Experimental Study of the Bending Properties and Deformation Analysis of Web-Reinforced Composite Sandwich Floor Slabs with Four Simply Supported Edges

Web-reinforced composite sandwich panels exhibit good mechanical properties in one-way bending, but few studies have investigated their flexural behavior and deformation calculation methods under conditions of four simply supported edges. This paper studies the bending performance of and deformation calculation methods for two-way web-reinforced composite sandwich panels with different web spacing and heights. Polyurethane foam, two-way orthogonal glass-fiber woven cloth and unsaturated resin were used as raw materials in this study. Vacuum infusion molding was used to prepare an ordinary composite sandwich panel and 5 web-reinforced composite sandwich panels with different spacing and web heights. The panels were subjected to two-way panel bending tests with simple support for all four edges. The mechanical properties of these sandwich panels during the elastic stage were determined by applying uniformly distributed loads. The non-linear mechanical characteristics and failure modes were obtained under centrally concentrated loading. Finally, simulations of the sandwich panels, which used the mechanical model established herein, were used to deduce the formulae for the deflection deformation for this type of sandwich panel. The experimental results show that webs can significantly improve the limit bearing capacity and flexural rigidity of sandwich panels, with smaller web spacing producing a stronger effect. When the web spacing is 75 mm, the limit bearing capacity is 4.63 times that of an ordinary sandwich panel. The deduced deflection calculation formulae provide values that agree well with the measurements (maximum error <15%). The results that are obtained herein can provide a foundation for the structural design of this type of panel.     

Length-dependence of flexural rigidity as a result of anisotropic elastic properties of microtubules

Unexplained length-dependence of flexural rigidity and Young's modulus of microtubules is studied using an orthotropic elastic shell model. It is showed that vibration frequencies and buckling load predicted by the accurate orthotropic shell model are much lower than that given by the approximate isotropic beam model for shorter microtubules, although the two models give almost identical results for sufficiently long microtubules. It is this inaccuracy of the isotropic beam model used by all previous researchers that leads to reported lower flexural rigidity and Young's modulus for shorter microtubules. In particular, much lower shear modulus and circumferential Young's modulus, which only weaken flexural rigidity of shorter microtubules, are responsible for the observed length-dependence of the flexural rigidity. These results confirm that longitudinal Young's modulus of microtubules is length-independent, and the observed length-dependence of the flexural rigidity and Young's modulus is a result of strongly anisotropic elastic properties of microtubules which have a length-dependent weakening effect on flexural rigidity of shorter microtubules.     

Twist-to-bend ratios of woody structures

Flexural rigidity (El), or resistance to bending loads, andtorsional rigidity (GJ), or resistance to twisting loads, weremeasured on a variety of woody structures-bamboo culms, threekinds of hardwood trunks, two softwood trunks, two vines, andpine roots. The ratios of these rigidities, EI/GJ, was highestand relatively constant for bamboo and hardwoods, slightly lowerfor softwoods, and lower still for vines and roots. All valueswere substantially above those for circular cylinders of ordinaryisotropic materials; since all specimens were nearly circularin cross-section, the high values reflect the elastic moduliof wood rather than geometric factors. While all material showedsubstantial creep under torsional loading, only the vine, Wisteria,crept appreciably under flexural loading as well. Key words: Wood, trees, flexural rigidity, torsional rigidity, biomechanics     

The Mechanical Significance of Clasping Leaf Sheaths in Grasses: Evidence from Two Cultivars of Avena sativa

The elastic (Young's) modulus and flexural rigidity of internodeswith and without their clasping leaf sheaths were determinedfor culms from two cultivars (‘Astro’) and (‘Garry’)of Avena sativa L. Data indicate that early in the developmentof culms, leaf sheaths can have a higher elastic modulus thanthe internodes they envelope, and by virtue of their location,leaf sheaths contribute significantly to the flexural rigidity(hence, resistance to bending) of internodal segments. As culmsmature, the elastic modulus of leaf sheath and internodal tissuesreach parity. However, because of the acropetal pattern by whichnew internodes are produced by shoot apices, sheaths continueto provide mechanical support to distal internodes, particularlythe peduncle. Data for the two cultivars indicate that the elasticmodulus and flexural rigidity of culms can vary significantlywithin the species. Comparisons between the flexural rigidityof the two cultures and the resistance of stems to lodging indicatethat flexural rigidity is not significant to lodging. The engineeringprinciples relevant to the mechanical advantages conferred byclasping leaf sheaths are discussed within the context of grassshoot morphology. Biomechanics, leaf sheath, Avena, elastic modulus     

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.     

Twist-to-Bend Ratios and Cross-Sectional Shapes of Petioles and Stems

Two structural properties, resistance to twisting (torsionalrigidity or torsional stiffness, GJ) and resistance to bending(flexural rigidity or flexural stiffness, El), were measuredon a variety of herbaceous stems and petioles. Specimens withnon-circular cross-sections had higher values of the ratio ofEl to GJ that is, such specimens were relatively more flexiblein twisting than in bending. But both kinds had higher ratiosthan those that characterize simple, isotropic materials, andthus both structural and material factors contribute to achievinga high twist-to-bend ratio. The composite property expressedas the dimensionless variable EI/GJ appears to be a functionallyrelevant parameter in many biological situations. Key words: Stems, petioles, flexural rigidity, torsional rigidity, biomechanics     

Anisotropy in sickle hemoglobin fibers from variations in bending and twist

We have studied the variations of twist and bend in sickle hemoglobin fibers. We find that these variations are consistent with an origin in equilibrium thermal fluctuations, which allows us to estimate the bending and torsional rigidities and effective corresponding material moduli. We measure bending by electron microscopy of frozen hydrated fibers and find that the bending persistence length, a measure of the length of fiber required before it starts to be significantly bent due to thermal fluctuations, is 130microm, somewhat shorter than that previously reported using light microscopy. The torsional persistence length, obtained by re-analysis of previously published experiments, is found to be only 2.5microm. Strikingly this means that the corresponding torsional rigidity of the fibers is only 6x10(-27)Jm, much less than their bending rigidity of 5x10(-25)Jm. For (normal) isotropic materials, one would instead expect these to be similar. Thus, we present the first quantitative evidence of a very significant material anisotropy in sickle hemoglobin fibers, as might arise from the difference between axial and lateral contacts within the fiber. We suggest that the relative softness of the fiber with respect to twist deformation contributes to the metastability of HbS fibers: HbS double strands are twisted in the fiber but not in the equilibrium crystalline state. Our measurements inform a theoretical model of the thermodynamic stability of fibers that takes account of both bending and extension/compression of hemoglobin (double) strands within the fiber.     

Elastic BucMing of Bionic Cylindrical Shells Based on Bamboo

High load-bearing efficiency is one of the advantages of biological structures after the evolution of billions of years. Biomimicking from nature may offer the potential for lightweight design. In the viewpoint ofrnechanics properties, the culm of bamboo comprises of two types of cells and the number of the vascular bundles takes a gradient of distribution. A three-point bending test was carried out to measure the elastic modulus. Results show that the elastic modulus of bamboo decreases gradually from the periphery towards the centre. Based on the structural characteristics of bamboo, a bionic cylindrical structure was designed to mimic the gradient distribution of vascular bundles and parenchyma cells. The buckling resistance of the bionic structure was compared with that of a traditional shell of equal mass under axial pressure by finite element simulations. Results show that the load-bearing capacity of bionic shell is increased by 124.8%. The buckling mode of bionic structure is global buckling while that of the conventional shell is local buckling.     

Elastic Buckling of Bionic Cylindrical Shells Based on Bamboo

High load-bearing efficiency is one of the advantages of biological structures after the evolution of billions of years.Biomimicking from nature may offer the potential for lightweight design. In the viewpoint of mechanics properties, the culm of bamboo comprises of two types of cells and the number of the vascular bundles takes a gradient of distribution. A three-point bending test was carried out to measure the elastic modulus. Results show that the elastic modulus of bamboo decreases gradually from the periphery towards the centre. Based on the structural characteristics of bamboo, a bionic cylindrical structure was designed to mimic the gradient distribution of vascular bundles and parenchyma cells. The buckling resistance of the bionic structure was compared with that of a traditional shell of equal mass under axial pressure by finite element simulations. Results show that the load-bearing capacity of bionic shell is increased by 124.8%. The buckling mode of bionic structure is global buckling while that of the conventional shell is local buckling.     

基于生物复合材料的双曲面分段式壳体展馆

生物复合材料由于成本低、可再生和对环境友好的特性，在建筑中获得了新颖又广泛的应用。通过一对一的双曲面、参数化设计形成的分段式壳体，来展示生物材料在承重结构中的应用。这种结构由轻质的单向弯曲木和生物复合材料组成，其中，木质纤维基核心由长木纤维以单板形式加固。进一步探讨了高 3.6 m，面积 55 m2 的展馆的建造技术以及生物复合材料应用的可能性。     

A patient-specific computer tomography-based finite element methodology to calculate the six dimensional stiffness matrix of human vertebral bodies

In most finite element (FE) studies of vertebral bodies, axial compression is the loading mode of choice to investigate structural properties, but this might not adequately reflect the various loads to which the spine is subjected during daily activities or the increased fracture risk associated with shearing or bending loads. This work aims at proposing a patient-specific computer tomography (CT)-based methodology, using the currently most advanced, clinically applicable finite element approach to perform a structural investigation of the vertebral body by calculation of its full six dimensional (6D) stiffness matrix. FE models were created from voxel images after smoothing of the peripheral voxels and extrusion of a cortical shell, with material laws describing heterogeneous, anisotropic elasticity for trabecular bone, isotropic elasticity for the cortex based on experimental data. Validated against experimental axial stiffness, these models were loaded in the six canonical modes and their 6D stiffness matrix calculated. Results show that, on average, the major vertebral rigidities correlated well or excellently with the axial rigidity but that weaker correlations were observed for the minor coupling rigidities and for the image-based density measurements. This suggests that axial rigidity is representative of the overall stiffness of the vertebral body and that finite element analysis brings more insight in vertebral fragility than densitometric approaches. Finally, this extended patient-specific FE methodology provides a more complete quantification of structural properties for clinical studies at the spine.     

Flexural rigidity of marginal bands isolated from erythrocytes of the newt

The marginal band is a bundle of microtubules residing at the periphery of nucleated erythrocytes of nonmammalian vertebrates and some invertebrates. Marginal bands from erythrocytes of the newt (Notopthalmus viridescens) were isolated from the cells as intact structures by treatment with detergent and either mild protease or high salt. Isolated bands were subjected to mechanical testing by stretching the band between a glass microhook and a calibrated glass fiber. The deflection of the fiber provided a measure of the force on the band. The flexural rigidity of the band was determined from measurements of the band deformation as a function of applied force. Bands isolated with either of two proteases (pepsin or elastase) or with high salt exhibited elastic behavior with a flexural rigidity of approximately 9.0 X 10(-12) dyn.cm2. Treatment of bands with chymopapain caused an increase in band rigidity and inelastic behavior. Estimates of the contribution of the band to cellular rigidity are made based on the measurements of the structural properties of the isolated band. The band provides the cell with a large resistance to indentations at the rim and to large extensions, while maintaining a high degree of flexibility in small extensions or flexure.     

The trajectory of a stiff rod in a curved potential energy trough. An initial result for short nucleosomal rods

The equilibrium trajectory of the axis of a rod subject to an externally imposed curved potential energy trough tends to conform to the shape of the curved trough, but also tends to be straight because of elastic resistance to bending. The actual path of the axis is a balance between the two extremes. We consider a potential energy trough centered along a circular arc of radius R. For a rod of small length compared to R, we show that the axis at equilibrium forms an arc of a circle of radius greater than R. The value of the radius of the axial path depends on the relative values of the Hooke's Law bending constant for the rod and the depth and width of the trough. Motivation for the calculation is provided by nucleosomal DNA, which conforms to the surface of a roughly cylindrical histone core at physiological ionic strength, but is observed to unwind into a partially extended conformation at very low ionic strength. We suggest that the rigidity to bending of short DNA segments becomes sufficiently great at low ionic strength to overcome attractive interactions with the histone surface. Alternately, of course, if during the cell cycle mutually attractive forces between DNA and histone core are weakened at constant ionic strength, the same type of unfolding would be expected to occur as the strength of the DNA-histone contacts drops below the level required to overcome elastic resistance to bending of the DNA rod.     

Cofilin increases the bending flexibility of actin filaments: implications for severing and cell mechanics

We determined the flexural (bending) rigidities of actin and cofilactin filaments from a cosine correlation function analysis of their thermally driven, two-dimensional fluctuations in shape. The persistence length of actin filaments is 9.8 μm, corresponding to a flexural rigidity of 0.040 pN μm². Cofilin binding lowers the persistence length ∼5-fold to a value of 2.2 μm and the filament flexural rigidity to 0.0091 pN μm². That cofilin-decorated filaments are more flexible than native filaments despite an increased mass indicates that cofilin binding weakens and redistributes stabilizing subunit interactions of filaments. We favor a mechanism in which the increased flexibility of cofilin-decorated filaments results from the linked dissociation of filament-stabilizing ions and reorganization of actin subdomain 2 and as a consequence promotes severing due to a mechanical asymmetry. Knowledge of the effects of cofilin on actin filament bending mechanics, together with our previous analysis of torsional stiffness, provide a quantitative measure of the mechanical changes in actin filaments associated with cofilin binding, and suggest that the overall mechanical and force-producing properties of cells can be modulated by cofilin activity.     

The mechanical role of bark

The ability of stem bark to resist bending forces was examined by testing in bending segments of Acer saccharum, Fraxinus americana, and Quercus robur branches with and without their bark. For each species, the bark contributed significantly to the ability of stem segments differing in age to resist bending forces, but its contribution was age-dependent and differed among the three species. The importance of the mechanical role of the bark decreased basipetally with increasing age of F. americana and Q. robur stem segments and was superceded by that of the wood for segments ≥ 6 yr old. A. saccharum bark was as mechanically important as the wood for stem segments 7 yr old but was not a significant stiffening agent for younger or older portions of stems. On average, the stiffness of the bark from all three species was 50% that of the wood. However, the geometric contribution to the flexural rigidity of stems made by the bark (i.e., the bark's second moment of area) was sufficiently large to offset its lower stiffness (Young's modulus) relative to that of the wood. A simple model is presented that shows that the bark must be as mechanically important as the wood when its radial thickness equals 32% that of the wood and its stiffness is 50% that of the wood. Based on this model, which is shown to comply with the data from three species purported to have stiff woods, it is evident that the role of the bark cannot be neglected when considering the mechanical behavior of juvenile woody stems subjected to externally applied bending forces.     

Evaluation of linear finite-element analysis models' assumptions for external fixation devices.

Linear finite-element models (FEMs) have enjoyed an increased use in orthopaedic research, including the use for modeling external fixation devices. These fixator FEMs depend on a number of basic assumptions concerning the overall fixation frame stability and the components' rigidity. Among the more important ones are: (i) rigid fixation at both ends of the pin and sidebar; (ii) that the sidebar can be treated essentially as a rigid entity, with all bending occurring in the bone pins; and (iii) that the system can be treated as linearly elastic. Prior work done by the authors questions some of these assumptions. Thus, this study sought an empirical evaluation of the validity of some of these a priori assumptions. A Hoffmann single half-frame was tested in its standard form and then according to a stepwise protocol wherein the frame was welded to eliminate any possible points of instability. These tests looked at the stability and rigidity in various modes (axial compression, torsion, and medial-lateral and anterior-posterior four-point bending). The basic assumptions concerning the frame stability, frame rigidity and the frame's response to loads were found to be erroneous. Component failure was common under minimal loads and statistically significant differences (p less than 0.05) of up to 75% were noted in frame rigidity among the various frame forms tested. Thus, considerable caution must be exercised when employing the FEM technique for evaluating the fixator properties.     

Base plate mechanics of the barnacle Balanus amphitrite (=Amphibalanus amphitrite)

The mechanical properties of barnacle base plates were measured using a punch test apparatus, with the purpose of examining the effect that the base plate flexural rigidity may have on adhesion mechanics. Base plate compliance was measured for 43 Balanus amphitrite (=Amphibalanus amphitrite) barnacles. Compliance measurements were used to determine flexural rigidity (assuming a fixed-edge circular plate approximation) and composite modulus of the base plates. The barnacles were categorized by age and cement type (hard or gummy) for statistical analyses. Barnacles that were 'hard' (> or =70% of the base plate thin, rigid cement) and 'gummy' (>30% of the base plate covered in compliant, tacky cement) showed statistically different composite moduli but did not show a difference in base plate flexural rigidity. The average flexural rigidity for all barnacles was 0.0020 Nm (SEM +/- 0.0003). Flexural rigidity and composite modulus did not differ significantly between 3-month and 14-month-old barnacles. The relatively low flexural rigidity measured for barnacles suggests that a rigid punch approximation is not sufficient to account for the contributions to adhesion mechanics due to flexing of real barnacles during release.     

Collagen fiber orientation and geometry effects on the mechanical properties of secondary osteons.

The effects of collagen fiber orientation and osteon geometry on the mechanical properties of secondary osteons under axial compression/tension and combined loadings (compression, bending and torsion) were investigated using a composite-beam finite-element model. Three cross-sectional shapes of secondary osteons were studied to show the effect of geometry. The results of stiffness are presented using the tension and compression properties for each lamella. The model shows that the mechanical properties of osteons are enhanced in bending and torsion when collagen fibers are oriented within 30 degrees of the loading axis. Osteons with alternating lamellar orientation are not well adapted to resist torsional moments, but alternate collagen fiber orientation has virtually no effect on the bending stiffness of osteons. Fiber orientation affects the mechanical properties less significantly when osteons are non-circular. Collagen fiber orientation and osteon geometry interact to determine the mechanical behavior of the osteon, and may act in a compensatory manner in the adaptive process.     

The trajectory of a stiff rod in a curved potential energy trough

The equilibrium trajectory of the axis of a rod subject to an externally imposed curved potential energy trough tends to conform to the shape of the curved trough, but also tends to be straight because of elastic resistance to bending. The actual path of the axis is a balance between the two extremes. We consider a potential energy trough centered along a circular arc of radiusR. For a rod of small length compared toR, we show that the axis at equilibrium forms an arc of a circle of radius greater thanR. The value of the radius of the axial path depends on the relative values of the Hooke’s Law bending constant for the rod and the depth and width of the trough. Motivation for the calculation is provided by nucleosomal DNA, which conforms to the surface of a roughtly cylindrical histone core at physiological ionic strength, but is observed to unwind into a partially extended conformation at very low ionic strength. We suggest that the rigidity to bending of short DNA segments becomes sufficiently great at low ionic strength to overcome attractive interactions with the histone surface. Alternately, of course, if during the cell cycle mutually attractive forces between DNA and histone core are weakened at constant ionic strength, the same type of unfolding would be expected to occur as the strength of the DNA-histone contacts drops below the level required to overcome elastic resistance to bending of the DNA rod.     

Mechanics of the Compression Wood Response: II. On the Location, Action, and Distribution of Compression Wood Formation

A new method for simulation of cross-sectional growth provided detailed information on the location of normal wood and compression wood increments in two tilted white pine (Pinus strobus L.) leaders. These data were combined with data on stiffness, slope, and curvature changes over a 16-week period to make the mechanical analysis. The location of compression wood changed from the under side to a flank side and then to the upper side of the leader as the geotropic stimulus decreased, owing to compression wood action. Its location shifted back to a flank side when the direction of movement of the leader reversed. A model for this action, based on elongation strains, was developed and predicted the observed curvature changes with elongation strains of 0.3 to 0.5%, or a maximal compressive stress of 60 to 300 kilograms per square centimeter. After tilting, new wood formation was distributed so as to maintain consistent strain levels along the leaders in bending under gravitational loads. The computed effective elastic moduli were about the same for the two leaders throughout the season.