Showing papers on "Flexural rigidity published in 2003"

Experiments and theory in strain gradient elasticity

Abstract: Conventional strain-based mechanics theory does not account for contributions from strain gradients. Failure to include strain gradient contributions can lead to underestimates of stresses and size-dependent behaviors in small-scale structures. In this paper, a new set of higher-order metrics is developed to characterize strain gradient behaviors. This set enables the application of the higher-order equilibrium conditions to strain gradient elasticity theory and reduces the number of independent elastic length scale parameters from five to three. On the basis of this new strain gradient theory, a strain gradient elastic bending theory for plane-strain beams is developed. Solutions for cantilever bending with a moment and line force applied at the free end are constructed based on the new higher-order bending theory. In classical bending theory, the normalized bending rigidity is independent of the length and thickness of the beam. In the solutions developed from the higher-order bending theory, the normalized higher-order bending rigidity has a new dependence on the thickness of the beam and on a higher-order bending parameter, bh. To determine the significance of the size dependence, we fabricated micron-sized beams and conducted bending tests using a nanoindenter. We found that the normalized beam rigidity exhibited an inverse squared dependence on the beam's thickness as predicted by the strain gradient elastic bending theory, and that the higher-order bending parameter, bh, is on the micron-scale. Potential errors from the experiments, model and fabrication were estimated and determined to be small relative to the observed increase in beam's bending rigidity. The present results indicate that the elastic strain gradient effect is significant in elastic deformation of small-scale structures.

Flexural stiffness in insect wings. I. Scaling and the influence of wing venation.

Abstract: During flight, many insect wings undergo dramatic deformations that are controlled largely by the architecture of the wing. The pattern of supporting veins in wings varies widely among insect orders and families, but the functional significance of phylogenetic trends in wing venation remains unknown, and measurements of the mechanical properties of wings are rare. In this study, we address the relationship between venation pattern and wing flexibility by measuring the flexural stiffness of wings (in both the spanwise and chordwise directions) and quantifying wing venation in 16 insect species from six orders. These measurements show that spanwise flexural stiffness scales strongly with the cube of wing span, whereas chordwise flexural stiffness scales with the square of chord length. Wing size accounts for over 95% of the variability in measured flexural stiffness; the residuals of this relationship are small and uncorrelated with standardized independent contrasts of wing venation characters. In all species tested, spanwise flexural stiffness is 1-2 orders of magnitude larger than chordwise flexural stiffness. A finite element model of an insect wing demonstrates that leading edge veins are crucial in generating this spanwise-chordwise anisotropy.

Flexural stiffness in insect wings II. Spatial distribution and dynamic wing bending

Abstract: The dynamic, three-dimensional shape of flapping insect wings may influence many aspects of flight performance. Insect wing deformations during flight are largely passive, and are controlled primarily by the architecture and material properties of the wing. Although many details of wing structure are well understood, the distribution of flexural stiffness in insect wings and its effects on wing bending are unknown. In this study, we developed a method of estimating spatial variation in flexural stiffness in both the spanwise and chordwise direction of insect wings. We measured displacement along the wing in response to a point force, and modeled flexural stiffness variation as a simple mathematical function capable of approximating this measured displacement. We used this method to estimate flexural stiffness variation in the hawkmoth Manduca sexta, and the dragonfly Aeshna multicolor. In both species, flexural stiffness declines sharply from the wing base to the tip, and from the leading edge to the trailing edge; this variation can be approximated by an exponential decline. The wings of M. sexta also display dorsal/ventral asymmetry in flexural stiffness and significant differences between males and females. Finite element models based on M. sexta forewings demonstrate that the measured spatial variation in flexural stiffness preserves rigidity in proximal regions of the wing, while transferring bending to the edges, where aerodynamic force production is most sensitive to subtle changes in shape.

Flexible Magnetic Filaments as Micromechanical Sensors

Abstract: We propose a new micromechanical approach to probe bending rigidity at molecular scale. Long flexible filaments made of magnetic colloids and linkers are shown to adopt under magnetic field a hairpin configuration. Measuring the hairpin curvature as a function of the field intensity and the linker length from diffracted light allows us to deduce the linker bending rigidity kappa. The technique is presented for two types of linkers: a spontaneously adsorbing polymer and a grafted biomolecular.

Deformation behavior of fiber-reinforced polymer reinforced engineered cementitious composite (ecc) flexural members under reversed cyclic loading conditions

Abstract: Research provided herein studies the response of fiber-reinforced polymer (FRP) reinforced engineered cementitious composite (ECC) members, focusing on flexural load-deformation behavior, residual deflection, damage evolution, and failure mode. Critical aspects of conventional FRP-reinforced concrete members are reviewed and compared to FRP reinforced ECC. The interaction of linear FRP reinforcement and ECC matrix with ductile stress-strain behavior in tension results in nonlinear elastic flexural response characteristics with stable hysteretic behavior, small residual deflection, and ultimately gradual compression failure. Compatible deformations of reinforcement and matrix lead to low interfacial bond stress and prevent composite disintegration by bond splitting and cover spalling. Flexural stiffness and strength as well as crack formation and widths in FRP-reinforced ECC members are found effectively independent of interfacial bond properties due to the tensile deformation characteristics of the cementitious matrix. A model for the load-deflection envelope based on a nonlinear moment-curvature relationship is suggested.

Effective Moment of Inertia for Glass Fiber-Reinforced Polymer-Reinforced Concrete Beams

Abstract: This paper investigates deflection behavior of concrete flexural members reinforced with glass fiber-reinforced polymer (GFRP) reinforcing bars. It is recognized that serviceability plays a major role in the design of GFRP-reinforced concrete beams. Therefore, accurate modeling of flexural stiffness is critical and the effect of influencing parameters must be considered. This study accounts for variations in concrete strength, reinforcement density, and shear span-depth ratio. Experimental results from 48 simply supported concrete beams reinforced with GFRP are compared with ACI Committee 440's published deflection model. The ACI 440.1R model is found to overestimate the effective moment of inertia, and an appropriate modification is presented.

Shear Strengthening of Interior Slab–Column Connections Using Carbon Fiber-Reinforced Polymer Sheets

Abstract: This paper presents the results of an experimental investigation undertaken to evaluate the punching shear capacity of interior slab–column connections, strengthened using flexible carbon fiber-reinforced polymer (CFRP) sheets. Sixteen square (670×670mm) slab–column connections with different slab thicknesses (55 and 75 mm) and reinforcement ratios (1 and 1.5%) were tested. Twelve specimens were strengthened using CFRP sheets and the remaining four specimens were kept as controls. Without strengthening, all specimens were designed to experience punching shear failure. The CFRP sheets were bonded to the tension face of the specimens in two perpendicular directions parallel to the internal ordinary steel reinforcement. The test results clearly demonstrate that using CFRP leads to significant improvements in the flexural stiffness, flexural strength, and shear capacity of beam–column connections. Depending on the content of the ordinary reinforcement, thickness of the slab, and area of CFRP sheet, the flexur...

The bending rigidity of an amphiphilic bilayer from equilibrium and nonequilibrium molecular dynamics

Abstract: Helfrich's theory predicts that the bending free energy of a tensionless amphiphilic bilayer is proportional to the square of the Fourier coefficients of the undulation modes. Equilibrium molecular dynamics simulations with coarse-grained amphiphiles confirm the correctness of this prediction for thermally excited undulations. The proportionality constant then provides the bending rigidity of the layer. Non-equilibrium methods, in particular umbrella sampling, potential of mean constraint force, and thermodynamic integration in Cartesian coordinates, have been used to extend the range of sampled amplitudes. For small amplitudes there is a good agreement with the equilibrium simulations, while beyond the thermally accessible amplitudes a clear deviation from theory is observed. Calculations of the elastic modulus showed a pronounced system size dependence.

Buckling loads of variable thickness thin isotropic plates

Abstract: This work presents accurate solutions for bifurcation buckling loads of rectangular thin plates with thickness that varies in the directions parallel to the two sides. The plates are subjected to biaxial compression and various combinations of boundary conditions are considered. The calculation of the critical loads was carried out by using the extended Kantorovich method. For the resulting ordinary differential equation, an exact method for the stability analysis of compressed members with variable flexural rigidity is used. The buckling load is found as the inplane load that makes the determinant of the stiffness matrix equal zero. New, exact results are given for many cases of uni-directional and bi-directional variation in thickness. The results are very accurate and exact for cases where an exact solution is available.

Classical and high-order computational models in the analysis of modern sandwich panels

Abstract: The classical and the high-order computational models of unidirectional sandwich panels with incompressible and compressible cores are presented The significant theoretical and practical differences are discussed and elaborated through some numerical examples of typical sandwich panels The classical models considered for the incompressible panel consists of two variants of the well-known splitted rigidity approach The first one, due to Allen and Plantema and many others, assumes that the plane section of the shear substructure takes a specific ‘zigzag’ pattern with no in-plane deformation in the face sheets and a vertical one when the flexural rigidity of the faces is ignored The second model, due to Frostig, assumes that the plane section of the core in the shear substructure remains vertical and the face sheets are subjected to in-plane deformation as well as flexural ones They are compared with the accurate incompressible model, denoted as ordinary sandwich panel theory (OSPT) and with the high-order sandwich panel theory (HSAPT) based on a variational approach In case of a sandwich panel with a compressible core the elastic foundation models based are compared with the high-order one The governing equations and the appropriate boundary conditions of the classical models have been rederived to clarify the ambiguity involved in the definition of the boundary conditions of the various computational models The cases of simply supported panel, cantilevered and a two-span panel are used to demonstrate numerically the differences in the overall response of the panel as well as in the near vicinity of the localized loads and supports

Diagnostic apparatus and methods for a coriolis flow meter

Abstract: A method for validating a flow calibration factor of a flow meter is provided according to an embodiment of the invention. The method for validating a flow calibration factor of a flow meter comprises determining an initial flexural stiffness of a component of the flow meter. The method for validating a flow calibration factor of a flow meter includes determining a current flexural stiffness of the component. The method for validating a flow calibration factor of a flow meter further includes comparing the initial flexural stiffness to the current flexural stiffness. The method for validating a flow calibration factor of a flow meter further includes detecting a calibration error condition responsive to comparing the initial flexural stiffness to the current flexural stiffness.

Twisting and Bending of Biological Beams: Distribution of Biological Beams in a Stiffness Mechanospace

Abstract: Most biological beams bend and twist relatively easily compared to human-made structures This paper investigates flexibility in 57 diverse biological beams in an effort to identify common patterns in the relationship between flexural stiffness and torsional stiffness The patterns are investigated by mapping both ideal and biological beams into a mechanospace defined by flexural and torsional stiffness The distribution of biological beams is not random, but is generally limited to particular regions of the mechanospace Biological beams that are stiff in bending are stiff in torsion, while those that bend easily also twist easily Unoccupied regions of the mechanospace represent rare combinations of mechanical properties, without proving that they are impossible The mechanical properties of biological beams closely resemble theoretical expectations for ideal beams Both distributions are potentially being driven by the interdependence of the material and structural properties determining stiffness The mechanospace can be used as a broadly comparative tool to highlight systems that fall outside the general pattern observed in this study These outlying beams may be of particular interest to both biologists and engineers due to either material or structural innovations

Numerical Analysis of Peirce's Cantilever Test for the Bending Rigidity of Textiles

Abstract: This paper deals with the numerical analysis of a test for the bending rigidity of textiles as proposed by Peirce. The mathematical model treats textile product as an elastica which is subject to large deflections. The results of the numerical calculations discussed in this paper are presented on the relevant graphs. The optimal conditions of Peirce’s test were also considered, in order to obtain the results of measurements most sensitive to changes of the input parameters. The results of the calculations are compared with the practical implementation of this test as commonly applied in textile laboratories.

Bending rigidity of stiff polyelectrolyte chains: A single chain and a bundle of multichains

Abstract: We study the bending rigidity of highly charged stiff polyelectrolytes, for both a single chain and many chains forming a bundle. A theory is developed to account for the interplay between competit...

New Design Rule for Intermediate Transverse Stiffeners Attached on Web Panels

Abstract: The equation for the required area of the intermediate transverse stiffener stipulated in the current AASHTO and AISC specifications was derived under the assumption that the transverse stiffener is subjected to an axial compression resulting from diagonal tension developed in the postbuckling stage as noted by Basler in 1963. However, the area requirement is known to be overly conservative. A recent study by Lee et al. in 2002 reported that the transverse stiffener is not necessarily subjected to an axial compressive force during postbuckling of the web panel and hence the current area requirement can be eliminated. The study also reported that the flexural rigidity should be increased several times higher than that required for elastic shear buckling in order for the web panel to develop its potential ultimate shear strength. In the present study, an experiment was conducted in order to investigate the behavior of the transverse stiffeners during postbuckling. The test results confirmed the earlier find...

Modeling of contact-induced radial cracking in ceramic bilayer coatings on compliant substrates

Abstract: Contact-induced radial cracking in ceramic coatings on compliant substrates was analyzed recently. Radial cracks initiate at the coating/substrate interface beneath the contact where maximum flexural tension occurs, and an analytical expression for the onset of radial cracking in monolayer coatings was formulated on the basis of the classical solution for flexing plates on elastic foundation. In the present study, the analytical expression was derived for the case of ceramic bilayer coatings on compliant substrates, which have significant applications in the structure of dental crowns. It was found that the analytical solution for bilayer-coating/substrate systems can be obtained from that of monolayer-coating/substrate systems by replacing the neutral surface position and the flexural rigidity of monolayer coating with those of bilayer coating. The predicted critical loads for initiating radial cracking were found to be in good agreement with existing measurements and finite element results for glass/alumina, glass/glass-ceramic, and glass/Y2O3-stabilized ZrO2 polycrystal bilayers on polycarbonate substrates. Limitations of the present analysis are discussed.

Inclusion of the Moment Interaction in the Calculation of the Flexural Rigidity of Nanostructures

Abstract: In recent years, in addition to the investigation of the electronic and optical properties of nanostructures [1], the study of their mechanical properties has become particularly important. Many works have been devoted to the production of nanotubes and investigation of their properties [2–8]. According to the data obtained in [4], nanotubes can retain their elastic properties under significant strains. The stress–strain state of nanotubes is usually calculated in the theory of elastic shells [9]. In this case, the elastic moduli are determined in discrete models, where only the force interaction between atoms forming a nanotube is taken into account. However, the existence of monolayer nanotubes [5–8] makes it necessary to consider also the moment interaction between atoms. Otherwise, the atomic layer forming the nanotube would have zero flexural rigidity, so that such a nanotube would be unstable.

Flexural and Shear Rigidity of Composite Sheet Piles

Abstract: The flexural and shear rigidity of pultruded composite sheet pile panels consisting of E-glass fiber-reinforced polyester are studied in this paper. The analysis consists of an experimental investigation and an analytical modeling to determine the resistance of the sheet pile panels to the deflections for design of composite sheet pile walls. Timoshenko’s beam theory was used to experimentally determine the flexural rigidity (EI) and shear rigidity (kAG) of the panel. Three- and four-point bending tests were performed on six different span lengths and the results were self-compared from the two independent tests. Analytical expressions for the flexural and shear rigidities were derived to allow the prediction based on the layered structure of pultruded shapes. The values computed from the analytical expressions were examined with the experimental results.

Shear in Flexure of Fiber Composites with Different End Supports

Abstract: The integrity of fiber-reinforced composite (FRC) prostheses is dependent, in part, on flexural rigidity The object of this study was to determine if the flexure behavior of uniform FRC beams with restrained or simply supported ends and various length/depth (L/d) aspect ratios could be more accurately modeled by correcting for shear Experimental results were compared with three analytical models All models were accurate at high L/d ratios, but the shear-corrected model was accurate to the lowest, more clinically relevant, L/d values In this range, more than 40% of the beam deflection was due to shear

Local and global instability and vibration of overbraced euler's column

Abstract: The theoretical and experimental research on the stability and free vibration of a geometrically non-linear Euler's column is presented in the paper. The influence of the asymmetry of the flexural stiffness distribution of the rod in an individual column on the value of the critical force and existence of local and global instability regions is determined. The column consists of three planar members. Two outside members have the same flexural stiffness while the third central one has different flexural stiffness. The members are jointed in such a way that their deflection at the joint points equals zero and the deflection angles are identical.

Characterization of fabric bending behavior: A review of measurement principles

Abstract: Various methods and the underlying principles to evaluate the bending characteristics of fabrics and fabric-like membranes are described. In comparing various methods, their limitations as well as utilities are also discussed. It has been observed that a number of relatively simpler methods produce a wealth of information useful in designing fabric structures and determining their appropriate applications.

Non-linear Performance of Slabs in Coupled Shear Wall Structures

Abstract: The non-linear coupling action of reinforced concrete slabs in shear wall structures is investigated by the finite element method and the results are validated by small scale model tests using micro-concrete. Flexural stiffness and effective width of the coupling slabs are found to be influenced by the geometric and non-linear material parameters of the structures. Design curves for the determination of flexural stiffness and effective width are presented as functions of geometric parameters in the pre-cracking, cracking and post-yielding stages of non-linear material response. Comparative study of numerical and experimental results suggested that the design curves are reliable and can be used in the analysis and design of shear wall structure in practical situations.