Showing papers on "Flexural rigidity published in 2000"

Observations of flexure and the rheology of oceanic lithosphere

Abstract: The principal evidence for the long-term (i.e. > 1 Myr) mechanical behaviour of the oceanic lithosphere has come from studies of how it deforms in response to large loads such as volcanoes and sediments. A model widely used to explain the deformation is an elastic plate in which flexural rigidity depends on the thermal age of the lithosphere at the time of loading. An elastic model, however, is time-invariant and does not take into account temporal changes that may occur in the flexural rigidity as a consequence of loading. There is evidence, for example, that the flexural rigidity of the oceanic lithosphere also depends on load age, being large at short times and small at long times. Thus, competing effects may exist between thermal cooling which strengthens the lithosphere and some form of load-induced stress relaxation which weakens it. In order to investigate the relative roles of these processes, we have developed a multilayered viscoelastic model which is based on the results of experimental rock mechanics that creep in the lithosphere is a thermally activated process, and on a thermal structure that is given by the plate-cooling model. By comparing the predictions of the model with a new compilation of flexural rigidity estimates, we have found that, if the upper mantle viscosity is 1020 Pa s, the activation energy that best describes the long-term mechanical behaviour of the oceanic lithosphere is 120 KJ mol−1. This parameter pair explains the dependence of flexural rigidity on both plate and load age. It also helps account for the subsidence and uplift history of oceanic islands and the stratigraphic patterns that develop in the flexural moats that flank them. At atolls, a multilayered viscoelastic model explains the rapid subsidence that follows shield building and does not require that the age of the lithosphere that supports a volcano is thermally ‘re-set’ to a younger value. Our studies suggest that, while the oceanic lithosphere has viscoelastic properties, the viscosity of its upper layers is so much higher than that of its lower layers that in effect it behaves as a thin elastic plate on long timescales. There will therefore be a certain permanence to the observations of oceanic flexure such that they may be used, with some confidence, to evaluate the tectonic setting of individual features of the seafloor and, in some cases, their age.

Effect of plate position relative to bending direction on the rigidity of a plate osteosynthesis. A theoretical analysis.

Abstract: Mechanical unloading of the plated bone segment is observed after plate osteosynthesis because the implant takes over a part of the physiological loading. Strain reduction in the bony tissue depends on the rigidity of the plate (cross-sectional area, geometrical form, and modulus of elasticity). The aim of the present study was to calculate theoretically the effect of plate position relative to bending direction on the overall bending stiffness of the composite system plate-bone. To calculate the rigidity, a cylindrical bone model with mechanical characteristics similar to a sheep tibia and a rectangular plate cross-section corresponding to a DC-plate with either a modulus of elasticity of steel or titanium was used. Calculations under different bending directions were performed according to the laws of the linear bending theory and the composite beam theory. The bending stiffness of a plate osteosynthesis reaches a minimum and a maximum respectively, in cases in which the bending moment acts in the direction of the main axis of the area moment of inertia of the plate. The minimum is present with the plate bent vertically, the maximum with the plate bent horizontally, e.g. on the tension side of the composite system--on the assumption that the bone structure opposite the plate is capable of withstanding compressive loading. For steel and titanium plates, factors of 2 and 2.25 respectively were calculated between the minimum and the maximum bending stiffnesses of the osteosynthesis. The bending rigidity of the plate alone has only a minimal effect on the total stiffness of the osteosynthesis. With a plate bent vertically, the difference between steel and titanium plates was 18%, with the plate bent horizontally (situated on the tension side), it was only 7%. The bending stiffness of a plate osteosynthesis depends on the cross-section, the geometrical form, and the modulus of elasticity of the plate, as well as on the plate position relative to the bending direction of the composite system. The modulus of elasticity of the plate is relatively unimportant, while with a given plate the individual plate position relative to the bending direction is of crucial importance. Thus, changing the modulus of elasticity of the plate cannot solve the problem of implant induced unloading of the bone cortex because the bending stiffness of the composite system depends much more on the plate position relative to the bending direction.

Drop test and analysis on micro-machined structures

Abstract: Drop testing of micro-machined accelerometers (experimental samples) from the height of a table top shows that a moderate impact can result in large percentage of device malfunctions (as much as 50%) which render the devices unusable. This paper is a first attempt at providing a detailed analysis of the consequences of dropping a micro-machined transducer structure to a solid surface. The theoretical analysis is composed of two parts; first, a micro-machined structure is treated as a single degree of freedom oscillator consisting of a mass, a spring and a dashpot, whose motion is governed by an ordinary differential equation. Then the flexibility of the micro-machined structure is examined by solving a governing partial differential equation. It was found that for a nominal micro-machined transducer structure, the drop induced proof-mass travel and the deflection of the structure itself can be as large as 20% of its lateral dimension depending on the structural rigidity. The drop induced acceleration or deceleration depends on drop height as well as structural properties such as mass, spring constant, flexural rigidity, and geometrical dimensions. It is shown that a table-top drop can generate decelerations ranging from tens of thousands to hundreds of thousands of g's.

Power transmission shaft

Abstract: A power transmission shaft to be used mainly in vehicles comprises metal joint elements and a metal pipe connected to each other. A fiber reinforced plastic pipe having a large flexural modulus of elasticity is inserted into the metal pipe, thus forming a composite FRP shaft having flexural rigidity sufficient to serve as a power transmission shaft.

Flexural stiffness patterns of butterfly wings (Papilionoidea)

Abstract: A flying insect generates aerodynamic forces through the ac- tive manipulation of the wing and the "passive" properties of deformability and wing shape. To investigate these "passive" properties, the flexural stiffness of dried forewings belonging to 10 butterfly species was compared to the butterflies' gross morphological parameters to determine allom- etric relationships. The results show that flexural stiffness scales with wing loading to nearly the fourth power (p w 3.9 ) and is highly correlated with wing area cubed (S 3.1 ). The generalized map of flexural stiffness along the wing span for Vanessa cardui has a reduction in stiffness near the distal tip and a large reduction near the base. The distal regions of the wings are stiffer against forces applied to the ventral side, while the basal region is much stiffer against forces applied dorsally. The null hypothesis of structural isom- etry as the explanation for flexural stiffness scaling is rejected. Instead, selection for a consistent dynamic wing geometry (angular deflection) in flight may be a major factor controlling general wing stiffness and deformability. Possible relationships to aerodynamic and flight habit fac- tors are discussed. This study proposes a new approach to addressing the mechanics of insect flight and these preliminary results need to be tested using fresh wings and more thorough sampling.

Elastic properties of surfactant monolayers at liquid–liquid interfaces: A molecular dynamics study

Abstract: Using a simple molecular model based on the Lennard–Jones potential, we systematically study the elastic properties of liquid–liquid interfaces containing surfactant molecules by means of extensive and large-scale molecular dynamics simulations. The main elastic constants of the interface, corresponding to the interfacial tension and the mean bending modulus are determined from the analyses of the long-wavelength behavior of the structure factor of the capillary waves. We found that the interfacial tension decreases with increasing surfactant interfacial coverage and/or surfactant chain length. However, we found that the corresponding change in the bending rigidity is nonmonotonic. Specifically, we found that the bending rigidity decreases with increasing surfactant interfacial coverage for small surfactant interface coverages, but then it increases as the surfactant interface coverage is further increased. Using a Gaussian theory on an interfacial Ginzburg–Landau model of surfactants, we find that the initial decrease of the bending rigidity is attributed to coupling between fluctuations of the surfactant orientation field to those in the interfacial height.

Kelvin Equation for Meniscuses of Nanosize Dimensions

Abstract: Curvature corrections to the Kelvin−Laplace equation (KLE) for a highly curved surface and its effect on the general picture of meniscus formation are considered in the frame of a flexural rigidity model of a liquid surface and the Helfrich expression for energy of flexural deformation of the interface. It is shown that the vapor pressure depends not only on surface tension of a liquid but also on flexural properties of the liquid surface. The generalized KLE accounting for the flexural rigidity of the interface explains the observed deviation from the original KLE for meniscuses of nanosize dimensions. The predicted limiting condensation pressure and the limiting curvature radius below, which the meniscus of nanosize dimensions cannot form, is in agreement with surface force apparatus studies.

Sensory Measurements of the Main Mechanical Parameters of Knitted Fabrics

Abstract: Mechanical parameters such as bending rigidity, thickness, compressibility, and coef ficient of friction are measured by a sensory method for a series of plain and rib weft knitted structures made from cashmere and polyester textured yarns. The values estimated by the sensory method are found to be in fairly good agreement with the values measured on the KES system. The results of our work indicate that by using a standard and controlling the handling manner, sensory assessments can be as successfully quantified as instrumental measurements. However, detectable differences in each mechanical param eter vary with the sensory assessment, depending on the property being considered. The sensory measurement of fabric thickness yields the most consistent and accurate results. Other parameters such as the bending rigidity, compressibility, and coefficient of friction are also reasonably estimated. In addition, the effectiveness of the sensory measurements is also discussed in terms of knit construction and fiber...

Characterization and modelling of matrix cracking in a (0/90)2s GFRP laminate loaded in flexure

Abstract: The matrix cracking behaviour of a (0/90) 2 s laminate loaded in flexure is studied analytically and experimentally. Simple bending theory is used in conjunction with a shear–lag analysis to develop an expression for the flexural stiffness as a function of crack density in the single 90° ply towards the tensile face of the beam. A flexural compliance approach is used to deduce the applied bending moment and associated in situ ply stress at initial failure. This method is extended to enable thermal effects to be incorporated. A thermo–elastic analysis is used to obtain an expression for the residual curvature, which develops as a result of cracking. Experimental data have been obtained for crack onset and accumulation in the single 90° ply of a (0/90) 2 s GFRP laminate as functions of applied bending moment and in situ ply strain, together with data for residual properties as a function of damage. Agreement between theory and experiment is satisfactory.

Effect of thermal undulations on the bending elasticity and spontaneous curvature of fluid membranes

Abstract: We amplify previous arguments why mean curvature should be used as measure of integration in calculating the effective bending rigidity of fluid membranes subjected to a weak background curvature. The stiffening of the membrane by its fluctuations, recently derived for spherical shapes, is recovered for cylindrical curvature. Employing curvilinear coordinates, we then discuss stiffening for arbitrary shapes, confirm that the elastic modulus of Gaussian curvature is not renormalized in the presence of fluctuations, and show for the first time that any spontaneous curvature also remains unchanged.

V-ribbed belt

Abstract: In a V-ribbed belt (B), a tension member is embedded and a plurality of ribs are formed in a bottom face thereof to extend in parallel with one another along the length of the belt (B). In order to supress production of vibration and associated noise, the V-ribbed belt (B) is characterised in that, when the V-ribbed belt (B) is subjected to a flexural rigidity test which is conducted to place the belt (B) between a pair of upper and lower pressing plates (14, 15) of a testing device constructed such that the upper and lower pressing plates (14, 15) are held in parallel with each other by a pair of links (16) and set a weight of 6,86 N on the upper pressing plate (14) to deform the belt in a flat-like shape, the flexural rigidity of the V-ribbed belt (B) determined, based on the distance I (unit: cm) between both portions of the tension member located respectively in upper and lower spans of the belt in deformed condition, from the following formula: Flexural rigidity (unit: N • cm 2 ) = 0,174 × W × I 2 , is 7,84 N • cm 2 or more per rib (Fig. 5a).

Statistical mechanics of membranes: freezing, undulations, and topology fluctuations

Abstract: Membranes are two-dimensional sheets of molecules which are embedded and fluctuate in three-dimensional space. The shape and out-of-plane fluctuations of tensionless membranes are controlled by their bending rigidity. Due to their out-of-plane fluctuations, flexible membranes exhibit very different behaviour to flat two-dimensional systems. We discuss three properties of membranes: (i) the renormalization of the bending rigidity in fluid membranes due to undulations on short length scales; (ii) the suppression of the crystalline phase, and the hexatic-to-fluid transition; and (iii) the lamellar-to-sponge transition in systems with variable topology. We focus on simulation studies, which are based on the numerical analysis of dynamically triangulated surface models.

The continuum of connection rigidity in timber structures

Abstract: The use of timber in rigid frames has been hampered by the debate surrounding the rigidity of the moment connections. Joint stiffness is a function of beam flexural stiffness, as well as of the rotational stiffness of the connection. The level of joint rigidity, which is predictable from joint stiffness, significantly affects the bending moments and forces that are transferred through the connection. We used joint-test data from the literature and computer models to assess the effect of various parameters on joint stiffness. There is a continuum of joint stiffness for moment-resisting connections where the deformed shapes of the beams in beam-to-column connections are described by pinned, semi-rigid, and rigid behavior. Engineers can assess the level of joint rigidity during the design process so that the resulting connections and frames meet performance expectations. It seems unlikely that a fully rigid joint can be designed for use in timber portal frames because of stiffness orthotropy. However, moment-resisting joints that are less than 50% rigid can be used in timber frames to develop frame-like behavior.

Propeller shaft and method of producing the same

Abstract: A propeller shaft has a metal pipe (1) with a joint element (3) joined at an end thereof A fiber reinforced plastic layer (5) having a thickness that achieves a flexural rigidity satisfying a required natural bending frequency is formed on an outer circumference of the metal pipe (1) satisfying a static torsional strength required as a propeller shaft The fiber reinforced plastic layer (5) has an interface strength between the reinforcing fiber and the matrix within a range of 20 to 200 MPa as measured by the microdroplet method

Effects of Yarn Bending and Fabric Structure on the Bending Properties of Plain and Rib Knitted Fabrics

Abstract: This work deals with the bending properties of a series of plain and rib weft knitted structures made from cashmere yarns. Additionally, some plain weft knitted fabrics made from polyester textured yarns (PET) are included for comparison. The experimental results are discussed in terms of the structural characteristics (cover factor, fabric weight) and their effects on the bending properties. Theoretical analyses of the effects of yarn bending properties and fabric structure on the bending rigidity and frictional bending moment of the fabrics are based on our straight parallel yarns (SPY) model. In this model, the knitted structure is assumed to consist of a series of straight yarns that have some overlapping regions at the interlocking points. The estimation of fabric bending parameters is based on summing up the bending parameters of these straight yarns, which have some overlapping regions lying in the direction of bending. The estimated values from this model are compared with the values measured on a...

Bending Hysteresis of Plain Woven Fabrics in Various Directions

Abstract: Many researchers have studied the bending rigidity of woven fabrics in various directions, but there have been no reports on anisotropy in bending hysteresis. In this work, existing models for predicting the bending rigidity of woven fabrics are applied to bending hysteresis in various directions. A wide range of cotton plain woven fabrics is examined by comparing theoretical data with experimental results. The results show that Cooper's model is the most reliable in predicting polar diagrams of bending hysteresis in cotton plain woven fabrics. The results also indicate that the shape of polar diagrams of bending hysteresis along the weft direction spreads outward with an increase in the ratio V introduced by Cooper.

Bending Behavior of Woven Fabrics with Vertical Seams

Abstract: This paper presents a study of the bending properties of fabric strips with vertical plain seam. The "second moment of area" of a seamed cross section determines the bending behavior of such a strip. Fabric thickness, seam thickness, distance of the neutral axis from the surface of the cross section, and seam allowance width are involved. Various woven fabrics with different seam allowances are investigated. Bending length and bending rigidity obtained from the experimental results are highly related to the second moment of area of the seamed fabric cross section.

Theory for the bending rigidity of protein-coated lipid membranes

Abstract: We study the bending rigidity of protein-coated lipid bilayer membranes by a continuum Landau theory. For up–down symmetric membrane proteins, the bending rigidity (κ) of the membrane is found to increase linearly with protein fraction (φ) and coupling strength (λ) due to the coupling between membrane curvature and local protein fraction. We estimate the coupling strength as λ∝κap2/al2, where ap and al are the lateral sizes of proteins and lipids, respectively. Estimated values of λ/κ are given for various combinations of membrane proteins and lipids. We show that the presence of membrane proteins leads to thinning of the effective membrane thickness and reduces the mean layer spacing of a stack of bilayers.

Phase Transition of a Model of Fluid Membrane

Abstract: A model of fluid membrane, which is not self-avoiding, such as two-dimensional spherical random surface is studied by using Monte Carlo simulation. Spherical surfaces in R3 are discretized by piecewise linear triangle. Dynamical variables are the positions X of the vertices and the triangulation g. The action of the model is sum of area energy and bending energy times bending rigidity b. The bending energy and the specific heat are measured, and the critical exponents of the phase transitions are obtained by a finite-size scaling technique. We find that our model of fluid membrane undergoes a second order phase transition.

Linear and nonlinear flexural stiffness models for concrete walls in high-rise buildings

Abstract: In the seismic design of high-rise wall buildings, the fundamental period of the building and the building drift are usually determined using linear elastic dynamic analysis. To carry out this analysis, designers need to assume a linear flexural stiffness of the wall sections that account for cracking. The commentary to the 1994 Canadian concrete code (CPCA 1995) suggests a stiffness value of 70% of the gross moment of inertia (Ig) of the wall section. The commentary to the 1995 New Zealand Standard (NZS 3101 1995) suggests much lower stiffness values. A wall subjected to axial compression of 10% of fj Ag is suggested to have half what is recommended in the CPCA Handbook (i.e. 0.35 Ig). The NEHRP Guidelines for the Seismic Rehabilitation of Buildings (FEMA 273) suggests stiffness values of 0.8 Ig and 0.5 Ig for uncracked and cracked concrete walls, respectively. While it is not clear which of the recommended stiffness values should be used, it is certainly clear that the choice of stiffness value will have a significant influence on the predicted period and drift of the building. The actual influence of cracking on the flexural stiffness of a concrete wall subjected to seismic loading is nonlinear. Nonlinear static analysis is increasingly used to capture this influence provided that an appropriate nonlinear model is used for the material. In this thesis, a simple nonlinear flexural (bending moment-curvature) model for concrete walls in high-rise buildings is proposed. To validate the model, a 40 ft high slender concrete wall was constructed and tested under simulated earthquake loading. Results from the test were compared with the proposed model and showed good agreement. Based on the proposed piece-wise linear model, a general method to determine the linear "effective" flexural stiffness of concrete walls was developed. Results from the general method for the effective flexural stiffness showed that the large variation in effective stiffness that is recommended by various design guidelines does actually exist for different wall configurations under certain conditions. The general method presented in this thesis gives the appropriate stiffness for a particular wall considering all important parameters that influence the stiffness. A study was conducted to examine the influence of a variety of parameters on the stiffness of concrete walls and a set of simplified expressions are proposed for the effective flexural stiffness of concrete walls.

Micro mirror apparatus and optical memory disk apparatus

Abstract: In a micro mirror apparatus pivoting on a hinge part as its axis, a movable part connected to a stationary part through the hinge part enhances exclusively the flexural rigidity of the hinge part without causing any significant change in the torsional rigidity of the hinge part and thus widens servo band. To this end, on at least a part of the hinge part 14 , a protrusion 14 b protruding in the direction of its thickness is formed. This greatly increases the flexural rigidity of the hinge part 14 and widens the servo band.

Effects of Belt Flexural Rigidity on the Transmission Error of a Carriage-driving System

Abstract: This paper investigates the effects of belt flexural rigidity and belt tension on transmission error of a carriage-driving system. The beam model associated with both the clamped and moving boundary conditions at two ends is utilized to derive the governing equation of the belt. The belt flexural rigidity is obtained and verified by an experimental technique. In addition, a numerical method is proposed to determine the belt profile, transmission error and transmission stiffness. Results show that transmission error of a carriage-driving system increases when the carriage moves away from the driving pulley due to finite belt flexural rigidity. According to the analyses, application of appropriate tension on the belt can significantly reduce the error. Furthermore, the transmission stiffness for representing the entire rigidity between the carriage and pulley is investigated based on the proposed beam model, A three-dimensional plot that indicates the relationship among the transmission stiffness, belt tension and the position of the carriage is obtained.

Deformation of a Single Helix Under Simultaneous Application of Extension, Compression, and Bending

Abstract: An idealized model for a twisted yarn structure assumes that each fiber or filament follows a helical path and the yarn has a circular cross section in the undeformed state. An investigation of the behavior of a single helix can therefore be considered as a first step toward the mechanical analysis of yarn deformation under simultaneous extension, compression, and bending, which is the kind of deformation that occurs in many textile processes and applications. This paper presents a theoretical model of the large-scale deformation of a single helix subjected to bending, compression, and extension. The work studies the effects of varying the ratio of the flexural rigidity to the torsional rigidity of the helix material and of varying the helix angle together with the variation of the deformation forces. The cross section of a deformed helix is discussed in relation to the position of the neutral axis and strain energy. Also, some experimental data are presented to show the relevance of the theoretical resul...

On the micromechanics theory of Reissner-Mindlin plates

Abstract: A micromechanics model is developed for the Reissner-Mindlin plate. A generalized eigenstrain formulation, i.e., an eigencurvature/eigen-rotation formulation, is proposed, which is the analogue or counterpart of the eigenstrain formulation in linear elasticity. The micromechanics model of the Reissner-Mindlin plate is useful in the study of mechanical behavior of composite plates that contain randomly distributed inhomogeneities, whose sizes are close to the order of thickness of the plate; under those circumstances, the use of micromechanics of linear elasticity is not justified, and moreover, it is inconsistent with structural theories, such as the Reissner-Mindlin plate theory, that are actually used in engineering design. In this paper, the analytical solution of an elliptical inclusion embedded in an infinite thick plate is sought. In particular, the first order asymptotic (or approximated) solution of the elliptical inclusion problem is obtained in explicit form. Accordingly, the Eshelby tensors of the Reissner-Mindlin plate are derived, which relate eigencurvature and eigen-rotation to the induced curvature and shear deformation fields. Several variational inequalities of the Reissner-Mindlin plate are discussed and derived, including the comparison variational principles of Hashin-Shtrikman/Talbot-Willis, type. As an application, variational bounds are derived to estimate the effective elastic stiffness of Reissner-Mindlin plates, specifically, the flexural rigidity and transverse shear modulus. The newly derived bounds are congruous with the Reissner-Mindlin plate theory, and they provide an optimal estimation on effective rigidity as well as effective transverse shear modulus for unstructured composite thick plates.