Flexural Rigidity Research Articles

As new concepts to protect marine structures from ocean waves, we propose the use of a floating elastic annulus. In this paper, two types of annuli are demonstrated. The first is a ‘wave shield’, which creates a calm free surface within an inner domain of the annulus by preventing wave penetration. The second is a ‘cloak’, which not only creates a calm space within the inner domain but also prevents wave scattering outside the annulus. To evaluate the calmness of the inner domain of the annulus, an inlet wave energy factor is newly defined. The wave shield is designed to minimise the inlet wave energy factor to nearly zero. However, the cloak is designed to minimise both the inlet wave energy factor and scattered-wave energy which evaluates the amount of wave scattering at far-field. Each annulus consists of several horizontal concentric annular plates, and the flexural rigidities of the plates are optimised to minimise objective functions at a target frequency. Numerical simulations demonstrate that both the wave shield and the cloak can create calm free surfaces within their inner domains. In addition, the cloak effectively suppresses the outgoing scattering waves and reduces the resultant wave drift force.

Thermally induced ripples are intrinsic features of nanometer-thick films, atomically thin materials, and cell membranes, significantly affecting their elastic properties. Despite decades of theoretical studies on the mechanics of suspended thermalized sheets, controversy still exists over the impact of these ripples, with conflicting predictions about whether elasticity is scale-dependent or scale-independent. Experimental progress has been hindered so far by the inability to have a platform capable of fully isolating and characterizing the effects of ripples. This knowledge gap limits the fundamental understanding of thin materials and their practical applications. Here, we show that thermal-like static ripples shape thin films into a class of metamaterials with scale-dependent, customizable elasticity. Utilizing a scalable semiconductor manufacturing process, we engineered nanometer-thick films with precisely controlled frozen random ripples, resembling snapshots of thermally fluctuating membranes. Resonant frequency measurements of rippled cantilevers reveal that random ripples effectively renormalize and enhance the average bending rigidity and sample-to-sample variations in a scale-dependent manner, consistent with recent theoretical estimations. The predictive power of the theoretical model, combined with the scalability of the fabrication process, was further exploited to create kirigami architectures with tailored bending rigidity and mechanical metamaterials with delayed buckling instability.

In this work, we compare the structural and dynamic behavior of active filaments in two dimensions using tangential and push-pull models, including a variant with passive end monomers, to bridge the two frameworks. These models serve as valuable frameworks for understanding self-organization in biological polymers and synthetic materials. At low activity, all models exhibit similar behavior; as activity increases, subtle differences emerge in intermediate regimes, but at high activity, their behaviors converge. Adjusting for differences in mean active force reveals nearly identical behavior across models, even across varying filament configurations and bending rigidities. Our results highlight the importance of force definitions in active polymer simulations and provide insights into phase transitions across varying filament configurations.

Endovascular procedures require sheaths with contradictory mechanical properties: flexibility for navigation through tortuous vessels, yet rigidity for device delivery. Current approaches rely on multiple device exchanges, increasing procedural time, and complication risks. Here we present a novel endovascular sheath design scheme with dynamically controllable flexural rigidity along its entire length. The device incorporates axially aligned metal string arrays between inner and outer lumens, enabling transition between flexible and rigid states through suction actuation. Three-point bend testing demonstrated that actuation increases flexural rigidity from the range associated with diagnostic catheters to that associated with support sheaths. In simulated contralateral access procedures, the device reduced access time to 1/3 of the time required when using conventional approaches. in vivo porcine studies validated the sheath's ability to navigate tortuous anatomy in its flexible state and successfully support advancement of increasingly rigid therapeutic devices when actuated. Technology enables single-sheath delivery of treatment, potentially reducing procedural complexity, decreasing complication rates, and improving patient outcomes across various endovascular interventions. This design represents a promising approach to combining catheter and sheath design that benefits both peripheral and neurovascular procedures.

This article presents a comprehensive investigation into the nanocontact mechanics of an elastic half-plane indented by a rigid circular indenter, accounting for both surface and couple-stress effects. To capture the surface phenomena at the upper boundary of the half-plane, the Steigmann–Ogden surface elasticity model is employed, while the bulk material is described using the classical asymmetric couple-stress theory. We derive the nonclassical boundary conditions and, combined with the continuity of displacements at the contact interface, formulate the integral equation governing the nanocontact problem through the application of Fourier integral transforms. The Gauss–Chebyshev numerical quadrature method is then applied to discretize and collocate the integral equation, supplemented by the force equilibrium condition. The accuracy and robustness of the proposed solution method are validated through comparison with existing literature results. A series of parametric studies are conducted to elucidate the critical influence of both surface and couple-stress effects on the size-dependent elastic behavior of the half-plane. When the contact area is equivalent to the order of magnitude of the characteristic material lengths associated with the bulk and surface, we explore the relative contributions of these two effects at the nanoscale, including the distinctive impact of surface flexural rigidity inherent to the Steigmann–Ogden model. The findings highlight the necessity of incorporating both surface and couple-stress effects in the design and analysis of nanostructured materials, particularly when the scale of the contact region approaches nanometer dimensions.

Abstract We consider the piecewise linear (PWL) vibrations in a cracked Rayleigh beam. The change in local stiffness at the crack site due to a mode-1 crack is introduced through a PWL flexural spring such that the local stiffness is higher in the closed crack configuration than in the open crack configuration. However, without loss of generality, we consider the closed crack configuration to be an intact/pristine beam disregarding the contact micromechanics and relative motion of the cracked surfaces. However, the presented method is applicable even when one considers loss of flexural rigidity in the closed crack configuration. Such a model results in slope discontinuity at the crack site in both open and closed crack configurations. It is recognized that the dynamics in these two mutually exclusive configurations are individually linear and support self-adjoint eigenvalue problems. However, the beam experiences the PWL character of the local stiffness at the crack site when it transits from one configuration to another. With this premise, a semi-analytical approach is evolved by invoking the expansion theorem in each of these configurations in terms of their respective orthonormal eigenfunctions. As the beam transits between the configurations governed by a switching condition, the displacement and velocity of the beam are matched at the very instant. The present study is unique in its semi-analytical approach based on the first principles, physical reasoning, mathematical validity, and the generality that it provides for further investigation. We present interesting results emerging in the free vibrations exhibiting energy exchange between nonclosely spaced modes. However, the forced vibrations exhibit resonance close to the ith PWL frequency, defined in terms of the ith eigenfrequencies of both configurations. Finally, a method based on the canonical action–angle (A–A) variables and the method of averaging is devised to study the forced vibrations of the cracked beam by deriving an averaged slow-flow model. We present the comparative results and discuss the limitations of some of these approaches in the study of such dynamical systems.

The flow-induced oscillation of a transversely clamped buckled flexible filament in a uniform flow was explored using the penalty immersed boundary method. Both inverted and conventional configurations were analysed. The effects of bending rigidity, filament length and Reynolds number were examined. As these parameters were varied, four distinct modes were identified: conventional transverse oscillation mode, deflected oscillation mode, inverted transverse oscillation mode and structurally steady mode. The filament exhibited a 2S wake pattern under the conventional transverse oscillation mode and the small-amplitude inverted transverse oscillation mode, a P wake pattern under the deflected oscillation mode and a 2S + 2P wake pattern for the large-amplitude inverted transverse oscillation mode. Irrespective of their initial conditions, all of the filaments converged to the conventional transverse oscillation mode under low bending rigidity. Multistability was observed in the transversely clamped buckled flexible filament under moderate bending rigidity. The deflection in the oscillation mode increased with increasing filament length. The inverted buckled filament was sensitive to the Reynolds number, unlike the conventional buckled filament. The transverse oscillation mode demonstrated superior energy-harvesting performance.

This study presents the development of nontoxic thermochromic phase change microcapsules (TPCMs) using a complex coacervation technique. The shell materials of the microcapsules are chitosan and sodium alginate natural polymers. The microencapsulation technique employed in this study has the advantage of using natural, nontoxic, biocompatible, and biodegradable capsule materials. In addition, the method is both simple and versatile, making it applicable to various industries. The microcapsules exhibited spherical morphology and a high latent heat of 129.6 J/g. Furthermore, the microcapsules demonstrated good thermal stability and excellent thermochromic performance. Microcapsule-treated fabric exhibited thermochromic and antibacterial activity. The air and water vapor permeability of the microcapsule-treated fabric was lower than that of the untreated fabric. However, the application of microcapsules did not have any effect on the bending rigidity and tear strength of the fabric. Therefore, the produced microcapsules show promise for various applications, including medical textiles, wearable sensors and various consumer goods.

The end-plate connections are most often used as a connection of beam to column and between beams that perceive a moment. Taking into account the difference in the strength of the end plate and the strength of high-strength bolts, which will lead to three different types of failure mechanisms, it is necessary to study the strength and stiffness of such joints using the component method. The most important parameters in this method are the calculated width of the bearing elements for bending and the stiffness coefficient. Determining the ratio of the strength of the connection elements to the failure mechanism and calculating the stiffness coefficient calculated on the basis of the T-shaped element is an important task. For this reason, the objective of this paper is to develop a method for calculating the bending stiffness and strength of the end-plate connections joints under monotonic loads. The proposed calculation method is based on the component method, structural mechanics and strength of materials. Verification is performed on the basis of the experiments performed, for which practical dependencies between the moment and the angle of rotation can be obtained. The practical implementation of the proposed method is demonstrated by calculating the bearing capacity and rigidity of the sample of the experiments performed.As results of the study, it is possible to highlight the method for calculating the rigidity of the end-plate connections of beam to column, the influence of the strength of different elements of such connections on the mechanism of destruction and a recommendation for designing connections under monotonous loads. Using the developed method, it is possible to accurately estimate the bearing capacity and rigidity of the connection, design a diagram of the relationship between the moment and the angle of rotation.

Many bacterial chromosomes show large-scale linear order, so that a locus's genomic position correlates with its position along the cell. In the model organism , for instance, the left and right arms of the circular chromosome lie in different cell halves. However, no mechanisms that anchor loci to the cell poles have been identified, and it remains unknown how this so-called “left--right” organization arises. Here we construct a biophysical model that explains how global chromosome order could be established via an active loop extrusion mechanism. Our model assumes that the motor protein complex MukBEF extrudes loops on most of the chromosome but is excluded from the terminal region by the protein MatP, giving rise to a partially looped ring polymer structure. Using three-dimensional simulations of loop extrusion on a chromosome, we find that our model can display stable left--right chromosomal order in a parameter regime consistent with prior experiments. We explain this behavior by considering the effect of loop extrusion on the bending rigidity of the chromosome, and derive necessary conditions for left--right order to emerge. Finally, we develop a phase diagram for the system, where order emerges when the loop size is large enough and the looped region is compacted enough. Our work provides a theoretical and mechanistic explanation for how loop-extruders can establish linear chromosome order in and how this order leads to accurate gene positioning within the cell, without locus anchoring. Published by the American Physical Society 2025

Semi-flexible polymers, such as actin filaments, can deform the shape of membrane when confined in a membrane vesicle, playing an important role in biological processes. Here, we use dynamic Monte Carlo simulations to study an active polymer chain confined in a membrane vesicle. For flexible polymer chains, the membrane shape is governed by the competition between membrane bending rigidity and polymer activity. Stiff membrane is unaffected by small active forces, but moderate forces cause the polymer to alternate between stretched and disordered configurations, increasing the asphericity of both the polymer and the vesicle. For semi-flexible polymer chains, their stiffness can significantly impact both the vesicle and polymer shapes. We identify distinct classes of configurations that emerge as a function of polymer stiffness, membrane bending rigidity, and polymer activity. A weak polymer activity can cause the polymer to align along its contour, effectively increasing its stiffness. However, a moderate polymer activity softens the polymer chain. For membranes with low bending rigidities κ, large-scale deformations, such as wormlike or tadpole-shaped vesicles, appear at a weak polymer activity and high polymer stiffness. In the wormlike configuration, the polymer chain adopts a hairpin configuration to minimize the polymer bending energy. As the polymer stiffness increases, a tadpole-like vesicle forms, with part of the polymer deforming the membrane into a protrusion while the rest remaining confined in a bud-like structure. For stiffer membranes, we observe oblate vesicles containing toroidal polymer chains, resulting from the high cost of membrane bending energy. A moderate polymer activity causes the softening of the polymer chain, leading to a nearly spherical vesicle with slight shape fluctuation. We further characterize the order parameter of toroidal polymer chains in oblate vesicles and reveal that a slight increase in polymer activity leads to a more ordered helical structure of polymer chains.

Profile Control of Large-Span Tapered Girder Bridges with Corrugated Steel Webs During Cantilever Construction Progress

ABSTRACTTrench weirs constructed across streams and rivers have been utilized for generations of hydropower due to their simplicity, cost‐effectiveness, and minimal disruption to natural water courses. This type of weir consists of rack bars to control the deposition of sediments and floating debris. This article presents the investigations of the effects of different parameters, particularly the spacing of rack bars, specific energy of flow in the approach channel, velocity head, and porosity of rack bars on the discharging ability of trench weirs. Due to their greater flexural rigidity, flat bars are chosen in the current investigation from a structural perspective. The experiment was carried out in an open channel taking different combinations of bed slope, rack slope, and spacing of flat rack bars while testing under free flow conditions and having a pre‐defined discharge in the approach channel. In addition, the discharge characteristics and coefficient of discharge (Cd) of the trench weir have been examined with varying clear spacing of rack bars, specific energy of approach flow, velocity head, and porosity of rack bars. The findings indicate that, in free flow conditions, Cd decreased as the porosity, clear spacing of rack bars, and specific energy of the approach flow increased. Further, during the analysis of experimental data, it was observed that Cd does not show any systematic pattern with velocity head. Thus, this study provides valuable insights on trench weir performance and the variables affecting discharge characteristics of trench weirs.

Translocation across barriers and through constrictions is a mechanism that is often used invivo for transporting material between compartments. A specific example is apicomplexan parasites invading host cells through the tight junction that acts as a pore, and a similar barrier crossing is involved in drug delivery using lipid vesicles penetrating intact skin. Here, we use triangulated membranes and energy minimization to study the translocation of vesicles through pores with fixed radii. The vesicles bind to a lipid bilayer spanning the pore, the adhesion-energy gain drives the translocation, and the vesicle deformation induces an energy barrier. In addition, the deformation-energy cost for deforming the pore-spanning membrane hinders the translocation. Increasing the bending rigidity of the pore-spanning membrane and decreasing the pore size both increase the barrier height and shift the maximum to smaller fractions of translocated vesicle membrane. We compare the translocation of initially spherical vesicles with fixed membrane area and freely adjustable volume to that of initially prolate vesicles with fixed membrane area and volume. In the latter case, translocation can be entirely suppressed. Our predictions may help rationalize the invasion of apicomplexan parasites into host cells and design measures to combat the diseases they transmit.

A static performance experimental study was conducted on six simply supported reinforced concrete truss hollow composite slabs to analyze their flexural rigidity. The study investigated the effects of the slab thickness, the dimensions of the hollow thin-walled boxes, and the composite interfaces on the flexural rigidity of the hollow composite slabs. The flexural rigidity was calculated using methods from American standards, Chinese standards, and the relevant literature, and the results were compared with the experimental data. Based on the experimental findings, a method for calculating the flexural rigidity of hollow composite slabs using a reduced moment of inertia equation was proposed, and the calculated results showed good agreement with the experimental results. The research indicates that the composite interface and the size of the hollow thin-walled boxes have minimal influence on the flexural performance of hollow composite slabs, while the slab thickness significantly impacts their flexural performance. By employing the effective moment of inertia method and substructure calculation theory, a calculation method for the flexural rigidity of hollow composite slabs was established, demonstrating high accuracy.

The study evaluates the mechanical properties of a woven bamboo structure made from bamboo strips using an analytical relation and finite element simulation. The bamboo studied is a recently discovered species, Bambusa Nghiana, characterized by long internodes. Bamboo strips have lower strength at the node junctions, a feature that can be advantageous for this species due to its extended internode length. Plain weave bamboo structures were handwoven from thin, rectangular bamboo strips cut from the bamboo culm along the radial direction. The high bending rigidity of the bamboo strips resulted in an asymmetric woven structure with curved warp strips and straight weft strips. The stiffness of the woven structure was correlated with the stiffness of the bamboo strips and the weave geometry. The in-plane shear resistance of the woven structure was significantly lower than its axial stiffness due to the asymmetric weaving. These in-plane properties were validated using finite element simulation through a user subroutine incorporating the woven structure and the Hashin damage criteria. The prediction of the puncture simulation showed good agreement with the corresponding experiment. These results confirm the proposed analytical relation between the mechanical properties of individual bamboo strips and those of the woven structure.

Emulating oscillations performed by natural swimmers can provide different functionalities than those of propeller-based underwater robots. Yet, to successfully accomplish specific missions under limited power, there is a need to design efficient bio-inspired robots. Adding an appropriate level of flexibility to flapping caudal fins (tails) of robots emulating the thunniform swimming mode has been shown to enhance the thrust generation over a finite range of the flapping frequency. Still, in many cases, adding flexibility to increase thrust generation may require increased input power, which may cause a significant reduction in the efficiency. These observations lead to the concept of enhanced performance by varying the stiffness of the tail as in the case of natural swimmers. This study is concerned with assessing the impact of varying the chordwise stiffness on the tail deflection and flow dynamics, including contributions of added mass and circulation forces to thrust generation and their impact on efficiency. The simulation data are used to identify specific flow dynamics and tail deflections associated with the enhanced thrust generation and/or efficiency, and to define a performance limit expressed as the maximum efficiency as a function of the thrust coefficient.

Though circular exercise is commonly used in equestrian disciplines, it may be at the detriment of horses' musculoskeletal system. To investigate the effects of circular exercise on bone and joint health, 42 lambs were randomly assigned to a non-exercised control, straight-line, small circle, or large circle exercise regime at a slow (1.3 m/s) or fast (2.0 m/s) speed for 12 wk. Blood samples were taken biweekly. Animals were humanely euthanized upon study completion, and the fused third and fourth metacarpals were collected for biomechanical testing and bone density analysis. Fast groups were found to have more bone formation and less resorption activity than slow groups as evidenced by serum biomarker concentrations (p < 0.05). Sheep in the large fast group tended to have greater flexural rigidity and fracture force for the outside leg compared to the inside leg (p < 0.1). Sheep in the small slow group tended to have increased bone mineral density of the outside leg compared to the inside leg, whereas the opposite occurred in the large slow group (p < 0.1). These results provide further evidence for potential asymmetric musculoskeletal adaptations to circular exercise while emphasizing the importance of speed as a positive influence on bone metabolism and strength.

Flexible vegetation is common in riverine and coastal ecosystems. The patch of flexible vegetation is influenced by various factors, resulting in a series of characteristic modes of motion. This study aims to investigate the influence of the Cauchy number (Ca, the ratio of the hydrodynamic drag force to the bending rigidity, i.e., the inverse of the dimensionless bending rigidity) and the solid volume fraction (which reflects the distribution density of a patch of flexible rods) on the motion modes. Additionally, the induction mechanism of fluid and flexible vegetation interaction on motion modes is investigated. A semi-resolved coupling numerical model was employed to simulate the fluid and structure interaction. The results show that the Cauchy number and solid volume fraction influence the motion modes to different extents. Notably, the effect of Ca was significant within the designed range of the two parameters. The wavelength of the monami mode generally shows little variation compared to that observed in the Kelvin–Helmholtz (K-H) vortex, which results from the mixing layer flow instability. The physical mechanism that the motion mode of a patch of flexible rods is induced by the interaction between water flow and flexible rods is further validated and cognized. When the K-H vortex frequency, the natural frequency of the patch in water, and the motion frequency of the patch are close, the patch exhibits motion in the monami mode. Otherwise, the patch will exhibit motion in erect, swaying, and prone mode.

A plate of Clamped Clamped Fixed Fixed orientationt, whose vertical axis rest on clamped and fixed supported edges while the horizontal axis rests on also clamped and fixed boundaries, forming a plate of CCFF shape orientation, remains the plate of focus in the work. Third order energy Functional was adopted in the research work. The clamped clamped fixed fixed plate was considered as the direct independent plate, meaning that the material properties are uniform round about the shape of the element. These includes the flexural rigidity, poison ratio and young elastic modulus of elasticity. Considering the plate arrangement, the shape functions were first formulated, after which the various integral values of the differentiated shape functions, of the various boundary conditions were all generated. Next to this was the formulation of the stiffness coefficients for the various boundary cases. Further minimization yielded the controlling functional known as the overall potential energy functional. The differential value of the Third Order Overall Potential Energy Functional, with respect to the amplitude was further integrated. The integration gave rise to the result known as the Lead equation. From the lead equation comes the derivation of the non-dimensional buckling load parameters. The rest of the analysis which is detailed below was conducted using the buckling equation