Plate Model Research Articles

Newly designed plate for the treatment of posterolateral tibial plateau fractures: a finite element analysis

BackgroundThis study investigated the biomechanical properties of a new plate used for the treatment of posterolateral tibial plateau fractures using finite element analysis.MethodsThe study groups were as follows: group PM, model of the new plate with posteromedial tibial plateau fracture; group PL, model of the new plate with posterolateral tibial plateau fracture; and group PC, model of the new plate with posterior tibial plateau fracture. We used two loading modes: uniform loading on the entire plateau, and loading on the posterior plateau. Data such as the displacement of the fracture and distribution of stress on the new plate and screws were recorded and analyzed.ResultsWhen the whole plateau was loaded, the displacement of fractures in groups PM, PL, and PC were 0.273, 0.114, and 0.265 mm, respectively. The maximum stresses on the plates in groups PM, PL, and PC were 118.131 MPa, 44.191 MPa, and 115.433 MPa. The maximum stresses on the screws in Groups PM, PL, and PC were 166.731, 80.330, and 164.439 MPa, respectively. When the posterior tibial plateau was loaded, the displacement of the fractures in groups PM, PL, and PC was 0.410, 0.213, and 0.390 mm, respectively. The maximum stresses on the plates in groups PM, PL, and PC were 194.012 MPa, 72.806 MPa, and 185.535 MPa. The maximum stresses on the screws in Groups PM, PL, and PC were 278.265, 114.839, and 266.396 MPa, respectively.ConclusionThe results of this study revealed that titanium plates have good fixation effects in all groups; therefore, the use of the new plate for posterolateral tibial plateau fractures appears to be safe and valid.

Error analysis of the element-free Galerkin method for a nonlinear plate problem

In this work, we derive a geometrically nonlinear plate model based on the Kirchhoff hypothesis and the large deflection hypothesis, and provide an error analysis of the corresponding element-free Galerkin method. The penalty method is employed to enforce boundary conditions. The error estimate explicitly depends on nodal spacing, number of monomial basis functions, continuity of weight functions, and penalty factors, which provides some practical choices among these key parameters in engineering applications. In addition, we offer guidance on selecting appropriate penalty factors to improve numerical accuracy. Numerical experiments, involving clamped square and circle plates with uniform and nonuniform nodes, as well as a plate model with a corner singularity, are presented to validate the theoretical results.

Equivalent plate model of shape memory polymer composite based variable height corrugated structure

In this work, an equivalent plate model for a shape memory polymer composite based corrugation structure with varying height, for morphing application, is developed. A thermodynamically consistent constitutive relation based on temperature dependent phase transformation concept for shape memory polymer matrix is used in the composite model. The homogenization model is based on the equivalence of strain energy of a representative unit volume. Following validation, as an application, commonly used airfoil profile NACA 63210 was considered to demonstrate the model utility. Parametric studies have been undertaken to investigate the influence of corrugation parameters like thickness and number of corrugations.

Zone‐based failure risk assessment of fatigue crack growth caused by initial defects in powder turbine disc

AbstractIn this research, A zone‐based failure risk assessment (FRA) method of fatigue crack growth (FCG) caused by initial defects in the FGH96 alloy turbine disc is developed. Firstly, the initial defects distribution in the FGH96 alloy turbine disc is calculated based on the defect data. Subsequently, a probabilistic short FCG life model is established, taking into account the dispersion in grain size. Meanwhile, a probabilistic long FCG life model is established, incorporating the life dispersion factor. To calculate the Stress Intensity Factor (SIF) at any position of the disc, the general weight function method and the rectangular plate model are established. Finally, the zoning process is established, enabling a FRA that considers the FCG due to initial defects. The results indicate that the number of cycles corresponding to a 0.13% failure probability of the turbine disc is 7150, and the percentage of failures in each zone is analyzed.

Detecting Cracks on Plates Using Reflections of Fundamental Symmetric and Anti-symmetric Lamb Waves from Defect

Introduction: Ultrasonic Lamb waves can achieve long-range inspection on plate-like structures and can even detect unreachable cracks and defects. There are multiple modes under a certain generation frequency with most of them dispersive. Method: The dispersion curves of Lamb wave in a steel plate were given by numerical calculation. A 2-D finite element (FE) model of a steel plate was promoted. The fundamental symmetric and antisymmetric Lamb waves were generated by uploading symmetrical and anti-symmetrical displacements on one side of the plane. The wave reflects when it comes across the defect and the edge of the plate. Mode conversion will occur after the asymmetrical discontinuities of the structure. Result: The theoretical and numerical results of the values of group velocities of S0 and A0 in a steel plate show well agreement. The maximum amplitude of the converted A0 wave from the interaction of the incident S0 wave with the cracks was observed. The amplitude will first rise then fall under any depth of the defects. The relationship between the defect reflection and the length as well as the depth of defects were simulated based on the FE model. Phase reversion and phase delay were discovered by controlling the defect size changing in one dimension. The reflection coefficient increases linearly with the defect length while the depth is constant, as well as the defect depth while the length is constant. method: Using finite element (FE) method to simulate Lamb wave motion in a plate, as well as experiments on steel plates with artificial defects. Conclusion: Experiments on steel plates with artificial defects including thorough holes and tapered holes were carried out using ISONICA STAR. The results also show that when the defect size changes in one dimension such as the thorough holes, the reflection coefficient increases linearly correspondingly. However, the testing results of the taper holes were inconsistent with the regulation as the size increases in both the length and the depth. result: The values of group velocities were calculated by time-of-flight method to identify specific modes. The results were calibrated and showed well agreement with theoretical data. Mode conversion will appear when the wave comes across asymmetric discontinuities of the structure.

Useful but overused? The “plate model” as a food educational tool in home economics

ABSTRACT The plate model is widely used to promote healthy eating. Despite extensive adoption in dietary guidelines, the model’s role in food educational practices is scarcely studied. The present study aimed to explore the plate model as a food educational tool in the school subject Home Economics (HE). Use of the plate model was investigated with Rogoff’s three planes of analysis as a framework. The research question was: “How is the plate model used in a food educational practice, considering institutional, interpersonal, and personal planes?” Data from video-recorded classroom observations, focus groups, interviews, and text documents were analyzed. The data were generated through a case study, with twelve students and two HE-teachers followed over the course of a school year. Results show how the plate model was framed as the right way of eating. Nutritionally “proper” food was described, with the model functioning as a bridge linking (abstract) nutritional content with (concrete) dishes. This way of using the model might hamper understandings of fundamental principles for nutritional classification. Moreover, those who do not eat plate model-type dishes may be wrongly judged. Supported by empirical events, this study shows how the plate model can be useful – but also overused – in food education.

Thin ferromagnetic plates with magnetostriction

In this paper, we establish the existence of global-in-time weak solutions for the Landau–Lifschitz–Gilbert equation with magnetostriction in the case of mixed boundary conditions. From this model, we derive by asymptotic method a two-dimensional model for thin ferromagnetic plates taking into account magnetostrictive effects.

Free-Vibration Analysis for Truncated Uflyand–Mindlin Plate Models: An Alternative Theoretical Formulation

Plates are flat structural elements whose thickness is small in relation to the size of the surface. Their use may include engine foundations, reinforced concrete bridge elements or parts of various floating structures. Consequently, knowledge of their mechanical behavior under static and dynamic loads is of primary importance in engineering applications and of interest from a structural point of view. As a result, numerous works existing in the literature have investigated the mechanical properties of plates using various plate models, such as Reissner’s theory, Levinson’s theory, Kirchhoff’s theory and Mindlin’s theory, and their static and dynamic behavior has been examined. In the present paper the truncated Uflyand–Mindlin plate equation is proposed. According to Uflyand–Mindlin theory, an alternative theoretical formulation is presented for the free-vibration analysis of plates, and the equations of motion and the general corresponding boundary conditions are derived. This paper develops the truncated Uflyand–Mindlin plate equation, i.e., without the fourth-order derivative, by means of the direct method and variational formulation. The first-order shear deformable plate theory developed by Elishakoff, which takes into account rotational inertia and shear deformation and does not include a fourth-order time derivative, is variationally derived here. This derivation complements that performed by Mindlin some 70 years ago. The innovative aspect of the suggested strategy is that variational and direct methods for studying plate dynamics are analogous. Finding the third equation of the reduced Uflyand–Mindlin equations, the accompanying boundary conditions and their mathematical resemblance are the goals of the presented formulations. In order to solve the dynamic equilibrium problem of a truncated Uflyand–Mindlin equation via a variational formulation, it is demonstrated that the differential equations and the corresponding boundary conditions have the same form as those found using the direct technique. This paper successfully completes this task. Finally, in order to validate the effectiveness and correctness of the proposed procedure, a numerical example of the case of a plate simply supported at all four ends is proposed.

Experimental study and optimal design of UHPC T‐shaped beam

AbstractIn this paper, the ordinary reinforced UHPC T‐shaped beam, steel plate reinforced UHPC T‐shaped beam and prestressed UHPC T‐shaped beam were compared by conducting the flexure test. The vertical displacement, crack development, strain change, and crack resistance were discussed. The steel plate reinforced UHPC T‐shaped beam shown better cracking resistance and mechanical properties. Based on the research, the multi‐scale finite element model of the steel plate reinforced UHPC T‐shaped beam was established, and the influence parameters were analyzed. The beam height, steel plate thickness and web thickness shown great influence on the ultimate bearing capacity of the beam. The bearing capacity calculation formulas of the steel plate reinforced UHPC T‐shaped beam based on the plastic strengthening model of the steel were proposed. The calculation results shown good agreement with the test value.

Nonlinear aero-thermo-elastic flutter analysis of stiffened graphene platelets reinforced metal foams plates with initial geometric imperfection

Due to its lightweight design and high load-bearing capacity, the stiffened plate structure is extensively applied in the passive control of aircraft flutter. However, the evolution mechanism of the nonlinear response of stiffened plates within the unstable region remains unclear. In particular, there is a lack of research on the nonlinear aero-thermo-elastic properties of stiffened plates with initial geometric imperfection. Inspired by this, this article investigates the stability and post-instability behavior of stiffened geometrical imperfect graphene platelets reinforced metal foams (GPLRMF) plates under combined thermal load and aerodynamic pressure. Graphene platelets (GPLs) and foam are distributed evenly or unevenly in the plates, while the material properties are calculated by modified Halpin-Tsai model and rule of mixture. Considering initial geometric imperfection, the models of plates and stiffeners are established by first-order shear deformation (FOSD) plate and Timoshenko beam theories, respectively. Using the linear piston theory to simulate supersonic aerodynamic pressure. The stability boundary of stiffened plates is determined by eigenvalue analysis. The Newton-Raphson approach is used to simulate the aero-thermo-elastic static response of stiffened plates, and the dynamic post-flutter behavior of the stiffened plate is determined through the Runge-Kutta method. Finally, the effects of initial geometric imperfection, material parameters (foam distribution type, porosity coefficient, GPLs weight fraction and GPLs distribution type), and stiffeners (size, position, and stiffening scheme) on the thermal aeroelastic behavior of stiffened GPLRMF plates are revealed. It can be found that the presence of initial geometric imperfection will significantly change the nonlinear flutter behavior of the stiffened plates.

Flexural Behavior of a New Precast Insulation Mortar Sandwich Panel

This article introduces the experimental and analytical research results of two precast insulation mortar concrete sandwich panels (PIMSP) and two precast concrete composite panels as one-way slabs under bending load. Obtaining a prefabricated floor slab that can balance thermal insulation and structural performance can reduce material consumption and increase inter-story usage height. As the sandwich material for PIMSP, insulation mortar with a strength of 6 MPa was used. Truss-shaped shear connectors were used for shear force transfer. Then, finite element analysis was used to analyze and study the unidirectional flat plate model. The results showed that the tested PIMSP achieved a complete composite effect in the elastic stage and a semi-composite effect in the plastic stage. The PIMSP crack pattern resembles that of a precast concrete slab when utilized as a one-way slab. The load transfer capacity of truss-shaped shear connectors is relatively small, and it is mainly used as a connection between floors. Experiments have demonstrated that PIMSP panels can serve as a structural substitute for regular concrete floors in residential buildings.

ANALGESIC EFFECT OF “DINH THONG PHONG” CAPSULES ON EXPERIMENTAL ANIMALS

Purpose: Evaluate the analgesic effect of “Dinh Thong Phong” capsules on experimental animals. Subjects and Methods: “Dinh Thong Phong” capsules, meeting the standard criteria, were evaluated for analgesic effect on white mice. In particular, the central analgesic effect was assessed using the hot plate model, peripheral analgesic effect was assessed using the writhing pain model. Results: In the hot plate model, “Dinh Thong Phong” capsules at a dosage of 860 mg/kg and 2,580 mg/kg significantly increased the reaction time to heat (p < 0.001) compared to the control group. The difference in reaction time to heat between the groups using “Dinh Thong Phong” capsules and the group using codeine phosphate at a dose of 20 mg/kg was not statistically significant (p > 0.05). In the writhing model, “Dinh Thong Phong” capsules at a dose of 860 mg/kg and 2,580 mg/kg significantly reduced the number of writhing episodes (p < 0.001) compared to the control group. The difference in the number of writhing episodes between the groups using “Dinh Thong Phong” capsules and the group using aspirin at a dose of 150 mg/kg was not statistically significant (p > 0.05).

Design a low-frequency vibration energy harvesting device based on a square spiral beam local resonant phononic crystal

Self-powered miniature wireless sensors play a crucial role in Internet of Things technology. Harvesting low-frequency environmental vibrations to achieve self-powering of sensors is a current hot topic in research. In this study, a square spiral beam local resonant phononic crystal is designed for low-frequency vibrational energy harvesting. Initially, the bandgap and vibrational modes of an ideal phononic crystal at infinite period are analyzed by the finite element method; the possibility of using the structure to harvest vibrational energy is explored. Subsequently, a PnC plate model with a unit cell is built, and its vibrational modes are analyzed, verifying that it possesses similar vibrational properties. Following this, a piezoelectric vibration energy harvesting device is assembled and its energy harvesting performance is analyzed. Numerical simulations indicate that the designed device can achieve a maximum power density of 52.14 μW/cm2. Physical experiments validate the excellent energy harvesting performance of the device. The device offering a new option for designing self-powered devices for wireless miniature sensors.

Asymptotically correct isoenergetic formulation of geometrically nonlinear anisotropic plates

In the present work, a new displacement-based Equivalent Single Layer (ESL) plate theory has been developed using the Variational Asymptotic Method (VAM) and the principle of isoenergetics. In contrast to the existing assumption-based ESL plate theories, the proposed VAM-based plate theory is devoid of any presuppositions. The VAM decouples the 3D plate problem into a 1D through the thickness analysis and a 2D planar problem. Closed form solutions have been obtained for the 1D problem in terms of 2D displacement variables and their higher-order derivatives. The complexity involving higher-order derivatives of 2D displacement variables has been simplified through the isoenergetic principle ensuring a similar rate of convergence for strains as well as displacements. Solutions for various field variables have been compared against the benchmark problems available in the literature and 3D FEA. These comparisons demonstrate the accuracy, efficiency, and versatility of the present methodology. Key contributions of the present work are (a) First principles-based derivation of the reduced-order 2D plate model from the 3D model energy. (b) The plane stress condition as well as the quadratic variation of transverse shear stress and strain are natural outcomes of the present mathematical framework. (c) This leads to zero tangential traction boundary conditions on the plate surface. (d) The effectiveness of capturing higher-order behavior at lower-order results in simplified analysis, reduced computational complexity and increased efficiency.

Application of Machine Learning in Fracture Analysis of Edge Crack Semi-Infinite Elastic Plate

This paper discusses the application of machine learning techniques, notably artificial neural networks (ANN), in the fracture analysis of semi-infinite elastic plates with edge cracks. The Stress Intensity Factor (SIF) model for a semi-infinite plate with a tip crack is employed in the study, and Finite Element Analysis (FEA) is performed via ABAQUS CAE to build a comprehensive dataset containing numerical simulations data. To improve accuracy and reliability, data preprocessing is implemented, and ANN as a valuable machine learning model is trained with various variables describing crack propagation, stress distribution, and plate structure as input parameters. The suggested method is compared to established fracture analysis methods, proving its accuracy in predicting crack behavior and stress distribution under a variety of loading circumstances. The model provides useful insights into the behavior of edge cracks in semi-infinite elastic plates, enhancing material engineering and structural mechanics. The study demonstrates the potential of combining FEA and machine learning to improve fracture analysis capabilities, and it discusses limitations and future research directions, encouraging the exploration of advanced machine learning techniques and broader fracture scenarios for future fracture mechanics innovation.

Investigation of anti-nociceptive, anti-inflammatory potential and ADMET studies of pure compounds isolated from Isodon rugosus Wall. ex Benth.

The strong ethnopharmacological utilization of Isodon rugosus Wall. Ex. Benth is evident in the treatment of several types of pain and inflammation, including toothache, earache, abdominal pain, gastric pain, and generalized body pain and inflammation. Based on this background, the antinociceptive effects of the crude extract, various fractions, and essential oil have been reported previously. In this research work, we isolate and characterize pure bioactive compounds from I. rugosus and evaluate possible mechanisms using various in vivo and in vitro models. The pure compounds were analyzed for analgesic and anti-inflammatory activities through various assays. The column chromatography of the chloroform fraction of I. rugosus led to the identification of two pure compounds, i.e., 1 and 2. Compound 1 demonstrated notable inhibition (62% writhing inhibition, 72.77% COX-2 inhibition, and 76.97% 5-LOX inhibition) and anti-inflammatory potential (>50% paw edema inhibition at various intervals). The possible mechanism involved in antinociception was considered primarily, a concept that has already been elucidated through the application of naloxone (an antagonist of opioid receptors). The involvement of adrenergic receptors was investigated using a hot plate model (an adrenergic receptor antagonist). The strong ethnomedicinal analgesic background of I. rugosus, supported by previous reports and current observations, leads to the conclusion that I. rugosus is a potential source of antinociceptive and anti-inflammatory bioactive compounds. It may be concluded from the results that the isolated analgesic compounds of I. rugosus may be a possible alternative remedy for pain and inflammation management with admirable efficacy and safety profiles.

Modified strain gradient plate model for nonlinear dynamics of sinusoidal impulsive actuated porous/piezoelectric laminated microharvesters

Size dependency plays an important role in mechanical responses of structures at microscale. In this regard, within the framework of the modified strain gradient theory (SGT), the nonlinear dynamic characteristics of porous/piezoelectric laminated energy microharvesters under sinusoidal impulsive mechanical actuation are explored. The through-thickness porosity dispersion pattern relevant to the passive core of the considered laminated microharvesters is assumed based upon three different functions including a uniform and two graded ones satisfying the necessary requirements associated with the rule of Gaussian random field. In order to derive numerically the solution of the constructed microscale-dependent energy harvester model, the meshless collocation approach as an efficient subset of the meshfree technique is utilized possessing multiquadric radial basis function. It is indicated that by considering a higher value for the microstructural gradient parameters utilized in the SGT-based microharvester model leads to a more prominent effect of the strain gradient tensors which makes more decrement in the value of attained voltage. In this regard, for the laminated energy microharvester under simply edge condition, the value of attained voltage reduces from 232.9795mv in the conventional case to the SGT-based value of 224.1054μv (3.81% decrement) associated with the microstructural gradient parameters equal to 15μm, to the SGT-based value of 208.8456mv (10.36% decrement) associated with the microstructural gradient parameters equal to 30μm, and to the SGT-based value of 175.1994mv (24.80% decrement) associated with the microstructural gradient parameters equal to 45μm. On the other hand, for the laminated energy microharvester under clamped edge condition, the value of attained voltage reduces from 119.3314mv in the conventional case to the SGT-based value of 114.6559mv (3.92% decrement) associated with the microstructural gradient parameters equal to 15μm, to the SGT-based value of 104.2985mv (12.60% decrement) associated with the microstructural gradient parameters equal to 30μm, and to the SGT-based value of 81.6482mv (31.58% decrement) associated with the microstructural gradient parameters equal to 45μm.

The flow-induced structural vibration noise suppression mechanism of a wing–plate model by the junction suction and trailing edge blowing

At medium to high speeds, the flow-induced structural vibration noise generated by structural vibration under the excitation of the turbulent fluctuating pressure can seriously damage the acoustic performance of underwater vehicles. In this paper, we have proposed a new and noiseless method, called junction suction and trailing edge blowing (JSTB), to reduce the flow-induced structural vibration noise of the wing–plate model. We have investigated the effects of JSTB on the flow and sound fields through a combination of numerical simulations and experimental tests. The experiments are conducted in a low-noise gravity water tunnel. Numerical results show that JSTB significantly reduces the peak values of the internal self-noise at 70 Hz, 180 Hz, 225 Hz, and 265 Hz when the velocity is 6.87ms−1. The model radiated noise reduction is more prominent in the 20–1000 Hz frequency range, with an optimal noise reduction level of 15.4 dB. The simulation results agree well with the experimental results. JSTB can effectively reduce the internal sound pressure level, turbulent fluctuating pressure, and radiated sound power of the model. This work provides a novel solution for the flow-induced structural vibration noise control of underwater vehicles.

Numerical simulation of water-bearing coal goaf using ground-borehole TEM—a case study of Tongxin Coal Mine, Shanxi Provice, China

Transient electromagnetic method (TEM) is widely used in coalfield hydrogeological exploration and goaf investigation. However, given the limitations of the method, the vertical resolution of ground TEM is somewhat low for effectively detecting water-bearing coal goaf. Compared with ground TEM, ground-borehole TEM is characterized by a relatively better ability for detecting low-resistivity target bodies. In this study, a low-resistivity thin plate model was established, and the ground-borehole TEM electromagnetic responses of different points (within and without of the plate) were numerically simulated. We considered an exploration project in Datong City (Shanxi Province, China) as a study case, to conduct the field investigation, examine the characteristics of ground-borehole TEM electromagnetic responses under different situations, and validate the numerical model as well, including (a) water-bearing coal goaf and (b) solid coal. The result showed that, (a) the longer the sampling time is, the weaker the electromagnetic response of ground-borehole TEM will be; (2) ground-borehole TEM stands out with a high vertical resolution for water-bearing coal goaf; (c) the extreme points of the Z component and the polarity changing points of the X and Y components can indicate the interface where the physical properties alternated.

Enhanced beam and plate finite elements with shear stress continuity for compressible sandwich structures

This paper concerns and presents new improved beam and plate finite elements for analysing sandwich structures from the structural and modal points of view. In this study, the material behaviour is supposed to be linear elastic and orthotropic, but the method could be extended for nonlinear problems as well. The current models are able to treat the compressibility of the soft core materials, besides the interlaminar continuity conditions and the zero shear stresses on the shear-free surfaces are granted by the Lagrange multiplier method. In order to provide stress continuity along the element boundaries, the Hermite interpolation is employed for the elementary formulations that yields subparametric finite elements. On the contrary, the semi-analytical solutions of these enhanced beam and plate models are also discussed here for particular boundary conditions. The verification of the new finite elements is carried out by two case studies. The test examples are modelled and solved in commercial finite element software (ANSYS) with general shell and solid elements, too. The results derived from different models are subjected to a comprehensive comparison. Also, the structural and modal analyses of the test examples are presented during the case studies. The structural analysis of an overconstrained sandwich panel is also discussed to point out the significance of the proper shear stress distributions. Finally, the advantages and disadvantages of the newly developed elements and semi-analytical solutions are revealed in detail.