Stiffness Of Plate Research Articles

Spatial and frequency identification of the dynamic properties of thin plates with the Frequency-Adapted Virtual Fields Method

Vibroacoustic inverse methods use the measured response of a vibrating structure to identify a structural parameter or a dynamic load. Two inverse methods are considered, the Force Analysis Technique (FAT) and the Virtual Fields Method (VFM). The Corrected Force Analysis Technique (CFAT) is a variant of FAT that corrects its singularity. This correction allows the method to be applied in the high-frequency domain, when the number of measurement points per flexural wavelength becomes small. In this study, the proposed novelty is the development of a Frequency-Adapted VFM (FA VFM) to the case of a Love–Kirchhoff plate. Thanks to this method, the VFM can now be applied to identify the equivalent bending stiffness and structural damping of a thin plate when the number of measurement points per wavelength is small. The method has previously been developed for an Euler–Bernoulli beam. An experimental identification of the complex bending stiffness of an locally damped aluminium plate using Laser Doppler Velocimetry (LDV) data and the developed method is performed. The experimental study shows for the first time that the FA VFM can be used to map the equivalent bending stiffness and structural damping as a function of position on a plate and identify these parameters as a function of frequency over a large frequency band. The results of the Frequency-Adapted VFM are compared with those of CFAT and the classical VFM approach. FA VFM results are more accurate than those of classical VFM and similar to those of CFAT.

Effect of Plate Screw Configuration on Construct Stiffness and Plate Strain in a Synthetic Short Fragment Small Gap Fracture Model Stabilized with a 12-Hole 3.5-mm Locking Compression Plate.

The aim of the study was to determine the effect of a short and long working length screw configuration on construct stiffness and plate strain in a synthetic, short fragment, small gap fracture model stabilized with a 12-hole 3.5-mm locking compression plate (LCP). Six replicates of short and long working length constructs on a short fragment, small gap fracture model underwent four-point bending. Construct stiffness and plate strain were compared across working length and along the plate. With the LCP on the compression surface (compression bending), the short working length had a significantly higher construct stiffness and lower plate strain than the long working length. Conversely, with the LCP on the tension surface (tension bending), transcortical contact between 150 and 155 N induced load sharing at the fracture gap, which significantly increased construct stiffness and decreased plate strain in the long working length. At 100 N (precontact), the short working length had a significantly higher construct stiffness and lower plate strain than the long working length, comparable with our compressing bending results. In compression bending, and before transcortical contact occurred in tension bending, the short working length had a significantly higher construct stiffness and lower plate strain than the long working length. Load sharing due to transcortical contact observed in our model in tension bending will vary with fracture gap, working length, and loading condition. These results must be interpreted with caution when considering clinical relevance or potential in vivo biomechanical advantages.

Experimental identification of the bending stiffness and damping of plates using the frequency-adapted virtual fields Method

Inverse vibroacoustic methods can be used to identify the complex bending stiffness of a plate from its vibratory response. This work focuses on the Virtual Fields Method (VFM) and the Force Analysis Technique (FAT). The VFM uses functions called virtual fields to solve the Principle of Virtual Work, a weak form of equilibrium, and identifies complex bending stiffness. Here, the virtual fields are defined as piecewise functions over a surface smaller than the plate (virtual window). FAT uses a finite-difference scheme to discretize the fourth-order spatial derivatives of the displacement in the local equilibrium of the plate and thus estimates the bending stiffness. The application of a finite-difference scheme creates a bias in the identified stiffness, which increases with frequency. The Corrected Force Analysis Technique (CFAT) corrects this bias in the high-frequency domain. In this study, it is proposed to apply the CFAT principles to the VFM to adapt the method, using the virtual window size, so it can be applied it in the high-frequency domain. FAT, CFAT, the VFM and the Frequency-Adapted VFM will be presented. The method was tested on experimental data to identify the complex bending stiffness of an aluminium plate partially covered with a damping material.

Extension of paperboard modelling with Föppl–von Karman terms for improved stress state under suction pressure

A practical method for solving the bending stiffness of a thin orthotropic plate based on measured deflection and known loading was studied. The target application was paperboard manufacturing and related process control. Here, finite element (FE) method was used to create virtual paperboard and its deflection data. The accuracy of the linear Kirchhoff plate model used in the practical method was tested against the FE model with known load and material properties. It was found that in the case of significant deflections, the linear Kirchoff model was not accurate. The non-linear Föppl--von Kàrmàn model takes into account the occurring membrane stresses and extends on the Kirchhoff model, allowing for larger deflection. The non-linear Föppl--von Kàrmàn model was found to successfully describe the simulated situation and could be used to better solve for the paperboard's bending stiffness values over two axes.

Mechanically compliant locking plates for diaphyseal fracture fixation: A biomechanical study.

Axial micromotion between bone fragments can stimulate callus formation and fracture healing. In this study, we propose a novel mechanically compliant locking plate which achieves up to 0.6 mm of interfragmentary motion as flexures machined into the plate elastically deflect under physiological load. We investigated the biomechanical performance of three compliant plate variations in comparison to rigid control plates with small and large working lengths in a comminuted bridge plating scenario using humeral diaphysis surrogates. Under static axial loading, average interfragmentary motion was 6 times larger at 100 N (0.38 vs. 0.05 mm) and nearly three times larger at 350 N (0.58 vs. 0.2 mm) for compliant plates than rigid plates, respectively. Compliant plates delivered between 2.5 and 3.4 times more symmetric interfragmentary motion than rigid plates (p < 0.01). The bi-phasic stiffness of compliant pates provided 74%-96% lower initial axial stiffness up to approximately 100 N (p < 0.01), after which compliant plate stiffness was similar to rigid plates with increased working length (p > 0.3). The strength to failure of compliant plates under dynamic loading was on average 48%-55% lower than rigid plate groups (p < 0.01); however, all plates survived cyclic fatigue loading of 100,000 cycles at 350 N. This work characterizes the improvement in interfragmentary motion and the reduction in strength to failure of compliant plates compared to control rigid plates. Compliant plates may offer potential in comminuted fracture healing due to their ability to deliver symmetric interfragmentary motion into the range known to stimulate callus formation while surviving moderate fatigue loading with no signs of failure.

Effect of process parameters on the mechanical performance of fusion-joined additively manufactured segments

Purpose Herein, the authors report the effects of printing parameters, joining method, and annealing conditions on the structural performance of fusion-joined short-beam sections produced by additive manufacturing. Design/methodology/approach The authors first identified appropriate printing parameters for joining segmented short beams and then used those parameters to print and fusion-join segments with different configurations of stiffeners to form a longer section of a wing or small wind turbine blade structure. Findings It was found that the beams with three lateral and three base stiffening ribs give the highest flexural strength among the three beams investigated. Results on joined beams annealed at different conditions showed that annealing at 70 °C for 0.5 h yields higher performance than annealing at the same temperature for longer times. It is also found that in the case of the hot-plate-welded three-dimensional (3D)-printed structures, no annealing is needed for reaching a high strength-to-weight ratio, but annealing is helpful for maximizing the modulus-to-weight ratio. Both thermal buckling and edge wrapping were observed under annealing at 70°C for 0.5 h for 3D-printed beams comprising two lateral and four base stiffening plates. Originality/value Fusion-joining of additively manufactured segments is needed owing to the constraint in building volume of a typical commercial 3D-printer. However, study of the effect of process parameters is needed to quantify their effect on mechanical performance. This investigation has therefore identified key printing parameters and annealing conditions for fusion-joining short segments to form larger structures, from multiple 3D-printed sections, such as wind blade structures.

Identifying significant factors affecting plate stiffness of innovative CLT using Random Forest analysis

Abstract Innovative cross-laminated timber (CLT) is a relatively new engineered timber product. It is a new version of CLT having large gaps between lateral lamellas. Since it is a new material, the mechanical performance of this innovative material is not studied yet despite these advantages. This paper explores the factors that influence membrane, bending, shear, and torsional stiffness in innovative CLT and their implications, acknowledging the significance of knowing the plate stiffness of these innovative materials in predicting their behaviour and promoting their use in construction as bio-based materials. Using a large database of plate stiffness moduli derived from finite element computations and incorporating microstructural characteristics such as layer thicknesses, board width, gap width, longitudinal modulus of elasticity, longitudinal shear modulus, and rolling shear modulus of timber, Random Forest analysis was employed to study the significance of factors affecting plate stiffness in innovative CLT. Our results show that the gap affects the membrane, shear, and torsional stiffness for innovative CLT. However, the trans-versal layer thickness primarily controls the bending stiffness.

Free Vibration of the Magneto-Electro-Elastic Plates Resting on Elastic Foundation Using the Refined Plate Theory with Two Variables

The objective of this article is to investigate the free vibration analyses of the functionally graded magneto-electro-elastic (FG MEE) plates supported by an elastic foundation using the refined plate theory (RPT) with two variables. The elastic foundation is modeled utilizing the Winkler-Pasternak theory. The power-law model is employed to characterize the graded material properties of the FG MEE plates. According to the RPT and Hamilton's principle, the governing equations of the FG MEE plate are derived. The displacement fields and electric and magnetic potentials are approximated using the Non-Uniform Rational B-Splines (NURBS) basic functions of the isogeometric approach (IGA). The proposed model’s advantages and accuracy are demonstrated by comparing the obtained results with those reported in the existing literature. The study comprehensively examines and discusses the impact of several parameters, including the power index, initial external magnetic potential and electric voltage, and the geometry, on the vibration frequency of the FG MEE plates. The numerical findings indicate that an increase in the power index leads to a decrease in the frequency of the FG MEE plates. Besides, the stiffness of FG MEE plates decreases with an increase in the initial external electric voltage, whereas it increases with an increase in the initial external magnetic potential. This article presents valuable perspectives on examining vibration analysis of the FG MEE plates, which can inform the design of innovative materials and structures with customized properties.

A biomechanical comparison of track spikes with advanced footwear technology to a traditional track spike in female distance runners.

The addition of highly responsive lightweight foam and a stiff plate in the midsole of long-distance road racing shoes has yielded significant energetic cost savings that have translated to notable improvements in performance. This new foam and stiff plate technology have since been implemented in long-distance track spikes, where performances have also improved. However, the impact of spikes with advanced footwear technology (AFT) on distance running biomechanics has been studied minimally to date. Therefore, the purpose of this study was to compare running biomechanics between two spikes which incorporate AFT (Nike ZoomX Dragonfly, Nike Air Zoom Victory) to a traditional spike (Nike Zoom Matumbo). Seventeen competitive collegiate female runners completed 60 m trials at their 5k race pace in each spike condition while outfitted with IMU sensors and plantar pressure insoles. We observed significantly lower peak ankle dorsiflexion in the Dragonfly and Victory compared to the Matumbo and lower whole foot, forefoot and rearfoot peak and average pressure in the Dragonfly compared to the Matumbo and Victory. The acute biomechanical alterations observed in this study warrant future investigation into the association between running biomechanics and racing performance in track spikes with advanced footwear technology.

Effect of adhesive ductility on the bond behavior of CFRP-steel cohesive interfaces made with toughened epoxy resin

The strengthening of steel structures can be effectively performed using carbon fiber-reinforced polymers (CFRP) plates. Specifically, the behavior of corroded and fatigue damaged steel bridges can be significantly improved using externally bonded (EB) or unbonded composite reinforcements. For bonded composites, the bond between the reinforcement and the steel substrate is the weak link of the system. Indeed, cohesive failure within the adhesive layer represents the main failure mode, which makes the selection of a proper adhesive fundamental to achieve an improvement of the system load carrying capacity and fatigue resistance. Within this context, the use of toughened adhesives represents a promising solution. However, research regarding these adhesives is still limited. In this paper, 18 single-lap direct shear tests are performed to evaluate the cohesive behavior of toughened and traditional adhesives. For some specimens, the full-range bond behavior, including the load response snap-back, was experimentally captured. The digital image correlation (DIC) technique is adopted to evaluate the adhesives cohesive material law (CML). The effect of adhesive ductility, plate stiffness, and bonded length on the joint load response is investigated. Finally, experimental results are validated and discussed against the analytical predictions of a cohesive model based on a trapezoidal CML.

Ultimate strength of multi-ring-stiffened tube-gusset joints with dual-function stiffeners under combined bending and compressive loads

Tube-gusset (TG) joints play a crucial role in connecting crossarm chords to tower bodies in steel-pipe power transmission towers, bearing the highest loads in the entire tower structure. This study investigated TG joints with five-ring stiffeners under combined bending and compressive loads, using the middle stiffener plate as the connecting plate. Through experimental studies, numerical simulations, and theoretical analyses, insights were obtained into the failure mechanism and mechanical characteristics of TG joints. This study identifies the key factors influencing the ultimate strength of TG joints under combined bending and compressive loads and proposes a method for determining the joint bearing capacity. Notably, the mechanical performance of multi-ring-stiffened tube-gusset joints was minimally affected by the initial geometric defects under combined compression and bending moments. The load exerted on the gusset plate was primarily supported by the stiffeners, with the gusset plate demonstrating minimal bending deformation, owing to its substantial in-plane stiffness. Consequently, the gusset plate underwent an overall rotation or translation under the combined effects of compression and the bending moment. The proposed method accurately predicted the joint bearing capacity, ensuring the safety of TG joints. These findings provide valuable insights into the meticulous design of joints in steel-pipe transmission towers, thereby ensuring the safety and stability of transmission lines in the field of civil engineering.

Material Properties and Engineering Performance of Bone Fracture Plates Made from Plant Fiber Reinforced Composites: A Review.

Bone fracture plates are usually made from titanium alloy or stainless steel, which are much stiffer than bone. However, overly stiff plates can restrict axial interfragmentary motion at the fracture leading to delayed callus formation and healing, as well as causing bone "stress shielding" under the plate leading to bone atrophy, bone resorption, and plate loosening. Consequently, there have been many prior efforts to develop nonmetallic bone fracture plates with customized material properties using synthetic fibers (e.g., aramid, carbon, glass) in polymer resin. Even so, plant fibers (e.g., flax, roselle, sisal) offer additional advantages over synthetic fibers, such as availability, biodegradability, less toxicity during processing, lower financial cost, and recyclability. As such, there is an emerging interest in using plant fibers alone, or combined with synthetic fibers, to reinforce polymers for various applications. Thus, this is the first review article on the material properties and engineering performance of innovative bone fracture plates made from composite materials reinforced by plant fibers alone or supplemented using synthetic fibers. This article presents material-level fiber properties (e.g., elastic modulus, ultimate strength), material-level plate properties (e.g., fatigue strength, impact toughness), and bone-plate engineering performance (e.g., overall stiffness, plate stress), as well as discussing general findings, study quality, and future work. This article may help engineers and surgeons to design, fabricate, analyze, and utilize novel bone fracture plates.

Fatigue performance of a steel truss web-concrete external joint in railway composite continuous girder bridges

ABSTRACT This study conducted fatigue tests on two 1:3 steel truss web-concrete external joints to investigate their fatigue performance. The fatigue failure mode of the external joints and the stress distribution of each component were investigated. In addition, a finite element analysis (FEA) model was established, and parametric analysis was carried out to discuss the influence of gusset plate thickness, stiffening plate layout, and gusset plate structural form on fatigue performance. The results show that the fatigue life of the external joints under the design load amplitude is 3.75 million times (187.5 years). Fatigue cracks appear in the junction area between the gusset plate and the end of the stiffening plate, which is a weak fatigue detail of the external joint. The fatigue cracks cause local stress redistribution of the gusset plate. The stress at the junction (GN3) between the gusset plate and the stiffening plate N3 can be reduced by up to 37%, 61%, and 21% by altering the above three factors. Furthermore, the fatigue life of the optimized joint is increased by 1.4 times, indicating that the fatigue performance can be significantly enhanced by improving the stiffening plate layout and the gusset plate structural form.

Exploiting interfacial instability during peeling a flexible plate from elastic films

Adhesive interactions between soft materials are prevalent in both biological systems and various engineering applications, including soft robots, flexible electronics, and antifouling coatings. Many studies have demonstrated that cavitation and fingering instabilities emerge at the adhesive interface between rigid objects and soft films, owing to the geometric attributes of the contact region. However, in the context of peeling configurations, defining the geometric features is challenging, resulting in relatively scant exploration of interfacial instabilities. Hence, the modulation of instability patterns during the peeling process of a flexible plate from a thin elastic film, alongside the consequential effects on mechanical responses, remains poorly understood. To elucidate the mechanisms underlying interfacial instability during peeling process and its impacts on peel-off force, we use finite element methods to simulate the evolution of interface separation. Consistent with previous experimental observations, we find that the interfacial instability will occur when the bending stiffness of the flexible plate is bigger than a critical value. We show that the interfacial instability is mainly induced by the competition between the adhesion energy and the strain energy of the film, and the incompressibility of the thin film is critical for the appearance of the interfacial instability. Combining theory and finite element simulation, we propose the scaling laws for the critical peel-off force for stable and unstable peelings, respectively, and show that the critical peel-off force will decrease when the interfacial instability occurs. Finally, we demonstrate that weakening the tangential adhesion strength and loosening the constraints between the film and the rigid substrate effectively suppress fingering instability. Collectively, our findings elucidate the pivotal factors influencing interfacial instability, offering invaluable insights for the design of structures or systems involving soft materials.

Free vibration analysis of functionally graded composite plates reinforced with linearly and nonlinearly distributed carbon nanotubes in hygrothermal environments

This article presents a novel investigation of the free vibration behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates under hygrothermal environments. It explores both uniform and non-uniform (functionally graded) distributions of CNTs across the plate thickness for the first time. The effective material properties of the CNTRC, considering temperature and moisture dependence, are determined using the extended rule of mixture. First-order shear deformation theory (FSDT) is employed to derive the governing equations incorporating hygro-elastic and thermo-elastic relations. These equations are solved using the finite element method. A validation study verifies the accuracy of the employed approaches. Subsequently, a comprehensive parametric study investigates the influence of plate geometry (length-to-width and width-to-thickness ratios), CNTs volume fraction, boundary conditions, linear and non-linear CNTs distributions, and hygrothermal environments on the free vibration behavior of polymeric nanocomposite plates reinforced with CNTs fillers is conducted. The results reveal that the increase in temperature and moisture leads to a decrease in the effective stiffness of the FG-CNTRC plates.

Comparative Biomechanical Study of Fragment-Specific Plates and Headless Screws for Radial Styloid and Lunate Facet Fixation in Distal Radius Fracture Evaluated in a Synthetic Composite

To evaluate the compressive stiffness (ability to resist compression under an applied load) of fragment-specific plate and headless screw fixation for radial styloid and volar lunate facet fractures in a synthetic composite distal radius. A simulated radial styloid fracture (AO type B1.1) and simulated volar lunate facet fracture (AO type B3.3) were created in synthetic composite distal radii and fixed with a fragment-specific plate (FSP) using a radial styloid or lunate facet plate or with two- or three-headless screws (2HS, 3HS), creating 6 fixation models: B1.1/FSP, B1.1/2HS, B1.1/3HS, B3.3/FSP, B3.3/2HS, and B3.3/3HS. Compressive stiffness of fixation constructs under initial static load, cyclic load, and final static load was investigated. Nonaxial loadings, including shearing and rotation, were not evaluated. Regarding AO type B1.1, the mean stiffness of the B1.1/FSP construct was not significantly different from the intact radius, and the mean stiffness was greatest in the B1.1/3HS and lowest in the B1.1/2HS construct. For AO type B3.3, the mean stiffness of the B3.3/3HS construct was not significantly different from the intact radius, and the mean stiffness of the B3.3/FSP and B3.3/2HS construct was greatest and lowest, respectively. Minimal differences in stiffness between initial and final static loads confirmed that there was no evidence of failure implant under cyclic compressive loads. Fragment-specific plates and two- or three-headless screw fixation maintained mechanical stability through compressive cyclic loading for radial styloid and volar lunate facet fractures. The FSPs and three-headless screws fixations provided superior stiffness over the two-headless screws fixation. There was no articular fracture failure in all fixation constructs with initial static compression, cyclic loading, and final compression. Fragment-specific plates and headless screws can both be considered as adequate fixation for radial styloid and volar lunate facet fractures.

Non-symmetric plate-lattices: Recurrent neural network-based design of optimal metamaterials

The elastic response of plate-lattices with cubic symmetry can reach the upper, isotropic Hashin-Shtrikman bound. Here, our primary objective is the design of stiff lattices with tailored properties beyond any symmetry or isotropy. We propose a general construction method of plate-lattices, defined as a sequence of plates. We present the large elastic property space, accessible via the geometric control offered by our construction method. Building upon this general formulation, we provide a large-scale comparison to the property spaces of truss- and shell-lattices. Additionally, we observe a distinct correlation between plate orientation and stiffness. To tailor the properties of plate-lattice, we employ a recurrent neural network mapping from a given property to the corresponding structure. Our results highlight the effectiveness of this inverse model in creating plate-lattices with desired properties. We believe that this work holds a paradigm shift in field of inverse design by enabling the efficient customization of the stiffest family of metamaterials.

Model Test and Numerical Simulation of Two Typical Close-Fitting Pile–Wall Integrated Structures in Deep Excavation

Compared to conventional support methods, the close-fitting pile–wall integration technique features a minimized construction spacing between the retaining pile and the basement retaining wall. This approach leverages the pile stiffness to minimize the wall thickness and enhance underground space utilization. However, it currently lacks significant discussions and measured data about the interaction laws between the pile and the wall. The model test and finite element method (FEM) are employed to study the deformation and internal force interaction laws of two typical close-fitting pile–wall integrated structures, and a comparison with conventional design is conducted. Furthermore, this study separately investigates the impact of sensitivity factors, specifically the pile–wall stiffness ratio and floor plate stiffness, on both structures during the basement construction and serviceability stages. The test results can closely match the numerical simulation. The study results reveal that the wall impacts the bending moment of the pile to some extent. The internal force in the wall is significantly influenced by the lateral deformation of the pile and the floor plate. Compared to conventional designs, this structure significantly reduces the bending moment of the wall, particularly in the composite structure. Additionally, the analysis of sensitivity factors reveals their considerable influence on the pile–wall interaction.

Early activation of hepatic stellate cells induces rapid initiation of retinyl ester breakdown while maintaining lecithin:retinol acyltransferase (LRAT) activity

Lecithin:retinol acyltransferase (LRAT) is the main enzyme producing retinyl esters (REs) in quiescent hepatic stellate cells (HSCs). When cultured on stiff plastic culture plates, quiescent HSCs activate and lose their RE stores in a process similar to that in the liver following tissue damage, leading to fibrosis. Here we validated HSC cultures in soft gels to study RE metabolism in stable quiescent HSCs and investigated RE synthesis and breakdown in activating HSCs.HSCs cultured in a soft gel maintained characteristics of quiescent HSCs, including the size, amount and composition of their characteristic large lipid droplets. Quiescent gel-cultured HSCs maintained high expression levels of Lrat and a RE storing phenotype with low levels of RE breakdown. Newly formed REs are highly enriched in retinyl palmitate (RP), similar to freshly isolated quiescent HSCs, which is associated with high LRAT activity. Comparison of these quiescent gel-cultured HSCs with activated plastic-cultured HSCs showed that although during early activation the total RE levels and RP-enrichment are reduced, levels of RE formation are maintained and mediated by LRAT. Loss of REs was caused by enhanced RE breakdown in activating HSCs. Upon prolonged culturing, activated HSCs have lost their LRAT activity and produce small amounts of REs by DGAT1. This study reveals unexpected dynamics in RE metabolism during early HSC activation, which might be important in liver disease as early stages are reversible. Soft gel cultures provide a promising model to study RE metabolism in quiescent HSCs, allowing detailed molecular investigations on the mechanisms for storage and release.

Broadening bandgaps in a multi-resonant piezoelectric metamaterial plate via bandgap merging phenomena

Locally resonant metamaterials usually have narrow bandgaps, which significantly limits their applications in realistic engineering environments. In this paper, an optimization method based on the genetic algorithm is proposed to broaden bandgaps in multi-resonant piezoelectric metamaterial through the merging of multiple separated bandgaps. Using the effective medium theory, the equivalent bending stiffness and dispersion relationship of a metamaterial plate are first obtained. Then, the criteria for determining the bandgap ranges for the two cases with and without damping are provided and analyzed. Furthermore, based on the bandgap merging phenomena, an optimization method for widening the bandgap is proposed based on the genetic algorithm. By investigating the bandgap widening effects in cases without and with damping, it is found that, when there is no damping, the bandgap can only be slightly widened; while after introducing damping into the transfer functions, the bandgap can be significantly widened by more than 200%. The bandgap widening effects are verified by comparing with finite element simulation results.