Flexural Rigidity Research Articles (Page 3)

This paper pursues two primary objectives. First, we develop a stochastic auxiliary problem principle to address stochastic variational inequalities. We establish the almost sure convergence of the proposed iterative scheme, derived using the stochastic auxiliary problem principle, under the assumptions of strong monotonicity and a growth condition on the involved mapping. Our results demonstrate convergence under highly general conditions on the random noise. While the step lengths α n are assumed to be diminishing, we also provide an alternative result that does not require the step lengths to converge to zero. The second objective is the development of an iteratively regularized stochastic auxiliary problem principle, which allows us to relax the strong monotonicity assumption. The practical relevance and effectiveness of the proposed framework are illustrated through its application to the stochastic inverse problem of estimating coefficients in stochastic partial differential equations. To be precise, we estimate the diffusion coefficient in the stochastic diffusion equation, the flexural rigidity coefficient in the stochastic fourth-order model, and the Lamé parameters in the stochastic linear elasticity. This is achieved by leveraging both a nonconvex output least-squares functional and a convex energy least-squares functional.

Exfoliation of layered materials is an important technique for preparing atomic-layer materials. To provide fundamental mechanistic insights for optimizing this process, we investigated the exfoliation process of nano graphite using molecular dynamics simulations with the ReaxFF force field. The impact of temperature, speed, and angle of removing the top layer has been examined to gain insight into obtaining thin, uniform layers. The bending rigidity of the ReaxFF graphite is temperature-dependent and affects the cleavage behavior. The impact of the Au overlayer, which has recently been utilized to obtain a large area, was also studied, and it was confirmed to be effective in improving repeatability.

Cycloparaphenylenes (CPPs), hoop-shaped conjugated macrocycles composed of para-linked phenyl units, have attracted significant interest due to their curved aromatic frameworks and para-conjugation, which give rise to unique (opto)electronic properties. Full planarization of their π-systems is structurally inaccessible, as it would further increase the inherent ring strain. However, partial planarization can be achieved by π-extension through incorporation of rigid bending units. Here, we report the on-surface synthesis of quasi-planar π-extended [2n]CPPs (n = 8-11) on Au(111), achieved via a bottom-up surface-assisted strategy, and their characterization by scanning tunneling microscopy/spectroscopy (STM/STS) and density functional theory (DFT). These π-extended CPPs are macrocycles with para-connected phenylenes forming the inner backbone and perylenyl groups bridging the phenylene units. The n = 8 CPP adopts a planar geometry on the surface, while the n = 9 to n = 11 homologues remain nonplanar. Nevertheless, substrate-induced flattening enhances π-orbital overlap and leads to a progressive reduction of the HOMO-LUMO gap with increasing ring size. This behavior is specific for planarized CPPs and contrasts with conventional, nonplanar CPPs. Moreover, π-extension results in a reduced gap compared to the unsubstituted planar parent [2n]CPP. dI/dV maps reveal orbital confinement at the edges and fjord regions, attributed to slower wave function decay. In larger CPPs, the tilted perylenyl groups modulate this confinement and affect the STM contrast in fjord regions. The unique structure of these strained, quasi-planar CPPs provides a well-defined platform for studying the interplay of curvature, conjugation, and electronic structure in bent benzenoid macrocycles.

Local enrichment of cardiolipin to transient membrane undulations.

Numerical assessment of wave-induced motions and rigid bending and torsional loads acting on large slender ships in various operating conditions using a 2D time domain method

Composite materials are increasingly used in structural applications due to the high strength-to-weight ratio, corrosion resistance, and design flexibility they offer; however, susceptibility to impact damage remains a critical concern, particularly in layered configurations. In the present research, low-velocity impact experiments were performed on 8-layer and 16-layer unidirectional E-glass/epoxy composite plates with [+45/-45/90/0]s and [+45/-45/90/0]2s stacking sequences, which were manufactured using the vacuum-assisted hand lay-up method, at impact energy levels of 10, 20, and 30 J. Findings indicated that a rise in impact energy resulted in an increase in maximum contact force and energy absorption for both 8-layer and 16-layer composite plates, with no noticeable change in bending rigidity. At the same energy level, an increase in the number of layers enhanced the maximum contact force and bending rigidity of the composite plates, whereas displacement and the amount of energy absorbed by the material decreased. For all energy levels, the damage observed in the 8-layer composite plates spread over a wider area compared to the damage in the 16-layer plates.

In closed circular ribbonlike polymers such as deoxyribonucleic acid, twist and writhe are known to be largely determined by the polymer's bending and torsional rigidities, and they must sum to a topological constant. Using molecular simulations and an analytically solvable Landau theory, we study the interplay between ribbon topology and chemically annealed charges in a model polyelectrolyte. We show that the repulsions between like-charged acidic sites trigger phase separation and coexistence of supercoiling domains, in turn unveiling a complex phase diagram and providing a route to control the properties of deoxyribonucleic acid-based materials.

This paper aims to study the free vibration and buckling behavior of a sandwich tapered column. The sandwich members are laterally-symmetrically laminated against the mid-depth of a square cross-section with the side length varying according to a parabolic function along the column axis. The closed-form stiffness of sandwich members is provided as a function of axial rigidity, flexural rigidity, mass per unit length, and mass moment of inertia. This formulated stiffness is implemented to the free vibration problem of the column under axial load. The differential equations governing vibrational and buckled mode shapes are derived. Numerical methods are presented to calculate natural frequencies and buckling loads of the column. The numerical results of this study are tabulated and illustrated in figures, accompanied by an extensive discussion of parametric study regarding natural frequencies and buckling loads. Natural frequencies and buckling loads increase with increasing the material property ratio and taper ratio, while decrease with increasing slenderness ratio and load parameter.

High-capacity alloy anodes (Si, Al, and Sn) promise critical materials for developing high-energy all-solid-state lithium batteries (ASSLBs). However, their implementation remains fundamentally constrained by severe interfacial stress, large volume changes, and high stack pressures. Here, a novel "creep localization" strategy is proposed to address these intrinsic limitations by coupling a creep-susceptible (InSn4)0.37·(InBi)0.63 alloy anode with a titanium mesh possessing a high area moment of inertia. The investigations reveal a synergistic interface stabilization mechanism: InSnBi undergoes adaptive creep to maintain ionic-electronic interpenetrating networks, while the titanium framework, through its flexural rigidity, redistributes localized stress and prevents heterogeneous stress concentrations from driving InSnBi creep toward the cathode. This hierarchical stress management mechanism ensures stable cycling by accommodating substantial volume fluctuations, thereby enabling ASSLBs to realize stable cycling at high loading (23.05 mAh cm-2) and low stack pressures (3MPa), respectively. Remarkably, the as-assembled LiCoO2||InSnBi full-cell with a capacity of 5.56 mAh cm-2 maintains a retention of 81.6% over 3000 cycles at a 2C rate. This work presents a new paradigm for addressing the electro-chemo-mechanical coupling degradation of ASSLBs, representing a milestone advancement for developing high-energy ASSLBs.

Current methods of diagnosing osteoporosis, such as DXA, have limitations in predicting fracture risk. Cortical bone mechanics technology (CBMT) offers a novel approach by using a three-point bend test with multifrequency vibration analysis to directly measure ulnar bending stiffness and calculate flexural rigidity, a mechanical property highly predictive of whole-bone strength under bending conditions. Cortical bone mechanics technology targets the diaphyseal ulna, a site composed primarily of cortical bone, enhancing its specificity for cortical bone quality. In this study of 388 postmenopausal women, we developed and validated a 20-point signal quality indicator (SQI) scoring system to quantify CBMT signal quality and evaluated its relationship to biometric characteristics. The SQI was developed through expert assessment of representative frequency response function (vibration data) trials and refined over 17 iterations. The final system achieved excellent classification performance (AUC = 0.974; sensitivity, specificity, and accuracy all >97%). A total of 22 740 trials were collected across 758 total arm tests, sampling 10 ulnar sites per arm under three vibration amplitudes. Two expert analysts evaluated signal features associated with high signal quality. The resulting SQI is fully automated and provides real-time feedback. All correlations between SQI scores and biometric attributes were weak or very weak (|ρ| < 0.30). The correlations with body weight (ρ = −0.11), BMI (ρ = −0.12), ulnar BMD (ρ = −0.17), CBMT-derived flexural rigidity (ρ = −0.28), and grip strength (ρ = 0.17) were statistically significant (p < .05) but remained small in magnitude. SQI scores were modestly lower in individuals with higher BMI or flexural rigidity (~2 to 3 points), but values remained in the acceptable-to-good range. This study introduces a robust, automated CBMT signal quality metric and demonstrates that its performance remains stable across a broad range of biometric profiles, supporting its application in both clinical and research settings.

The current bending cantilever test method can only measure the bending property of the fabric in one direction each time, thus repeated testing operations are required even for one kind of fabric, which takes a lot of time and energy. Besides, the test results of the commonly used the cantilever method are bending length or bending rigidity, which cannot reflect, visualize and distinguish the bending behavior of different fabrics vividly. In view of this situation, a multi-directional and visual fabric bending measurement method was proposed, by which 20 fabric strips can be tested at one time, including 2 directions and 2 sides of the fabric or four directions of the fabric. 32 kinds of fabrics were used for the pilot experimentation and four new parameters, i.e. the projection length, projection area, falling height and bending resistance coefficient were extracted. The results showed that there was good correlation between the new parameters and the bending length in the conventional cantilever method, which indicates that the new method is feasible. For most fabrics, the coefficient of variation (CV) of the bending length measured by the cantilever method was greater than that of H whose test stability is the lowest in the four new parameters, indicating that the new method has better test stability. The novel method put forward in this paper can visualize not only the bending properties of different directions for one fabric, but also the bending behavior of different fabrics.

Abstract An effective method for transforming traditional textiles into multifarious smart textiles is to functionalize textiles by conductive nanomaterial coating. The incorporation of nanoparticles on textile surfaces brings vital features, including antibacterial, antistatic, conductive, superhydrophobic, etc., thus enabling a multifunctional fabric with desirable attributes, including low weight, flexibility, mechanical stability, etc. The developing disciplines of nanoscience have revamped the field of high‐performance textiles. The present work synthesizes graphene oxide (GO) from graphite flakes using a modified Hummers mechanochemical approach and then dip‐coating polyester (PET) fabric, followed by drying; subsequently, in situ reduction with l‐ascorbic acid was conducted to form reduced GO‐coated PET. The endurance of the coating over the fabric was evaluated after ten washes. Defense users can take advantage of such conductive multipurpose smart fabrics. Structural, morphological, elemental and thermal analyses confirmed the effective synthesis of GO from graphite flakes as well as successful coating performance over the fabric. Other performance tests were conducted, including water contact angle, antibacterial, conductivity, flexural rigidity (FR), water vapor transfer (WVT) rate and air permeability (AP) measurements. The finally obtained reduced GO‐coated PET fabric samples show superhydrophobicity (148.6° ± 4.43), antimicrobial properties against E. coli bacteria, lowest surface resistivity (1.63 × 106 Ω sq−1), increased AP (144 cm3 cm−2 s−1), maximum FR (275.373 mg cm) and WVT rate (216.82 g m−2 (24 h)−1). These properties were satisfactorily retained after ten washing cycles. © 2025 Society of Chemical Industry.

ABSTRACT The use of timber in construction has seen a rapid increase in demand in recent years. However, some question the capacity of the industry to supply sufficient amounts of structural grade timber in a sustainable and affordable manner as the demand will increase further. As such, the motivation for using all the available timber and increasing the efficiency of the timber is high. Currently, a large fraction of the available timber is used for non-structural purposes because of their unknown or unfavourable mechanical properties, or because of alternative use. To utilise more of the available timber for structural purposes and to increase the material efficiency, flexurally reinforced timber beams are attractive options. In this study, analytical bending capacity models for reinforced timber beams were derived. The bending capacity models were experimentally validated on full-size reinforced glued laminated timber beams with carbon-fiber reinforced polymer sheets. The experimental results showed an increase in the flexural rigidity of up to 65% and a strength increase of 74% when compared with unreinforced beams under pure bending. Moreover, a 44% reduction in the timber volume and three times higher global warming potential was demonstrated for reinforced timber beams when compared with unreinforced timber beams.

The textile industry is a major waste producer due to its high production volume and increasing consumption rates. Therefore, recycling and re-using textile waste for production is crucial for environmental sustainability. This study examines the physical properties of cotton/polyester blended knitted fabrics produced with yarns containing four different recycled cotton fiber ratios. In the first part, yarns with varying recycled fiber content were evaluated for unevenness, tensile strength, and friction properties by changing yarn count and twist. In the second part, rib and interlock fabrics were knitted, and fabric tests for weight, thickness, bending rigidity, bursting strength, air permeability, and pilling were conducted. Reference fabrics were produced using virgin yarn with the same blend ratio as the highest recycled fiber yarns for comparison. The results show that recycled yarns can replace virgin yarns, contributing to reducing environmental impacts through textile waste recycling, and recycled yarn quality significantly affects fabric properties.

Ultra High Performance Concrete (UHPC) has the advantages of high strength and good durability. The new technology of unbonded prestressed UHPC to strengthen ordinary concrete beams can give full play to the performance of prestressed “high efficiency” and UHPC “light durability”. In this paper, through the test and theoretical analysis of 10 unbonded prestressed UHPC reinforced beams, the bearing capacity of prestressed UHPC reinforced beams and the key parameters affecting the flexural performance (i.e., UHPC strength, thickness, prestressed tensile degree and prestressed reinforcement ratio) are studied. The test results show that: UHPC and concrete beam using chisel processing technology, unbonded prestressed by end anchorage can achieve effective interface bonding while ensure the reinforcement effect with a simple construction process; Prestressed UHPC reinforced beams can greatly improve the cracking performance, flexural bearing capacity and rigidity; Through theoretical research, the formula of flexural bearing capacity of ordinary concrete beams reinforced by prestressed UHPC is deduced, which is conducive to subsequent engineering application.

Shear lag effect commonly exists in engineering structures, particularly in box girders. Thin-walled box girders, known for their high bending and torsional rigidity, are extensively utilized in modern bridge engineering. At present, research has mainly focused on the shear lag effect of constant cross-section box girders as well as varying height box girders, and there is relatively little research on the shear lag effect of box girders with varying width. With a linear increase in width, the variables exhibit different shear lag effects along the axial direction of the bridge compared to constant cross-section box girders. To address this problem, the present study proposes a novel theoretical method for calculating the shear lag coefficient in varying cross-section box girders. This method conceptualizes the additional deflection induced by the shear lag effect as a generalized displacement and employs the variational method for analysis. The results of the proposed method were validated through comparison with numerical simulations, demonstrating an error margin within ± 6%, which is considered acceptable. This innovative method not only provides an accurate and reliable tool for quantifying shear lag effects but also enables the assessment of its impact on deflection and stress distribution in box girders.

To evaluate engineering seismology, strong ground movements, and seismic risks, investigating local site effects analysis is essential. In the last decade, Slope construction and deep excavations reinforced using soil nails have developed extensively in earthquake-prone zones. Therefore, it is important to study site effect and dynamic response of the reinforced walls under seismic conditions. In this research, in a site with two different types of dense and loose soil using the finite element analysis, dynamic response and site effects for the restrained wall by nailing system have been investigated. The study revealed that by increasing the underground water table, the wall’s flexural rigidity, and the face batter angle enhance stability and decrease the wall’s tendency to display more nonlinear behavior via larger deformations under dynamic loading. Consequently, this leads to the creation of smaller shear strains and the dissipation of less energy in the model, ultimately increasing the amplification factor. Conversely, the increase in the surcharge magnitude and the stages of excavation would decrease the wall’s stability, respectively, both increasing the nonlinear behavior, shear strains, and the reinforced system’s energy dissipation, all of which contribute to reducing the amplification factor.

Regenerated cellulose fibers for preparation of alginate and lornoxicam-loaded medical knitted textiles: A response surface optimization study.

Accurate measurement of a bone surrogate flexural rigidity in three- and four-point bending.

This study investigates the scattering of oblique waves by a submerged rigid block and a floating elastic plate. The plate is positioned at a defined distance from the rigid block and experiences localized forcing. Three edge conditions, free, simply supported, and built-in, are considered for the plate. The fluid domain is divided into sub-regions, and the Eigenfunction expansion matching method is employed to determine the velocity potential in each region. Numerical results are specifically presented for the built-in edge condition, examining the effects of wave, rigid block, plate, and fluid parameters. The results indicate that at smaller angles of incidence, a taller rigid block produces higher reflections. Reflection is also pronounced when there is no gap between the rigid block and the plate. Over time, a significant reduction in the amplitude of free surface deflection is observed. Additionally, the angle of incidence, flexural rigidity, and fluid depth play a crucial role in determining the amplitude of the deflection of the plate in the time domain.