Plate Model Research Articles

Transient analysis of functionally graded axisymmetric plates via finite element method in the Laplace domain

The principal goal of this research article is to examine the forced vibration of Functionally Graded Material (FGM) axisymmetric plates with the aid of the finite element method in the Laplace space. The material properties are assumed to be isotropic, linear viscoelastic, or elastic and vary continuously in the direction of the thickness of the plate. The governing equations of motion are transferred to the Laplace domain and solved for a set of Laplace parameters. Then, a modified Durbin’s inverse Laplace method is employed to retransfer the obtained results back to the time domain. A convergence analysis is conducted to optimize the number of Laplace parameters and time steps. An 8-node quadratic quadrilateral element featuring two degrees of freedom per node is employed to generate the model of the axisymmetric plates. Different loads such as step load, square wave, and sawtooth wave loads are used to observe the impact of load type on the transient response of FGM plates. In viscoelastic analysis, the Kelvin damping model is preferred, and the effect of the damping ratio is investigated. The obtained results are validated with the aid of the available literature and the accuracy of the suggested model is confirmed. It is carried out that the material variation significantly affects the dynamic behavior of the plates, for instance as the material coefficient increases, displacement amplitudes decrease, and periods increase. The novelty of this paper is the employment of the finite element method together with Laplace transformation for addressing the present class of problems for the first time.

A FRACTAL PORE-SCALE MODEL OF STRESS-DEPENDENT THERMAL CONDUCTIVITY IN A RECTANGULAR CROSS-SECTION TREE-LIKE MICROFRACTURE NETWORK

Stress is an important external element influencing effective thermal conductivity (ETC). However, previous theoretical investigations of stress-dependent effective thermal conductivity have used a simplified parallel plate model, overlooking the complex structure of rock fracture networks. Therefore, this paper establishes a new fractal model for the stress-dependent ETC of a rectangular cross-section tree-like microfracture network. The model derives a constitutive equation between the stress-dependent ETC and the microscopic geometry structural parameters of the microfracture network. The model’s validity is confirmed by the error of less than 0.291% between the theoretical predictions and the experimental data. The influence of geometry structural parameters of the microfracture network (length ratio, width ratio, height ratio, angle, total number of branches and ratios of soft part, hard part, etc.) on the ETC under the low-stress state has been analyzed. It was discovered that the soft part of the rock microfracture network has the most impact on ETC. The fractal pore-scale model clarifies heat transfer mechanism in rock microfracture network under effective stress, with each parameter physically defined and independent of empirical constants.

Free Vibration and Buckling Analyses of Functionally Graded Plates With Graphene Platelets Reinforcement

Abstract While existing research has focused on using graphene platelets (GPLs) as reinforcement for homogeneous matrices, this study proposes a new nanocomposite for plate structures consisting of GPLs incorporated into a conventional functionally graded matrix with the aim of enhancing their overall stiffness. The performance of such plates is evaluated via free vibration and buckling analyses in the present study. Note that the matrix phase is graded continuously with the power law distribution across the plate's thickness, whereas various GPL dispersion patterns along the thickness are studied. The material properties of the typical functionally graded matrix are determined by the rule of mixture, and then those of the composite are estimated by the modified Halpin–Tsai model as well as the rule of mixture. Based on Hamilton's principle and the novel four-unknown refined plate theory (RPT4), the governing equations of the plate are developed. The Navier-type solution scheme is then adopted to get the critical buckling load and natural frequency of the nanocomposite plate. Numerical findings are examined to evaluate the novel nanocomposite plate model, and a parametric study is also conducted. In addition, high-accurate results are provided via the Navier-type solution here as benchmark solutions for further studies on functionally graded material structures reinforced by GPLs.

Estimation, tuning, and evaluation of propagation direction behavior in superimposed orthogonal two-dimensional structure-borne traveling waves

Abstract Structure-borne traveling waves (SBTW) are observed in nature as a means for propulsion and locomotion of creatures on land and in the ocean. Recently, various approaches have been investigated to replicate this phenomenon. Previous studies have successfully generated SBTWs suitable for propulsion applications and particle motion on active surfaces. Much recent literature has focused on generating traveling waves that propagate only along a single axis for 1D and 2D structures. This limits their potential and does not take advantage of the full potential of 2D structures.
This study examines the potential of employing superposition to control the propagation direction of 2D SBTW. This is investigated numerically using an experimentally validated Finite Element model of a 2D plate with piezoelectric actuators. The individual SBTWs are superimposed by simultaneously exciting two pairs of actuators that are aligned orthogonally on the surface of a plate. Traveling waves are excited in the plate using two-mode excitation. Structural intensity is utilized to develop quantifiable metrics to describe the overall propagation direction and uniformity, which are necessary for describing the complex propagation patterns encountered with 2D SBTW. The potential of the proposed approach along with developed tuning and evaluation methods are demonstrated through case studies of two plates, one square and one rectangular. For both cases, the overall direction of the SBTW is tuned to propagate for any direction between the individual SBTW. This was achieved while maintaining a high-quality overall SBTW. With this approach, 2D SBTW can be steered for wave-driven motion applications such as propulsion of the structure itself or conveying particles in any direction along the structure's surface without compromising the quality of the overall traveling wave.

Geometric nonlinear analysis of smart composite laminates

Abstract In order to create an adaptable system, active piezoelectric layers are fused or inserted into a host structure to create smart composite laminates (SCLs). SCL’s prospective applications in form modification, self-health sensing, and active vibration control demonstrate how important it is. In this paper, the static deformation characteristics and dynamic properties of SCL under voltage and mechanical loads are investigated. A completely coupled field program for SCL is constructed using Matlab. It describes mechanical displacements based on the shear deformation assumption and compares two displacement-strain models: linear and von K´arman nonlinear. The coupled nonlinear electromechanical equations are reduced to a finite element form that can be solved with convenience. Based on the program written, we have done a comparative study of linear and geometric nonlinearities of the SCL plate and also compared it with the existing articles. The results of the geometric nonlinear model of the SCL plate are quite different compared to linear and the nonlinear model results are more accurate.

Effects of Connecting Structures in Double-Hulled Water-Filled Cylindrical Shells on Shock Wave Propagation and the Structural Response to Underwater Explosion

In conventional double-hulled submarines, the connecting structures that facilitate the linkage between the two hulls are crucial for load transmission. This paper aims to elucidate the effect of these connecting structures on resistance to shock waves generated by underwater explosions. Firstly, a self-developed numerical solver is built for the one-dimensional water-filled elastically connected double-layer plate model. The shock wave propagation characteristics, shock response of structure, water cavitation, and impact loads transmitted through the gap water and the connecting structures are analyzed quantitatively. The results reveal that the majority of the shock impulse is transmitted by the gap water if the equivalent stiffness of the connecting structures is much less than that of the gap water. Then, a three-dimensional model of the double-hulled, water-filled cylindrical shell is constructed in Abaqus/Explicit, utilizing the acoustic-structural coupling methodology. The analysis focuses on the influence of the thickness and density distribution of the connecting structures on the system’s shock response. The results indicate that a densely arranged connecting structure results in a wavy deformation of the outer hull and a notable reduction in both the impact response and strain energy of the inner hull. When the stiffness of the densely arranged connecting structure is comparatively low, the internal energy and plastic energy of the inner hull are decreased by 16.5% and 24.1%, respectively. The findings of this research are useful for assessing shock resistance and for the design of connecting structures within conventional double-hulled submarines.

Research on mechanism of controlling water and stabilizing production in heavy oil reservoirs with edge-bottom water

The development of edge-bottom water heavy oil reservoirs typically involves short water-free production period and a rapid increase in water cut, leading to generally low oil recovery factors. Combining the advantages of foam and viscosity reducers for composite development can effectively address the challenges in edge-bottom water reservoirs; however, the mechanism of action remains unclear. In this study, the concentrations of foaming agent and viscosity reducer were initially determined using a foam evaluator and an Anton Paar rheometer. Subsequently, a 2D large flat plate model was employed to conduct a composite group production experiment after water flooding, and then the change in oil saturation during flooding was analyzed by measuring electrical resistance. Finally, the dynamic curves of flooding were compared to analyze the mechanism of water control and oil stabilization (WCOS). The results indicate that the 2D large flat plate model and the method of inverting saturation field maps can effectively simulate the oil-water flow behavior during the composite flooding process after water flooding. The synergistic mechanism of N2 foam controlling bottom water coning and CO2 enhanced viscosity reducer to reduce viscosity in deep areas was revealed, increasing the overall recovery factor by 10.3% compared to water flooding. The mechanism of the combined oil recovery is clarified, which providing a reference for formulating WCOS plans following water flooding.

Numerical Optimization of Functionally Graded Ti-HAP Material for Tibial Bone Fixation System.

Functionally graded materials (FGMs) are heterogeneous composites characterized by outstanding properties. They are built from two or more components with a gradient distribution of chemical composition along a given direction. A promising graded material for biomedical engineering as an implant could be a FGM made of titanium (Ti) and hydroxyapatite (HAP). It would allow us to counteract the difference between the stiffness modulus of pure titanium and bone tissue. Moreover, it can be a good solution to the problem of stress shielding for bone fixation plates made of conventional titanium or steel. The presented paper aims to perform micromechanical modeling and optimization of a functionally Ti-HAP graded plate, followed by numerical analysis of a fractured tibia stabilization system under specific boundary conditions. Finite element analysis was performed using ANSYS Workbench 2021 software. The models of the FGM plate and tibial fixation system were made using the Space Claim tool. The ANSYS software allowed the optimization of the model considered and the selection of the appropriate structural parameters of the FGM Ti-HAP material. In general, the results proved that the osteosynthesis plate built of graded Ti-HAP material resulted in lower bone stress compared to titanium and steel plates. The results obtained confirmed the validity of the design and the possibility to use functionally graded Ti-HAP bone fixation plates.

Reverse design and application of phononic crystals based on deep learning

Abstract This paper reverse-design phononic crystals with band gaps within a targeted frequency band using the trained Conditional Variational Autoencoder (CVAE) and further studies the vibro-acoustic characteristics of a composite sandwich plate with a phononic crystal panel as the core layer. Firstly, a matrix composed of 0s and 1s, representing scatterers and substrates, is randomly generated by MATLAB to represent two-dimensional phononic crystals. The three-dimensional phononic crystals are obtained by stretching the two-dimensional phononic crystals along the average direction, and COMSOL Multiphysics is used to calculate the band gap. In order to maximize the production of phononic crystals with a band gap distribution, the Convolutional Neural Network (CNN) is trained to predict whether the generated phononic crystals have band gaps. Finally, using data on the structures of phononic crystals and their band gap distributions, the CVAE is trained to achieve the reverse design of artificial periodic structures based on the target band gap. To verify the effectiveness of the structures obtained through the reverse design method on vibration and noise reduction, the submerged vibro-acoustic characteristics of a composite sandwich plate consisting of a phononic crystal panel and carbon fiber panels are studied. The model of the composite sandwich plate is fabricated, and its submerged vibro-acoustic characteristics are tested and compared with numerical results. Finally, the submerged vibro-acoustic response levels of composite sandwich plates with phononic crystal panels and honeycomb panels as core layers are compared using numerical methods to assess the phononic crystal panel's vibration and noise reduction effects.

Fatigue life prediction of CFRP flat-fold-flat adhesive joints

Taking the flat-fold-flat (FJF) adhesive joints of carbon fiber reinforced bismaleimide resin-based composite materials as the object, the regularized fatigue life model and residual stiffness model of the one-way plate and the cohesive model parameters of the adhesive layer were fitted experimentally, and based on this, the fatigue life of the adhesive joint was predicted by ABAQUS software. The results show that under specific maximum load conditions, the predicted cracking life of the adhesive layer at the end of the lap joint and the final fatigue life are not greater than the error values of the test results 3% , which has a relatively good calculation accuracy. The cracking life of the adhesive layer at the end of the lap joint is approximately equal to the final fatigue life of the adhesive joint, indicating that the cracking of the adhesive layer at the end of the lap joint accounts for the main part of the total life of the adhesive joint, and the crack propagation life of the adhesive layer can be ignored.

The effective elastic thickness along the Emperor Seamount Chain and its tectonic implications

Summary The Hawaiian-Emperor Seamount Chain, a pre-eminent example of a hotspot-generated intraplate seamount chain, provides key constraints not only on the kinematics of plates but also on their rigidity. Previous studies have shown that the effective elastic thickness, Te, a proxy for the long-term strength of the lithosphere, changes abruptly at the Hawaiian-Emperor ‘bend’ from low values (∼16 km) at the Emperor Seamounts to high values (∼27 km) at the Hawaiian Ridge. To better constrain Te along the poorly explored Emperor Seamounts we have used a free-air gravity anomaly and bathymetry gridded data set, together with fully 3-dimensional elastic plate (flexure) models, to estimate the continuity of Te and volcano load and infill densities along 1000 profiles spaced 2 km apart of the chain. Results show that Te generally decreases northward along the chain. The decrease is most systematic between Ojin and Jimmu guyots where Te depends on the age of the lithosphere at the time of volcano loading and is controlled by the 340°C and 400°C oceanic isotherms. The largest variation from these isotherms occurs at the northern and southern ends of the chain where Te is smaller than expected suggesting the influence of pre-existing, older, loads. We use these results to constrain the subsidence, flexural tilt, rheological properties, and tectonic setting along the seamount chain. We found an excess subsidence in the range 1.2-2.4 km, a tilt as large as 2-3°, oceanic lithosphere that is weaker than it is seaward of the weak zone at subduction zones, and a tectonic setting at Detroit and Koko seamounts that, despite their forming an integral part of the hotspot generated seamount chain, retains a memory of their proximity to earlier loads associated with plume influenced mid-oceanic ridges.

Personalized 3D Printing of Artificial Vertebrae: A Predictive Bone Density Modeling Approach for Robotic Cutting Applications

Robotic vertebral plate cutting poses significant challenges due to the complex bone structures of the lumbar spine, which consist of varying densities in cortical and cancellous regions. This study addresses these challenges by developing a predictive model for robotic vertebral plate cutting force and bone quality recognition through the fabrication of artificial vertebrae with controlled, consistent bone density. To address the variability in bone density between cortical and cancellous regions, CT data are utilized to predict target bone density, serving as a foundation for determining the optimal 3D printing process parameters. The proposed methodology integrates a Response Surface Methodology (RSM), Back Propagation (BP) neural network, and genetic algorithm (GA) to systematically evaluate the effects of key process parameters, such as the filling density, material flow rate, and layer thickness, on the printed vertebrae’s density. A one-factor experimental approach and RSM-based central composite design are applied to build an initial bone density prediction model, followed by Sobol’s sensitivity analysis to quantify the influence of each parameter. The GA-BP neural network model is then employed to rapidly and accurately identify optimal printing parameters for different bone layer densities. The resulting optimized models are used to fabricate personalized artificial lumbar vertebrae, which are subsequently validated through robotic cutting experiments. This research not only contributes to the advancement in personalized 3D printing technology but also provides a reliable framework for developing patient-specific surgical planning models in robot-assisted orthopedic surgery.

Distance-regularized level set inversion of magnetic data

Inversion is one of the key and difficult issues in potential field data processing and interpretation, and high-precision inversion has long been a popular research topic. We develop the distance-regularized level set inversion of the magnetic data (DRLSI-M) method. A double-well function is introduced into the objective function of the level set inversion, and we take advantage of its mathematical properties to minimize the gradient of the level set function so that it reaches a minimum value at points 0 and 1. As a result, the distance-regularized term not only replaces the costly reinitialization process so that the level set function maintains a signed distance property but also stabilizes the evolution of the level set function. When solving for the minimum value of the objective function, we transform the optimization problem into an initial-boundary value problem and solve it with the finite-difference method. The distance-regularized level set inversion method and the reinitialization level set inversion method are tested using three models: a single-level-set double-inclined plate model, a double-level-set double-inclined plate model, and a multiple-level-set three-cuboid model. Through model tests, the soundness of our method is verified and compared with the reinitialization level set inversion method. Our method avoids the limitations such as low efficiency and instability caused by the reinitialization of the level set inversion method. Furthermore, we apply our method for the inversion of aeromagnetic data from the Jinchuan copper-nickel mine. The results are consistent with the known geologic information, thus validating the practicality and effectiveness of DRLSI-M. The distance-regularized level set inversion method provides a theoretical basis for deep mine exploration.

Multi-Criteria Calibration of a Thermo-Mechanical Model of Steel Plate Welding in Vacuum

This paper proposes a procedurefor multi-criteria calibration of a thermo-mechanical model for numerical simulation of welding in the space vacuum. A finite-element model of a steel plate is created. Experimental and computational data are obtained. An inverse problem is formulated for the vector identification of five calibration parameters from the heat-flow model. They are evaluated for adequacy with controlled accuracy according to four criteria. An optimization problem is solved using a two-step interactive procedure. The parameter space studying method (PSI) has been applied to the study of multidimensional regions by means of quasi-uniform sounding. A Pareto-optimal set is defined. It is used to determine reduced ranked Pareto subsets by μ-selection. Salukvadze optimum is also determined.

A linear shaped charge cutting model for brittle flat plates

The dynamic response and damage fracture of brittle materials under explosive cutting have always been important research issues in the fields of military, aerospace, and other engineering fields. In this paper, a linear shaped charge cutting model for explosive cutting of brittle materials is proposed. This model suggests that explosive cutting is caused by the combined effects of jet penetration, spallation, and impact fracture. Theoretical calculation models for jet penetration, spallation, and impact fracture were constructed, and the concept of impact strength was introduced to establish dynamic mechanical performance parameters for brittle materials. A calculation program for explosive cutting of brittle materials was developed using the Python language, which can calculate the jet penetration depth, spallation thickness, and impact fracture thickness by inputting parameters such as the size and mechanical properties of the linear shaped charge and target plate, and determine whether the target plate can be successfully cut. Subsequently, a series of explosion cutting experiments and numerical simulations for brittle target plates were conducted to verify the accuracy of the calculation program. The results indicate a high degree of consistency between simulation, experimentation, and program calculation results. This work can provide guidance and promotion for the design and application of explosive energy harvesting cutters.

Buckling of thin films: Lateral growth and kinetic evolution of telephone cords

We conduct a thorough investigation of the lateral growth and kinetic evolution of telephone cord buckles within thin films, employing both experimental and numerical techniques. Our exploration begins with in-situ experiments conducted on annealed silicon nitride films, aimed at capturing empirical data on the formation and evolution of these distinctive patterns. These experiments yield valuable insights into the morphological changes of telephone cords, such as wave flipping and merging, which lead to the enlargement of buckles at double wavelengths and widths. Subsequently, we employ a combined approach of geometrically nonlinear plate modeling and surface-based cohesive interface framework within a finite element numerical model to analyze the interplay between buckling-induced delamination and growth triggered by mode mixity-dependent interfacial toughness. Through this integrated approach, we effectively capture the mutual evolution of buckling and delamination occurrences, thus highlighting their inherently dynamic nature. Our numerical simulations show that the width and wavelength of telephone cords are doubled, consistent with experimental findings.

Study on analogy principle of overall cooling effectiveness for high temperature cooling structure considering thermal radiation heat transfer

With the continuous advancement of aero-engine technology, the performance of hot-end components such as combustion chambers and turbines has significantly improved, leading to a rapid increase in the working environment temperature surrounding these components and an increasingly prominent thermal radiation effect. Due to the non-gray body characteristics and spectral selectivity of thermal radiation, it is difficult to replicate the actual working environment of turbine components under laboratory conditions, causing many scholars to ignore or simplify the thermal radiation effect. Focusing on the overall cooling effectiveness of hot-end components such as turbine guide vanes, this paper proposes a method for modeling the overall cooling effectiveness of cooling structures under radiation-convection coupling conditions by matching parameters such as Burger number (Bu) and Boltzmann number (Bo). Based on the impingement effusion plate model and turbine guide vane model, this study investigates the matching of the overall cooling effectiveness under full coupled heat transfer for cooling structures in high and low operating conditions in laboratory settings. Additionally, the effects of momentum ratio, temperature ratio, and gas composition on the overall cooling effectiveness are examined. The results indicate that this matching method can provide important references for the design of hot-end components such as turbine blades.

Comprehensive influence of dimensionless wave velocity and expansion ratio on energy absorption characteristics of variable wavelength traveling wave turbine

Based on the traveling wave motion of fish, this paper introduces a new type of variable wavelength traveling wave turbine that significantly differs from traditional turbine designs in its mechanical structure. By developing a two-dimensional traveling wavy plate model and conducting numerical simulations, this study investigates the relationship between the dimensionless wave velocity, variable wavelength coefficient, and expansion ratio, as well as their combined effects on the energy absorption characteristics of the variable wavelength traveling wave turbine. The results reveal that energy absorption efficiency peaks at an optimal dimensionless wave velocity, which is unaffected by changes in the variable wavelength coefficient. Furthermore, the expansion ratio significantly influences both the dimensionless wave velocity and the variable wavelength coefficient, with an optimal ratio of π∗ = 2.5 achieving 90.42 % efficiency. The energy absorption characteristics of the plate with a larger variable wavelength coefficient are found to be constrained by the expansion ratio. Additional analysis reveals that flow characteristics, such as the pressure distribution, vortex street, and velocity field surrounding the traveling wavy plate, are closely related to its energy absorption performance. These findings provide valuable insights for the design of variable wavelength traveling wave turbine.

New astrometric positions for six Jovian irregular satellites using Gaia DR3 in 2016 — 2021

The Jovian system is like a miniature solar system, with the system being more than twice as massive as all the other planets combined and having many natural satellites. Its formation and early evolution had a profound influence on our knowledge of the sculpting of the architecture of the solar system. Astrometric observations are of importance, based on these observations, its orbital dynamics, as well as its origin sometimes, of a solar system object can be determined. We aimed to obtain good astrometric positions of some irregular satellites Elara, Pasiphae, Sinope, Lysithea, Carme and Ananke to refine their orbits and ephemerides, and to understand their dynamics. We have taken, processed and reduced 964 ground-based CCD frames obtained between 2016 and 2021 by the 2.4 m telescope at the Lijiang Station of Yunnan Observatory over 27 nights. Among CCD image processing, the image subtraction technique of ISIS is employed to eliminate star images that are close to or/and almost overlapped with those of our targets in 2019. The star catalog Gaia DR3 is utilized for astrometric calibration, in which a weight scheme is applied to solve more accurate plate model. For all targets, their theoretical positions are retrieved from the Institut de Mécanique Céleste et de Calcul des Éphémérides (IMCCE) ephemeris. Our results show the mean (O - C)s (observed minus computed) of the positional residuals of all targets are −0′′.007 and 0′′.011 in R.A. and Dec., respectively. Their corresponding standard deviations are about 0′′.05 in each direction, except for Ananke (the faintest satellite) with its standard deviation about 0′′.08 in each direction.

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.