18.9 ± 2.2 N/m. Insertion forces for the 100-μm-diameter waveguides into an acrylic human-size scala tympani model were < 25 mN. For the waveguides with 306 and 940 μm total diameter, the propagation losses ranged between 0.43 and 2.40 dB/cm at 534, 680, 1,375, and 1,550 nm, between 2.19 and 3.78 dB/cm at 450 and 1,460 nm. Bending losses for 360 degrees at 1,375 nm were 5.0, 2.4, and 0.46 for a bending radius of 2.5-, 3-, and 4-mm. Discussion Our study demonstrated that the polymer OrmoComp ® is suitable for fabricating waveguides to transmit near-infrared radiation. In-vivo experiments showed optically evoked auditory responses originating from optical stimulation in the guinea pigs' first cochlear turn while radiation was delivered. Incoming experiments will focus on evaluating long-term performance of these waveguides in guinea pigs and cats. This study will be designed to provide insights into the waveguides' performance and biocompatibility over extended periods, essential for their potential clinical application in future oCIs.
Kim, Matthew↗
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.↗
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.↗