Simple Bending Research Articles

Flutter Boundary Prediction Based on Nonstationary Data Measurement

A time-domain method for the e utter boundary prediction of a wing based on the nonstationary random response is proposed. The feature of this method is that a stability parameter is used as the measure of the aeroelastic stability margin instead of a conventional modal damping. The effectiveness of a stability parameter for the e utter boundary prediction is shown using a simple bending ‐ torsion wing model. Numerical studies are conducted to examine the performance of the method under the nonstationary condition. An application to supersonic wind-tunnel e utter testing data shows that the proposed method is effective to the prediction of the e utter boundary in the actual e utter testing.

Size- and Age-dependent Variation in the Properties of Sap- and Heartwood in Black Locust (Robinia pseudoacacia L.)

Dissection and mechanical bending experiments showed that the cross-sectional area and elastic moduli of sap- and heartwood varied within the trunk and branches as a function of the distance from the top of a 43-year-old black locust tree ( Robinia pseudoacacia L.). Wood in branches less than I m from the top of the tree consisted entirely of sapwood; the majority of the wood from more basipetal (and older) parts of the tree was heartwood. The Young's elastic moduli of sap- and heartwood increased towards the base of the trunk, and, on average, the modulus of the sapwood was 35 % less than that of the heartwood. Younger, more distal tree limbs, therefore, were more flexible than older portions of the same tree. Simple bending experiments showed that the flexural rigidity of young limbs was governed by the location, physical properties, and the relative quantities of the two types of wood. The rigidity of limbs increased toward the base of the tree, and was dominated by sapwood in young limbs and by heartwood in the oldest parts of the tree. These trends predict that the younger, distal limbs of this tree can more easily deflect and bend in the wind, thereby reducing drag and the total bending moment on the tree trunk, while older limbs and the trunk are sufficiently rigid to support static self-loadings. Further study, however, is required to determine whether the trends reported here apply to all trees of this species and to trees of different species.

Size- and Age-dependent Variation in the Properties of Sap- and Heartwood in Black Locust (Robinia pseudoacaciaL.)

Dissection and mechanical bending experiments showed that the cross-sectional area and elastic moduli of sap- and heartwood varied within the trunk and branches as a function of the distance from the top of a 43-year-old black locust tree (Robinia pseudoacaciaL.). Wood in branches less than 1 m from the top of the tree consisted entirely of sapwood; the majority of the wood from more basipetal (and older) parts of the tree was heartwood. The Young's elastic moduli of sap- and heartwood increased towards the base of the trunk, and, on average, the modulus of the sapwood was 35%less than that of the heartwood. Younger, more distal tree limbs, therefore, were more flexible than older portions of the same tree. Simple bending experiments showed that the flexural rigidity of young limbs was governed by the location, physical properties, and the relative quantities of the two types of wood. The rigidity of limbs increased toward the base of the tree, and was dominated by sapwood in young limbs and by heartwood in the oldest parts of the tree. These trends predict that the younger, distal limbs of this tree can more easily deflect and bend in the wind, thereby reducing drag and the total bending moment on the tree trunk, while older limbs and the trunk are sufficiently rigid to support static self-loadings. Further study, however, is required to determine whether the trends reported here apply to all trees of this species and to trees of different species.

Elliptical flexure hinges

This paper presents closed form equations based on a modification of those originally derived by Paros and Weisbord in 1965, for the mechanical compliance of a simple monolithic flexure hinge of elliptic cross section, the geometry of which is determined by the ratio ε of the major and minor axes. It is shown that these equations converge at ε=1 to the Paros and Weisbord equations for a hinge of circular section and at ε ⇒∞ to the equations predicted from simple beam bending theory for the compliance of a cantilever beam. These equations are then assessed by comparison with results from finite element analysis over a range of geometries typical of many hinge designs. Based on the finite element analysis, stress concentration factors for the elliptical hinge are also presented. As a further verification of these equations, a number of elliptical hinges were manufactured on a CNC milling machine. Experimental data were produced by applying a bending moment using dead weight loading and measuring subsequent angular deflections with a laser interferometer. In general, it was found that predictions for the compliance of elliptical hinges are likely to be within 12% for a range of geometries with the ratio βx (=t/2ax) between 0.06 and 0.2 and for values of ε between 1 and 10.

Mechanical properties of thin and thick coatings applied to various substrates. Part I. An elastic analysis of residual stresses within coating materials

Internal residual stresses significantly influence the overall mechanical properties of multi-layer systems and consequently affect the coated material's performance. The determination of residual stresses within coatings has been extensively carried out for thin (the coating thickness being less than the substrate thickness) films (Stoney, Röll, etc.) and for thick (the coating thickness being approximately equal to the substrate thickness) films (Timoshenko, Inoue, etc.). This work extends currently existing models to cover cases where the coating thickness approaches that of the sheet substrate. We developed relationships for the determination of the first-order residual stress. The construction of these models was carried out using a one-dimensional analysis based on beam theory (the width-to-thickness ratio of the system being less than 5). As suggested by Timoshenko and later on by Hoffman, we also introduced the bi-axial modulus for isotropic stresses when the thin plate theory (the width-to-thickness ratio of the system being greater than 5) is used. Under forces and moments resulting from coating initial residual stresses, we consider that the bi-layer material exhibits a radius of curvature, R. The final equilibrium state is obtained by the simple and pure bending of the bi-layer material. From the two equilibrium conditions (force and moment), the model for the initial residual stress is derived as a function of mechanical (Young's modulus and Poisson's ratio of the substrate and of the coating) and geometrical (thickness of the substrate and of the coating) characteristics of the bi-layered system. This model derived for initial residual stresses ignores the in-plane deformation of the bi-layer material and can be applied to compliant coating materials deposited onto stiff substrates or to thin coating layers deposited onto thick substrates. Furthermore, in order to consider the in-plane deformation which implies that the strain in the coating causes a strain in the substrate (as opposed to the above situation where the substrate imposes the strain in the coating one-sidedly), this model was rewritten by introducing the stiffness ratio. The relationship obtained (for the in-plane deformation) is equivalent to that of Inoue and it is, of course, the most applicable since it can be applied to thin and thick coating layers of compliant or stiff materials deposited onto compliant or stiff substrates.

On the validity of applying the elastic work factor approach to determine GIc of fiber-reinforced laminated composites

Previously, the elastic work factor, η el of a DCB specimen was derived from a simple bending theory. In this study, the η el derived from simple bending theory was compared with that calculated from a finite-element method. The η el derived from simple bending theory was applied experimentally to DCB specimens with two stacking sequences in order to determine G Ic of fiber-reinforced composites (AS4/3501). The stacking sequences used were [0] 16 and [ 0 2± 45 2 0 2 ] s . G Ic determined from the work factor approach was compared with that determined from the compliance method for each stacking sequence. The results showed that the work factor approach and the compliance method produce comparable results of G Ic for each stacking sequence. Thus, G Ic can be determined from a single DCB specimen using ν el derived from simple bending theory.

In simple synthetic promoters YY1-induced DNA bending is important in transcription activation and repression.

Depending on promoter context, YY1 can activate or repress transcription, or provide a site for transcription initiation. To investigate whether the ability of YY1 to induce DNA bending influenced its ability to activate and repress transcription, simple synthetic promoters were constructed in which the YY1 binding site was inserted between the TATA box and either the NF1 or AP1 recognition sequences. In transient transfections of COS cells, the NF1YY1TATA and NF1RYY1TATA promoters exhibited a dramatic 15-20-fold increase in correctly initiated transcription. These promoters exhibited even larger 60-80-fold increases in transcription in HeLa cells. Neither multiple copies of the YY1 binding site alone, nor placement of a YY1 site upstream of the NF1 site activated transcription. Deletion of 4 bp between the NF1 and YY1 sites, which changes the phase of the DNA bends, abolished the 16-fold activation of transcription by NF1YY1TATA. Insertion of the YY1 site between the AP1 site and the TATA box decreased transcription approximately 3-fold. Replacing the YY1 binding site with an intrinsic DNA bending sequence mimicked this transcription repression. Sequences of similar length which do not bend DNA fail to repress AP1-mediated transcription. Gel mobility shift assays were used to show that binding of YY1 to its recognition sequence did not repress binding of AP1 to its recognition sequences. Our data indicate that YY1-induced DNA bending may activate and repress transcription by changing the spatial relationships between transcription activators and components of the basal transcription apparatus.

Deformation of sandwich panels in cylindrical bending by point forces. 1. Analytical construction

A refined model for bending of a three-layered panel with a soft filler is proposed. The modified model permits us to consider the asymmetry of elastic properties and thickness of the outer layer relative to the middle plane of the panel in a composite sandwich structure. In constructing the deformation mechanism, a heterogeneous kinematic model was adopted, which, in contrast to the assumptions for the deformation of the whole stack of layers, features four degrees of displacement freedom permitting consideration of the separate nature of the deformation of the outer layers in bending and of the intermediate layer in transverse compression combined with shear. This approach is postulated according to an energetic evaluation of the deformation of the layers [2]. The specific features of the stress from point forces in cylindrical bending are considered using the operational Laplace method, which avoids the additional difficulties in analyzing the solution convergence arising when it is represented by a series of eigenfunctions of the boundary value problem. The fundamental functions of a twelfth-order set of equations are used to construct the boundary problem reduced to a Cauchy problem. Various boundary effects of the point stress are described using a generalized Dirac function. Variants are examined for the limiting transformation of the model parameters leading to a qualitative change in its kinematics and the corresponding simplified bending models.

In-plane and out-of-plane waves’ power transmission through an L-plate junction using the mobility power flow approach

The structural power flow through the junction between two flat plates, coupled in an L-shaped configuration, is considered using the mobility power flow (MPF) approach, for both in-plane (longitudinal and shear) and out-of-plane (bending) waves’ propagation. Power flow by both types of waves is included by considering the junction edge between the two plates, when uncoupled, to be free. Mobility expressions are then derived for both in-plane and out-of-plane degrees of freedom forces and responses. The results of the analysis show that the in-plane waves do not significantly contribute to the structural power flow at relatively low frequencies, that is, for frequencies below a bending wave number and plate thickness product of approximately 0.1. In this case, the power flow results are not different from those obtained if the junction is assumed to be pinned, and power is transmitted by only the out-of-plane waves. However, as the frequency increases, the significance of the in-plane waves’ contribution increases, and for a bending wave number and plate thickness product greater than approximately 1.0, the contribution from the in-plane waves dominates. This condition is different from the well-known result that if the thickness is greater than approximately 10% of the bending wavelength, simple bending theory does not apply. This condition deals with the significance of the in-plane waves. In the frequency region where the in-plane waves dominate, the in-plane longitudinal waves are more significant than the in-plane shear waves, although this has some dependence on the selected L-shaped configuration. The in-plane longitudinal waves couple directly to the out-of-plane waves because of the 90 degree junction.

Electrical Conductivity and Dielectric Properties of Bi4Ti3O12

The present paper deals with the investigation of electrical and dielectric properties of structures based on Bi 4 Ti 3 O 12 films. It has been found that the nonlinearity of the I - U characteristics in Me-Bi 4 Ti 3 O 12 -Me structures is attributed to intercrystalline potential barriers. The height of the intercrystalline barrier (Φ 0 = 0.12 eV) and the mean size of crystallise (L = 0.3 μm) have been determined. At rather low temperatures, the hopping conductivity with a mean length of hopping, ∼2.6 x 10 19 cm -3 eV -1 , is shown to be a dominant process at the charge transfer. It has been found that the electrical conductivity (σ) in the direction parallel to the C-axis (sandwich configuration) shows an anomaly in the phase transition region (∼ 950 K), while in the direction perpendicular to the C-axis, a simple bending of σ vs. T is observed. The latter is explained by the change of spontaneous polarization in Bi 4 Ti 3 O 12 films. The temperature dependence of the dielectric constant and the dielectric loss tangent have the maxima in the range of the phase transition temperature. The dielectric constant values are ∼650 ∼120 for the structures of sandwich and planar configurations, respectively. This fact indicates the presence of a polarization component in the given direction. The diffusion of the phase transition is explained by the imperfection of the film structure.

Bending, flanging, and hemming of aluminum sheet—an experimental study

Hemming is often used as the last stage of stamping operations. It is used either to improve appearance (to create a smooth edge rather than a razor edge with burrs) or to attach one sheet metal part to another. Hemming is defined as folding of bent or flanged sheet 180° or more. However, the deformation mechanism, and hence the process, is different and more complex than simple bending and flanging process. Therefore, very little information is available in research literature, and most of the hemming dies are designed based on trial and error. This paper gives the results obtained from the hemming experiments that were conducted at the Engineering Research Center for Net Shape Manufacturing (ERC/NSM) by using Aluminum Alloy 1050.

Aspherically bent SiC mirror: Bending test

A bending test of an elliptically bent SiC mirror was performed. The result shows that a desired figure of the surface can be generated with a high accuracy by using a simple bending mechanism.

Inelastic models of lithospheric stress-11. Implications for outer-rise seismicity and dynamics

SUMMARY Outer-rise seismicity and dynamics are examined using inelastic models of lithospheric deformation, which allow a more realistic characterization of stress distributions and failure behaviour. We conclude that thrust- and normal-faulting outer-rise earthquakes represent substantially different states of stress within the oceanic lithosphere. Specifically, the normal-faulting events occur in response to downward plate bending, which establishes the 'standard', bending-dominated state of outer-rise stress, and the thrust-faulting events occur in response to an elevated level of in-plane compression, which develops only in response to exceptional circumstances. This interpretation accounts for the observation that normal-faulting outer-rise earthquakes occur more frequently and are more widely distributed than their thrust-faulting counterparts, an observation for which the simple bending model offers no explanation. In addition, attributing both thrust- and normal-faulting outer-rise earthquakes to plate bending implies that both classes of events should occur within relatively close lateral proximity to one another because both are allegedly a manifestation of the same bendingdominated stress distribution, whereas, in reality, this is not observed. We propose that the tendency for thrust-faulting outer-rise earthquakes to exhibit greater source depths than their normal-faulting counterparts (an observation that is frequently cited in support of the bending interpretation of the former) is merely a consequence of the fact that bending-induced tension is confined to the upper lithosphere. Our model predicts that outer-rise in-plane-force variations may promote thrust-faulting outerrise activity prior to an underthrusting interplate subduction earthquake and normalfaulting outer-rise activity following such an earthquake, but that both forms of outerrise activity are unlikely to be associated with the same subduction earthquake. A corollary implication of our model is that subduction earthquakes are likely to be either preceded by or followed by an absence of large outer-rise earthquakes. Levels of in-plane compression necessary to generate thrust-faulting outer-rise earthquakes are attributed to stress concentrations within the subducting plate that are induced by relatively localized resistance to regionally distributed plate-driving forces. Resistance of this nature may result from either the attempted subduction of relatively buoyant (i.e. isostatically compensated) bathymetric features or the existence of strong interplate

ASSUMED STRESS C 0 QUADRILATERAL/TRIANGULAR PLATE ELEMENTS BY INTERRELATED EDGE DISPLACEMENTS

This paper presents two simple quadrilateral C0 plate bending elements with explicit element stiffness matrix. The element formulation is based on assumed element stress fields and the interrelated transverse displacement and rotation along element boundaries. The interrelated edge displacements not only can result in higher-order displacements interpolations for higher accuracy element and overcome the shear locking in thin plate analysis encountered by C0 plate elements, but can also unify the four-noded quadrilateral element and its corresponding three-noded triangular element. The latter cannot be achieved by the assumed displacement formulation. The numerical examples demonstrate the accuracy and robustness of the present assumed stress C0 plate elements.

Shallow morphology of the subducted Pacific plate along the Hikurangi margin, New Zealand

Along the east coast of the North Island, New Zealand, the Pacific plate is subducted beneath the Australian plate. The seismicity associated with this subduction has been determined using the results from a number of temporary and permanent microearthquake networks. A synthesis of the microearthquake seismicity, the depths of thrust events, the depth of S to P conversions, and deep reflection seismic studies leads to a coherent picture of the subducting slab, both in terms of its mechanical structure and in terms of the general morphology. The slab is initially subducted at a low angle of a few degrees, is bent through a circular arc of few hundred kilometre radius and then becomes planar again below 120 km depth. The radius of curvature varies along strike from about 280 km, just north of Wellington, to 240 km, north of Hawke Bay. The slab shape, between depths of 15–45 km, is thus approximately conical. It also approximates, within the errors of hypocentre location, a surface of constant Gaussian curvature, as would be geometrically expected from the simple bending of a thin spherical lithospheric shell. Observed seismicity is primarily concentrated within what is interpreted as the subducted crust of the Pacific plate, with a lower level of activity within the subducted mantle. Normal fault mechanisms at the top of the plate probably reflect tensional stress associated with the plate bending whereas thrust events observed at the lower bound of the observed seismicity probably reflect compression below the neutral plane.

Distortion Effects in BL Lac Radio Jets

BL Lac objects often show a quite distorted radio morphology. Almost 75% of the BL Lacs for which the information is available show an apparent misalignment angle ΔPA between the VLBI jet and the large scale radio structure larger than 45 degrees. This can be explained by strong enhancement of slight bending due to projection effects, especially if BL Lacs are the most highly beamed sources. However we recently performed a statistical analysis of misalignment angle histograms for 155 extragalactic radio sources of different types and found that the intrinsic distortion is significantly more important in BL Lacs than in quasars and even CSS sources. Indeed the best fits of the δPA histograms by a simple bend model correspond to γɸ = 123° for BL Lacs, 37° for quasars and 36° for CSS sources, where ɸ and γ are the jet typical intrinsic bend and Lorentz factor within a given class of sources (Appl et al, 1995). If, as currently thought, jets in BL Lacs have smaller Lorentz factors than in quasars, high intrinsic bending and misalignment appear to be the rule in BL Lac sources.

Determination of Mode I Fracture Toughness of Fiber Reinforced Composites by the Elastic Work Factor

The work factor approach was applied to determine of fiber reinforced composites (AS4/3501) from a single unidirectional (0-deg) DCB specimen. Elastic work factors of DCB specimen for three different symmetrical staking sequences were derived from a simple bending theory and a finite element method. The results showed that elastic work factors calculated from both methods were comparable each other. In particular, the elastic work factor of DCB specimen with symmetrical stacking sequence is independent of stacking sequence. The determined from the work factor approach was compared with that determined by the compliance method. The results showed that the work factor approach and the compliance method produce comparable results of . Thus, can be determined from a single DCB specimen using the work factor approach.

Effect of W Addition on the Martensitic Transformation and Shape Memory Behaviour of the TiNi-Base Alloys

The effect of W addition on the martensitic transformation (MT) and SM effect, especially reversible shape memory(two way shape memory) effect of the TiNi base alloys was investigated. It was found that addition of W in the TiNi and TiNi-Cu SM alloys does not affect essentially MT itself. Transformation temperatures slightly decrease with increasing W content (3 to 5K/at%W) and transformation hysteresis does not widen. By measuring change in bending strain above and below Af and Ms of the specimen of W added alloys showed that quite clear RSM effect is obtained even in the specimen slightly deformed by simple bending with bending strain 0.05 below Ms. It was found that W is less soluble in the TiNi matrix and makes fine particles with the size around 20 microns by EPMA analysis. It is expected that fine and hard W precipitates would make the origin of strain field for MT during the 2nd and further heating and cooling cycle. It is thus quite hopeful to develope TiNi alloys with good RSM effect by using these W added alloys.

Determination of the Curvatures and Bending Strains in Open Trileaflet Heart Valves

The leaflets of trileaflet artificial heart valves manufactured from polyurethane, gluteraldehyde-treated porcine aortic valves and pericardial tissue are subject to cyclic stresses and strains which can reduce the lifetime of the implanted valves through leaflet calcification and fatigue failure. A detailed knowledge of the stress state within a valve leaflet throughout a cardiac cycle is desirable in order to improve the geometry of the valve leaflets and ultimately improve the valve performance. An experimental method to evaluate the radius of curvature at the free edge of the open valve leaflet is presented. The technique has been applied to polyurethane trileaflet heart valves manufactured within the authors' laboratory and to commercially available bioprosthetic valves in the fully open position under steady and pulsatile flow conditions. Simple bending theory has been applied to the polyurethane valves to calculate bending stresses and strains at the free leaflet edge based on the measured curvature. The results showed that in the fully open position the highest curvatures occurred at the commissural regions for all the valves analysed. Additional areas of high curvature were present along the free leaflet edge. Average curvatures as high as 0.85 mm-1 were observed at the leaflet commissures for the polyurethane valves with a resultant bending stress of 0.72 MPa. The porcine bioprosthetic valves showed average curvatures as high as 2.5 mm-1 which also occurred at the leaflet commissures. The results of the study have been compared to values of stress obtained from numerical analysis of closed polyurethane valve leaflets reported in the literature.(ABSTRACT TRUNCATED AT 250 WORDS)

The pure bending of sheet

The bending of sheets is a widely used metal-forming process. When analyzing the various sheet-bending processes, there is a need for an appropriate model to describe the bending couple-curvature relationship over the whole range of bending radii (from infinite curves to sharp bends). Apart from some sheet-bending processes, such as stretch-bending (where the normal force cannot be neglected) and in cases of very sharp bends (where the transverse force has some influence), the pure bending concept, for describing the local deformation behaviour of a sheet, can be used to analyze various sheet-bending processes. In the present research a simple explicit bending couple curvature relation is derived. Comparison of this model with two almost complete solutions (one for small and one for large curvatures) shows that, from a theoretical point of view, this model appears to be good. For the experimental verification of the model, use was made of an especially designed sheet-bending apparatus. It was shown that a fairly good agreement exists between the explicit relationship and the measured curves. Combining model and experiment leads to an accurate description of the bending couple curvature relationship that is very useful for the analysis of sheet-bending processes.