Plate Model Research Articles

Evaluation of Unicortical Locking Screw Placement for Torsional Loads in Distal Radius Fractures: A Biomechanical Study in Cadavers.

Background We aimed to compare bio-mechanical outcomes of short-length 75%-length uni-cortical screw (SL75UCS) and full-length 100%-lengthscrews (FL100S) under axial compression (AXC) and torsional compression (TRC) in cadaveric distal radius volar plate model. Methodology A total of 20 wrists from 10 fresh frozen cadavers were included. A 2.5 mm titanium alloy distal radius anatomical platewas placed to the distal radii in full anatomical position, just proximal to the watershed line. Three bi-cortical screws to the shaft of the radius, followed by uni-cortical drilling for distal screwing were placed. Measurement by pulling the drill once it reached the opposite cortex was applied. We selected the screw lengths such that they corresponded to the SL75UCS. In the same configuration for each of the cadavers, we delivered six screws from distal radius holes of the anatomical plate. An oscillating handsaw was used to create an extra-articular distal radius fracture model (AO 23-A3.2). We created a dorsal AP model by performing a 1-cm wedge osteotomy from the dorsal aspect. Complete separation of the volar cortex was achieved. Potting was performed by embedding the shaft of the prepared radius into the polyurethane medium. We placed aluminum apparatus into the distal end to ensure applying of AXC and TRC in bio-mechanistic tests. Results No statistically significant difference of stiffness between the SL75UCS and FL100S both under AXC (p=0.88) and TRC (p=0.82). SL75UCSand FL100S groups did not differ in elastic limit under AXC (p=0.71) and TRC (p=0.71). Maximal force on SL75UCSand FL100S groups were also similar under both AXC (p=0.71) and TRC (p=0.50). Conclusions Our study findings suggest that drilling the dorsal cortex may not be necessary in the management of distal radius fractures. Instead, utilizing SL75UCS could serve as a viable alternative. This approach offers potential advantages in reducing the risk of extensor tendon complications associated with drilling or screw protrusion. It is a safe method under torsional load to avoid drilling of the dorsal cortex and SL75UCS could be performed in order to prevent from extensor tendon complications secondary to drilling or screw protrusion.

On the strength of many-layer fiber-reinforced plates

In Kolpakov and Rakin (2021), the concept of a representative model for multilayer plates was introduced. It was shown that a three-layer representative plate model provides us with complete information about the local stress-strain state (SSS) in a multilayer plate formed from an arbitrary number of layers. In this paper, it is shown that for a many-layer plate (the number of layers is more than 300), the periodicity cell problems (PCPs) corresponding to in-plane (tension/shear) make the main contribution to the local SSS. On one hand, it is a similarity with the uniform plate. On another hand, the solutions to the PCPs corresponding to in-plane (tension/shear) for fiber-reinforced plate are very different from the solutions corresponding to uniform plate.If the number of layers is less than 60, it is necessary to take into account the solutions to the bending/torsion cell problem. In both cases, it is necessary to take into account the skin-boundary layers (which occurs both in tension/shear and bending/torsion PCPs).Using the idea of a representative model, we construct a homogenized strength criterion (HSC) for fiber reinforced plates. As a result of the complex form of the local stress-strain stale in the components of composite, the HSC is built as a computer procedure. Since the representative model is low-dimension one, the procedure is fast.In general, the failure surface is a 5-dimensional surface in 6-dimensional space. For a multilayer plate, the strength criterion depends on three variables (three combinations of tension/shear and bending/torsion). In this case, the failure surface is a 2D surface in 3D space and can be visualized. In multilayer plates, we find many similarities with the classical theory of plates, but at the same time we clearly see quantitative and qualitative differences between multilayer plates and classical information plates. In particular, we see that the maximum of the local stress in composite plate occurs not at the top/bottom surfaces of the plate, but in the deep of the plate.

Crack propagation and induced vibration characteristics of cracked cantilever plates under resonance state: Experiment and simulation

Cracks in aero-engine blades have caused great economic losses and safety hazards in the past decades. High cycle fatigue, as one of the main causes of blade crack propagation, has been of increasing interest in recent years. In this paper, the cantilever plate specimens are selected as the research object to analyze the real crack propagation path and the change of resonance frequencies under the resonance state. First, a joint simulation analysis method based on FRANC3D and ANSYS software is proposed for the analysis of the crack propagation path. The proposed method is verified through crack propagation experiments. Second, a dynamic model for cantilever plates with a real crack propagation path is proposed based on the shell element theory. Finally, the associations between crack propagation lengths and resonance frequencies are studied. Some interesting phenomena are found: the resonance frequency decreases as the crack propagation length increases and the resonance frequencies show a slow decrease, then a constant decrease, and finally a rapid decrease; the nearer the initial crack location is to the root of the cantilever plate, the greater the curvature of the crack propagation path. This study can provide a better understanding of blade fatigue and the reference for analysis of blade crack propagation paths.

New insights into the crustal architecture and tectonic evolution of the Eastern Gulf of Mexico

AbstractThe Gulf of Mexico is an intraplate oceanic basin where rifting commenced in the Late Triassic, leading to drifting and ensuing oceanic accretion by Middle‐Late Jurassic, which ceased by the Early Cretaceous. Its tectonic evolution encompasses multiple rifting phases dominated by orthogonal extension, variable magmatism and salt deposition. This complex tectonic history is recorded within the rifted margins of the Gulf of Mexico, including along the eastern part of the basin, where considerable uncertainty remains regarding the tectonic evolution and resulting crustal configuration. This study presents new insights into the crustal types and an updated tectonic framework for the Florida margin. An integrated analysis of seismic and potential field data allows us to characterize the nature of the crust, which shows wide zones of hyperextended continental crust, seaward dipping reflection (SDR) packages, exhumed mantle and magmatic crust. Our results propose elements that could improve the plate model of the Gulf of Mexico, by accounting for the polyphase nature of rifting, the counter‐clockwise rotation of the Yucatan block and the observed increase in magmatic supply.

A numerical study of palatal snoring.

The main purpose of this paper is to investigate the upper airway (oral and/or nasal) with different inhalation speeds and obstruction depths to generate remarkable notes on palatal snoring and obstructive sleep apnea (OSA). Another important aspect is to study different soft palate biomechanical properties and their relationships with different physical parameters on palatal snoring and OSA. The human upper-airway is modelled in 2D, and a cantilever plate model principle is adopted for the soft palate during fluid-structure interaction (FSI) simulations. Various scenarios are investigated under different inhalation speeds to characterize palatal snoring and OSA in terms of relevant physical parameters. The parameters most prone for palatal snoring andOSA are obtained for soft material, the highest obstruction depth, and oral inhalation. Also, it is shown that the biomechanical properties of the human upper airway are the most sensitive parameters affecting the dynamics of the soft palate. The numerical modeling approach presented allows a better understanding of palatal snoring and may be useful for confirming clinical results as well as for further design of new treatments and therapies.

Influence of Tuning Potential Parameters on Wettability of Smooth Copper Plate: A Molecular Dynamic Study

The influences of interactions between copper plate and nano-water droplets on wettability with different solid–liquid potential parameters were studied, and the spread of droplets was compared and analyzed using the molecular dynamics method. The diameter of droplet spreading and the amount of water molecules adsorbed on the copper gradually increased with the potential parameters, whereas the absolute potential energy value between copper and water also increased. Negative potential energy represents the attraction force between solid atoms and liquid molecules, and the attraction grows stronger with the large absolute value of negative potential energy. The heat transfer performance of the wettability surface can be explained by analyzing the force of solid and liquid from the perspective of energy. These results are of great significance for establishing the wettability model of a smooth plate correctly and the design and manufacture of a special functional surface.

Comparison of curative effect between OBS assisted by 3D printing and PFNA in the treatment of AO/OTA type 31-A3 femoral intertrochanteric fractures in elderly patients.

To compare and analyze the Ortho-Bridge System (OBS) clinical efficacy assisted by 3D printing and proximal femoral nail anti-rotation (PFNA) of AO/OTA type 31-A3 femoral intertrochanteric fractures in elderly patients. A retrospective analysis of 25 elderly patients diagnosed with AO/OTA type 31-A3 femoral intertrochanteric fracture was conducted from January 2020 to August 2022 at Yan'an Hospital, affiliated to Kunming Medical University. The patients were divided into 10 patients in the OBS group and 15 in the PFNA group according to different surgical methods. The OBS group reconstructed the bone models and designed the guide plate by computer before the operation, imported the data of the guide plate and bone models into a stereolithography apparatus (SLA) 3D printer, and printed them using photosensitive resin, thus obtaining the physical object, then simulating the operation and finally applying the guide plate to assist OBS to complete the operation; the PFNA group was treated by proximal femoral nail anti-rotation. The operation time, the intraoperative blood loss, Harris hip score (HHS), Oxford Hip Score (OHS), and complications were compared between the two groups. The operation time and the intraoperative blood loss in the PFNA group were less than that in the OBS group, and there was a significant difference between the two groups (P < 0.05). The HHS during the 6th month using OBS was statistically higher than PFNA (P < 0.05), however, there were no significant differences in OHS during the 6th month between the OBS group and PFNA group (P > 0.05). The HHS and OHS during the 12th month in the OBS group were statistically better than in the PFNA group (P < 0.05). The OBS assisted by 3D printing and PFNA are effective measures for treating intertrochanteric fractures. Prior to making any decisions regarding internal fixation, it is crucial to evaluate the distinct circumstances of each patient thoroughly.

Himalayan Pyracantha crenulata (D.Don) M.Roem. leaf and fruit extracts alleviate algesia through COX-2 and Mu-opioid receptor mediated pathways

Ethnopharmacological relevancePyracantha crenulata (D.Don) M.Roem., a plant of high nutritional and medicinal value is traditionally employed for its analgesic property in joint and body pain in the Kumaun region of Western Himalaya. Aim of the studyTo validate the traditional claims for analgesic property of Pyracantha crenulata. MethodsHydroethanolic extract of P. crenulata leaves and fruits were tested for their analgesic potential in rodent models for algesia by tail immersion test, tail flick test, Eddy's hot plate model, and formalin induced paw irritation test in Wistar rats. Molecular docking and dynamics studies were also performed to understand the possible mechanisms. ResultsBoth P. crenulata fruit extract and leaf extract exhibited significant amelioration in all the tested experimental models of algesia acting through central and peripheral mechanisms. The efficacy in reducing nociception was found comparable to diclofenac that was used as a reference standard. Molecular docking and dynamic simulation studies further established binding affinity of gallic acid (confirmed to be present in P. crenulata leaf extract through HPTLC profiling) with cyclooxygenase-2 (COX-2) and mu-opioid receptors, suggesting the modulatory effect of these extracts on COX-2 and mu-opioid receptors in combating algesia. ConclusionP. crenulata extracts produce analgesic effects plausibly through COX-2 and mu-opioid receptor mediated pathways.

Formulation of non-local space-fractional plate model and validation for composite micro-plates

It is challenging to design nano/micro-devices because of their small size and tight engineering tolerances. Computer-aided design uses mathematical models of device parts, but contemporary models are not precise enough to capture all characteristics of the materials at the nano/micro-scale. In this work, we propose a novel mathematical model for composite nano/micro-plates in bending in the framework of a space-fractional continuum mechanics approach. This model yields closer mapping of experimental results compared to existing formulations. The developed theory is named the space-Fractional Kirchhoff–Love Plate (s-FKLP). We investigate how the parameters of the s-FKLP model, responsible for the scale effect description, affect the bending behavior of the micro-plates, considering different support conditions. In addition, we compare the results predicted by s-FKLP with the previously developed simpler (one-dimensional) space-Fractional Euler–Bernoulli Beam (s-FEBB) model to show that the choice of structural analysis strategy can influence design decisions. Despite its greater complexity, the s-FKLP is a more versatile approach to modeling micro-sized structures than the s-FEBB. The proposed s-FKLP model is empirically validated using real sandwich micro-plates. We conclude model alignment with the experimental data indicating that the model is suitable for representing sandwich micro-plates. We also find that the model’s length scale parameter corresponds to the microstructure’s grain size. The findings of this research may have implications for future work in the design and optimization of micro-sized devices.

Extra-Articular Distal Humerus Plate 3D Model Creation by Using the Method of Anatomical Features.

Proper fixation techniques are crucial in orthopedic surgery for the treatment of various medical conditions. Fractures of the distal humerus can occur due to either high-energy trauma with skin rupture or low-energy trauma in osteoporotic bone. The recommended surgical approach for treating these extra-articular distal humerus fractures involves performing an open reduction and internal fixation procedure using plate implants. This surgical intervention plays a crucial role in enhancing patient recovery and minimizing soft tissue complications. Dynamic Compression Plates (DCPs) and Locking Compression Plates (LCPs) are commonly used for bone fixation, with LCP extra-articular distal humerus plates being the preferred choice for extra-articular fractures. These fixation systems have anatomically shaped designs that provide angular stability to the bone. However, depending on the shape and position of the bone fracture, additional plate bending may be required during surgery. This can pose challenges such as increased surgery time and the risk of incorrect plate shaping. To enhance the accuracy of plate placement, the study introduces the Method of Anatomical Features (MAF) in conjunction with the Characteristic Product Features methodology (CPF). The utilization of the MAF enables the development of a parametric model for the contact surface between the plate and the humerus. This model is created using specialized Referential Geometrical Entities (RGEs), Constitutive Geometrical Entities (CGEs), and Regions of Interest (ROI) that are specific to the human humerus bone. By utilizing this anatomically tailored contact surface model, the standard plate model can be customized (bent) to precisely conform to the distinct shape of the patient's humerus bone during the pre-operative planning phase. Alternatively, the newly designed model can be fabricated using a specific manufacturing technology. This approach aims to improve geometrical accuracy of plate fixation, thus optimizing surgical outcomes and patient recovery.

A Simplified Lattice Boltzmann Boundary Conditions for Gas Transport in Self-Affine Microchannels with an Inherent Roughness of in a Tight Reservoir

A simplified method of determining lattice Boltzmann boundary conditions based on self-affine microchannels with an inherent roughness in a tight reservoir is presented in this paper to address nonlinear efficiency problems in fluid simulation. This approach effectively combines the influence of rough surfaces in the simulation of the flow field, the description of L-fractal theory applied to rough surfaces, and a generalized lattice Boltzmann method with equivalent composite slip boundary conditions for inherent roughness. The numerical simulations of gas slippage in a two-dimensional plate model and rough surfaces to induce gas vortex reflux flow are also successfully carried out, and the results are in good agreement with the simulation results, which establishes the reliability and flexibility of the proposed simplified method of rough surfaces. The effects of relative average height and fractal dimensions of the rough surfaces under exact boundary conditions and equivalent coarsened ones are investigated from three perspectives, namely those of the average lattice velocity, the lattice velocity at average height position at the outlet, and the coefficient of variation for lattice velocity at average height position. It was found that the roughness effect on gas flow behavior was more obvious when it was associated with the enhanced rarefaction effect. In addition, the area of gas seepage was reduced, and the gas flow resistance was increased. When the fractal dimension of the wall was about 1.20, it has the greatest impact on the fluid flow law. In addition, excessive roughness of the wall surface tends to lead to vortex backflow of the gas in the region adjacent to the wall, which greatly reduces its flow velocity. For gas flow in the nanoscale seepage space, wall roughness hindered gas migration rate by 84.7%. For pores larger than 200 nm, the effects of wall roughness on gas flow are generally negligible.

Numerical Investigation on Effect of Bubbles Arrangement and Volume Fraction on Apparent Viscosity of Bubbly Suspensions

Background:: Bubbly suspensions can be often run into in natural and industrial processes. The addition of bubbles with different sizes can lead to a significant change in the rheological properties of a matrix liquid. It is extremely significant to fully understand the rheological properties of bubbly suspensions for improving process efficiencies and optimizing productive processes. background: Bubbly suspensions can be often run into in natural and industrial processes. The addition of bubbles of different sizes can greatly change the rheological properties of matrix liquid. It is extremely significant to fully understand the rheological properties of bubbly suspensions for improving process efficiencies and optimizing productive processes. Objective:: The objective of this study is to explore qualitatively the physical law and internal mechanism of the apparent viscosity of suspensions formed by a Newtonian liquid containing different bubbles. Methods:: Based on the parallel plate model of shear flow, the volume of fluid method (VOF) was used to investigate the effect of bubble arrangement and volume fraction on the apparent viscosity of bubbly suspensions at low volume fractions. The piecewise linear interface calculation (PLIC) method was applied to reconstruct the interface based on the phase function. Results:: The present results show that the relative viscosity (ηr) of bubbly suspensions shows a nonlinear change with an increase in bubble volume fraction (ϕ). When the capillary number (Ca) is less than 0.6, ηr shows a nonlinear increase with an increase in ϕ (ηr increases from 1 to 1.03 with an increase in ϕ from 0 to 2.94% at Ca=0.1). However, Ca is greater than or equal to 0.6, ηr shows a nonlinear decrease with an increase in ϕ (ηr decreases from 1 to 0.92 with an increase in ϕ from 0 to 2.94% at Ca=2.5). Even if ϕ is the same, different arrangements of bubbles can lead to different magnitudes of apparent viscosity of bubbly suspensions Conclusion:: As ϕ increases, the region of low shear rate increases, which leads to a non−linear decrease in the relative viscosity. When ϕ is the same, the different arrangements of bubbles can lead to different effects on bubble dynamics and flow fields. This results in different viscous dissipation in bubbly suspensions. Thus, the apparent viscosity of bubbly suspensions is different. other: Nothing

Flexural-gravity wave interaction with multiple vertical cylinders of arbitrary cross section frozen in an ice sheet

The interaction problem of flexural-gravity wave with multiple vertical cylinders frozen in an ice sheet on the surface of water with finite water depth is considered. The linearized velocity potential theory is adopted for fluid flow, and the thin elastic plate model is applied for ice sheet deflection. Each cylinder is bottom-mounted, and the shape of its cross section can be arbitrary while remaining constant in the vertical direction. The velocity potential is expanded into an eigenfunction series in the vertical direction, which satisfies the boundary condition on the ice sheet automatically. The horizontal modes, which satisfy the Helmholtz equations, are then transformed into a series of boundary integral equations along the ice sheet edges or the intersection of the ice sheet with the cylinders. The problem is then solved numerically by imposing the ice sheet edge condition together with the impermeable condition on the cylinders. The solution is exact in the sense that the error is only due to numerical discretization and truncation. Computations are first carried out for single and multiple vertical circular cylinders, and good agreements are obtained with the semi-analytical solution. To resolve the difficulty of excessive computation at a large number of cylinders, the effect of the evanescent wave of a cylinder on those at large distance is ignored. This allows for the case of a large number of cylinders in different arrangements to be simulated. Extensive results are provided. Their physics and practical relevance are discussed.

In-vitro and in-vivo assessment of the anti-diabetic, analgesic, and anti-inflammatory potenstials of metal-based carboxylates derivative

In the current research work, an amide based metal carboxylate chemical ([((5-((5-(2-hydroxyethyl)-4-methylthiazol-3-ium-3-yl)methyl)-2-methylpyrimidin-4-yl)amino)bis((4-((4-methoxy-2-nitrophenyl)amino)-4-oxobutanoyl)oxy)zinc]) was identified as anti-diabetic analgesic and anti-inflammatory. The identified chemical(MT-1) was tested for acute toxicity (the MT-1 was fund safe), antidiabetic analgesic, and anti-inflammatory potentials. The in-vitro study was conducted for antidiabetic enzyme inhibition (α-amylase and α-glucosidase) and the in-vivo studies included analgesic (acetic acid-induced writing and hot plate model) and anti-inflammatory (carrageenan etc induced edema) effects. The tested compound showed 88.63% (IC50 = 3.23 μg/ml) and 89.10%(IC50 = 5.10 μg/ml) againstα-amylase and α-glucosidase respectively. A significant (p < 0.001) analgesic effect was noted by MT-1 in acetic acid-induced animal models with a percent effect of 86.00, 60.,06, and 55.29 at the tested doses of 20, 1,0, and 5 mg/kg respectively. In the case of the hot plate model, the MT-1 showed a significant (p < 0.001) effect with maximum percent prolongation in latency observed after 60 min.08, 22.2,9, and 11.61) against 20, 1,0, and 5 mg/kg. The analgesic effect in the hot plate model was significantly (p < 0.01) reversed by the injection of naloxone (0.125 mg/kg). The paw edema induced by carrageenan, histamine, bradykinin, arachidonic acid, and PGE2 was significantly antagonized with percent attenuation of 34.09, 33.57, 34.60, 34.14, and 48.04 respectively. Furthermore, to predict the interactions between the MT-1 compound and COX-2 molecular docking was carried out and the result was compared with the standard compound. The docking score of MT-1 was predicted as −6.30 while that of Diclofenac was predicted as −6.82. Both compounds made several hydrogen bond interactions with the active site of the COX-2 enzyme. The docking study revealed the potent inhibitory potential of the compound MT-1 against the COX-2 receptor.

Free vibration analysis of a skew sandwich plate with bamboo biocomposite and polylactic acid core under temperature and moisture conditions

This article investigates the impact of moisture and temperature on vibration characteristics of bio-composite skew-laminated composite sandwich (SLCS) plates. The bio-composite SLCS plates with bamboo face sheets and polylactic acid (PLA) cores are biodegradable, radiolucent, lightweight, high strength, and withstand vibrations. The coupled thermo-elastic and hygro-elastic finite element (FE) model of the SLCS plate is derived using the higher-order shear deformation theory (HSDT). An initial stress stiffness matrix is developed using the nonlinear strain-displacement relations to incorporate the effect of temperature and moisture in FE modeling. Temperature and moisture-dependent material properties of bamboo fiber-reinforced biocomposite (BFB) and PLA core are employed for the analysis. A comprehensive investigation has been carried out to study the impact of moisture and temperature situations with different geometrical parameters and various skew angles on the frequency of the SLCS plate. The results indicate that the biocomposite sandwich material has excellent potential for structural applications under different environmental conditions in various applications like food processing, and biomedical applications, including MRI and CT scan beds.

A Thin Elastic Plate Model for Thermally Contracting Young Oceanic Lithosphere: Insights From Comparison With Modern Seafloor Observations

AbstractWe find at fast‐ and intermediate‐spreading seafloor that their ridge‐parallel bathymetric profiles between two neighboring fracture zones, excluding the part of the seafloor inward to fracture zone (FZ) valley, are predominantly upward concave. The temporal evolution of the bathymetric profiles from the lithosphere formed at the Chile Rise is characterized by (a) the rapid growth of the middle deflection to about 200 m relative to the ends for the first few millions of years and (b) a steady state afterward. We show that these characteristics and the upward‐concave sense of bending can be reasonably explained as the flexure of a thin elastic plate contracting thermally from the top while cooling. The best‐fitting model needs only about 10% of the thermal bending moment based on the half‐space cooling model and the free‐end assumption. Our model is consistent with the recent observations that oceanic lithosphere is cut open at a FZ valley, which disprove the previous assumption that ocean floor is bent down forming the valley walls.

Twisting tubes as soft robotic valves

Soft materials and structures have been blooming with utmost popularity, showing great potential as soft machines for delicate design and new application. Among them, the simple structures of soft tubes are widely applied in engineering. However, a comprehensive understanding of their twisting behaviors is still lacking. In this study, the complete response of hyperelastic tubes under large-scale torsion is explored. The helical-buckling critical conditions and post-buckling characteristics of twisting tubes are revealed via simulations and experiments. Notably, it is found that a sequence of equal-length kinks along the tubing axis appear as the subsequent buckling of twist after the first helical buckling. And the factors determining the geometry of the periodic kink structure are discussed. To efficiently interpret and predict the kink responses, we employ an equivalent plate model based on finite element analysis. Additionally, the self-locking mechanism of kink for gas-blocking purpose and the pre-stretch effect on the twisting behaviours are investigated. Finally, mechanics design of twisting tubes served as soft valves and its application in soft robotics are demonstrated. This study with insights in extreme twist of elastic tubes is hoped to provide a reference to the off-the-shelf tubes widely applied in industry and inspire new flashes of soft machines.

Electro-mechanical vibro-acoustic characteristics of submerged functionally graded piezoelectric plates with general boundary conditions

The present paper focuses on studying the underwater electro-mechanical vibro-acoustic characteristics of functionally graded piezoelectric material (FGPM) plates with general boundary conditions. For this purpose, the collocation points method is firstly developed to handle vibro-acoustic coupling, which can directly calculate the virtual work of secondary sound pressure via an easy double integral, without pre-simplifying the complex quadruple integral. The proposed FGPM plate model is established in the framework of first-order shear deformation theory (FSDT) and second type constitutive equations of piezoelectric materials, and the macroscopically inhomogeneous electro-mechanical properties are considered by means of Voigt model. The multi-physical fields including electric, mechanical and acoustic fields are uniformly extended in Chebyshev polynomials. Meanwhile, penalty function method is introduced to satisfy the arbitrary mechanical and electric constraints. All energy formulations are processed by Rayleigh-Ritz procedure and a standard governing equation is finally derived. Based on the proposed unified model, the convergence and accuracy for solving vibration and acoustic radiation of FGPM plates are validated firstly. Additionally, the influence of some key parameters on underwater vibro-acoustic characteristics of FGPM plates is fully examined. The results of this paper may provide a reference for future application of FGPM-based smart structures.

Geometric eccentricity effect on thickness-shear vibration of an elliptical flexoelectric crystal plate

In this paper, a thickness-shear vibration model for a two-dimensional finite flexoelectric crystal plate with slowly varying thickness and elliptical cross section is presented. The influences of eccentricity and flexoelectricity on the fundamental frequencies of thickness-shear vibration and electric potential distributions under short circuit boundary condition are investigated. The proposed model uses the first order McLaughlin series to approximate the elliptical function and the first derivative of elliptical function is ignored since the plate thickness varies slowly. For the finite plate, the symmetric mode in length and antisymmetric mode in thickness are adopted for the displacement function. In addition, only the shear strain gradient through the thickness is used in the mathematical model for the thin and long flexoelectric crystal plate. By implementing the variational principle, the governing equations are obtained and further solved by the Galerkin method. The obtained frequencies of thickness-shear mode are expressed in terms of eccentricity and length-to-thickness ratio. The results show that the eccentricity has great influence on the nondimensional fundamental frequencies. A small reduction in eccentricity results in significant increment of the nondimensional frequency implying that it is possible to increase the fundamental frequency by changing the cross section of the elliptical flexoelectric plate. The flexoelectric effect is also found to affect the nondimensional frequency and electric potential distribution significantly. Thus, for accurate design of nano/micro scale high precision and high frequency flexoelectric/piezoelectric devices, flexoelectricity must be taken into consideration.

Finite element modeling of programmable liquid crystal elastomer plates and its application in text display

AbstractLiquid crystal elastomers (LCEs) have wide and potential applications in artificial muscles, soft robots, biomedical devices, and so on. On the application of LCE plate in text display, different from others' work where specially shaped ultraviolet (UV) lighting is used, in this paper, the programmable deformation of LCE plates with arbitrary liquid crystal orientation subjected to uniform light illumination is investigated. A photomechanical coupling finite element method (FEM) is developed, in which the impact of the shear strains induced by light is taken into account. Inspired by the FEM, the LCE plate is divided into finite small regions. By altering the liquid crystal orientation of each region in the LCE plate, the ability to generate 24 letters and 10 numbers through light‐induced deformations is demonstrated. Matrixes of the liquid crystal orientation corresponding to each letter and number are provided. This work indicates that it is possible for blind people to read text information by touching the deformed LCE plate.