Multilayered Plates Research Articles

Numerical analysis of X-ray multilayer Fresnel zone plates with high aspect ratios

Abstract A partition calculation method (PCM) for calculating the diffraction efficiency of multilayer Fresnel zone plate with high aspect ratio is proposed. In contrast to the traditional theory, PCM designs and evaluates Fresnel zone plate (FZP) considering material pairs, all zone widths, thicknesses and X-ray energy more completely. The results obtained through PCM are validated by comparing them with the complex amplitude superposition theory and coupled wave theory numerical results. The PCM satisfies the requirements of the theoretical investigation of FZP with small outermost zone width (drN) and large thickness (t). Combining proper numerical analysis with the experimental conditions will present a great potential to break through the imaging performance of X-ray microscopy.

The Explosive Crack Propagation Mechanism of Layered Rock Mass

Layered joints significantly affect the propagation and attenuation of engineering blasting stress waves and have a significant influence on rock breakage. In this study, the explosion crack propagation mechanism of a stratified rock mass with weak or no cementation is analyzed. Multilayer plexiglass plates are employed to simulate a layered rock mass, establishing an experimental model to investigate the vertical interaction between explosive charges and layered rock masses. The extent of ruptures and damage within the charging and sealing sections of the rock mass is analyzed. The explosion cracks at the bottom of the hole are relatively dense, whereas those at the hole opening are relatively sparse. The range of the crushing and fracture zones around the gun hole in the charging section is larger than that in the blocking section. Moreover, as the blocking section approaches the free plane, the crushing zone size decreases. A notable area of rapid damage escalation is identified between the blocking and charging sections, leading to a significant increase in damage intensity. The numerical analysis results indicate that the cumulative explosive energy within the charging section surpasses that of the blocking section, and the rate of energy accumulation is notably higher in the charging region.

FEA of stress-strain state and vibrations of a three-layer plate

Solar panels are considered as three-layer plates with a thick, rigid outer layer and a thin, soft inner layer. The model for anti-sandwich plates was used to describe the mechanical behavior of the plates in the example of a solar panel. The literature review includes scientific articles describing models for analytical and numerical calculations of three-layer plates. During the scientific study of the mechanical behavior of the solar plate under the influence of external factors, the finite element analysis method for multilayer plates was used. The shell elements were used to calculate and model the natural waveforms of three-layer plates. The paper presents scientific research under static loading under various conditions of influence, analyzes the natural frequencies, and vibration forms, and investigates the stress-strain state depending on the vibration frequencies of the three-layer plate. As part of the scientific work, a mechanical model of a thin solar panel was studied using finite element analysis in the ANSYS program, taking into account various temperature conditions and comparing the results with existing studies.

One-step fast fabrication of multi-layer quantum dot diffusion plate for stable display and ultra-long life, a novel quantum dot packaging strategy

Quantum dots (QDs), renowned for their distinctive optical and physical attributes, are extensively employed in diverse fields such as lighting, displays, electronics, sensors, and solar cells. Nonetheless, the susceptibility to light, oxygen, and moisture is a major obstacle to the development of QDs. Achieving simple, efficient, and universal modification or encapsulation for enhanced stability remains a challenge. Herein, a one-step fast fabrication of multi-layer quantum dot diffusion plate (QD-DP) with excellent barrier and optical properties was proposed, which is alternately stacked by MS-EVOH and MS-QDs layers. The barrier phase morphology undergoes a fiber-flake transition induced by the bidirectional tensile force field during multiplication, and layer-by-layer encapsulation synergistically enhances the barrier performance, photo-oxygen stability, thermal-oxygen stability, and fluorescence lifetime of QD-DP in backlight applications. Under high-power UV irradiation, the fluorescence intensity ofMS/MS-QD 128L dropped to 90 % (T90) in only about 10 minutes, while the T90 of MS-E/MS-QD 128L was close to 216 hours, improved more than 1200 times. Concurrently, the quantum dot diffusion plate (QD-DP), characterized by an alternating multi-layer structure, demonstrated an elevated backlight color gamut value of ∼ 120 % NTSC, outperforming conventional quantum dot light emitting diodes (QLED). Compared with existing QDs backlight modules, a simpler structure, more efficient preparation process, and longer fluorescence lifetime of QD-DP were achieved.Moreover, unlike prevalent modification or packaging technologies that only target specific QD types, our alternating multilayer coextrusion packaging technology is applicable to all kinds of QDs and is simple, efficient, and universal.It was believed that this work could provide new opportunities for all kinds of QDs encapsulation and application in many fields and will be the dawn of large-scale commercialization of QDs.

DETERMINATION AND ANALYSIS OF THE TEMPERATURE FIELD IN A THREE-LAYER ISOTROPIC PLATE WITH A GIVENINITIAL TEMPERATURE DISTRIBUTION

An approximate system of two-dimensional heat conduction equations for a multilayer isotropic plate is written down. Boundary conditions for a rectangular plate of finite dimensions are formulated. A general solution of the non-stationary heat conduction problem for this plate was found using integral Fourier transforms in spatial variables and Laplace transform in time.On the basis of the obtained general solutions, the solution of the thermal conductivity problem for a three-layer plate, which at the initial moment of time is heated by a temperature field linear in its thickness, which is uniformly distributed over the surface of the plate in a rectangular region, was analyzed.The numerical analysis of the temperature field was performed for a three-layer plate, the middle layer of which is made of metal, and the outer layers are made of ceramics.

Investigation of the vibration problem of sandwich heterogeneous orthotropic plates

In this study, the solution of the free vibration problem of sandwich plates consisting of heterogeneous orthotropic layers is presented. First, the Kirchhoff-Love theory (KLT) for homogeneous plates is extended to sandwich plates composed of heterogeneous orthotropic layers. Within the framework of Donnell theory, after establishing the basic relations of multilayer plates, governing equations are derived based on Airy stress and deflection functions. The solution of the governing equations is carried out by the Galerkin method and the analytical expression is found for the linear frequency of sandwich plates consisting of heterogeneous orthotropic layers. Finally, the effects of various factors such as heterogeneity, number of layers and their arrangement on the free vibration frequency of sandwich plates are examined.

Investigation into the ballistic characterization of polyurea-coated spliced-shaped multilayer ceramic plates

As a new protective structure, composite ceramic structures have become a research focus and new breakthrough direction. We using a ballistic gun to fire a 12.7 mm bullet at a speed of 500 m/s to penetrate the polyurea-coated spliced-shaped multilayer ceramic plates. The energy absorption effects of the polyurea and ceramic on fracture were analyzed. The ceramic fracture microstructure was subsequently investigated by scanning electron microscopy (SEM), and the fracture principle was elucidated. The residual velocity of the projectile was predicted from energy dissipation. In addition, the failure process of polyurea/ceramic composite plates was explained in detail using numerical simulations, and the ballistic limit of different configuration composite plates was explored through theoretical and numerical simulation methods. This research showed that polyurea could effectively improve the ballistic limit of composite structures and increase its ballistic limit from 133.9 to 174 m/s, resulting in an increase of ∼30.4 %. However, polyurea had little effect on the ballistic performance of the structure under the condition of equal area density. The energy absorption process of five structures was mainly divided into four stages, and the coating of polyurea could effectively improve the energy absorption of ceramics, reaching 253.84 %.

SOLUTION OF THE FIRST BASIC BOUNDARY VALUE PROBLEM OF THE PLANE ELASTICITY THEORY FOR A MULTILAYER BASE WITH ORTHOTROPIC LAYERS

The paper deals with the problem of determining stresses and displacements at the points of a multilayer base consisting of orthotropic layers and coupled to a half-space. The external loads on the top layer are known, such that the deformation of the body becomes flat. At infinity, the stresses are zero. This paper presents a brief review of scientific studies that highlight methods and approaches to solving problems related to the theory of elasticity for studying the stress-strain state of multilayer bodies, plates, plates, and strips. The article formulates an algorithm for analytically solving the problem for a multilayer base, in which all the basic equations of the problem and boundary conditions are subjected to a direct Fourier transform. The stress function is found as a solution of the analog of a biharmonic differential equation in the space of transformants in the case of an orthotropic material. The relationships between the stress function transformant and the stress and displacement transformants are established. For each layer, four auxiliary functions are introduced that are associated with the stress and displacement transformants of points on the surface of the layers. From the conditions on the common boundaries between the layers, recurrent relations are constructed that express the auxiliary functions of the lower layer through the functions of the previous layer. By expressing the four auxiliary functions for the first layer, we can find similar functions for any layer using recurrent formulas. After substituting the found expressions into the stress and displacement transforms and applying the inverse Fourier integral transform, we obtain the true values of stresses and displacements at the points of the multilayer orthotropic base. The proposed algorithm takes into account the peculiarities of the properties of the orthotropic material and allows us to obtain analytical solutions of the stress-strain state in each layer of the base.

Nonlinear geometric fluid-structure interaction model of multilayered sandwich plates in contact with unbounded or bounded fluid flow

Based on the Kirchhoff-Love theory and von Kármán's geometric nonlinearity, the nonlinear vibration analysis of multilayered sandwich plates under ideal flow is presented. Rectangular plates are considered to be laminated of orthotropic composite layers as upper and lower face sheets as well as a central lightweight core made of functionally graded (FG), anisogrid lattice or metal foam materials. Three coupled equations of motion are reformulated into one decoupled governing equation in terms of transverse deflection (w) using the method of inverse differential operator. For the first time, an impermeability condition is developed that considers the moderately large deflection of the contact surface in order to correct the pressure distribution of fluid flow. Based on the potential flow theory, closed-form expressions of hydrodynamic pressure are obtained for different fluid boundary conditions including infinite depth of fluid, flow bounded by a rigid wall and flow between two identical elastic plates. Then, the Galerkin and multiple-scale perturbation methods are used to obtain closed-form solution of nonlinear natural frequency in terms of maximum vibration amplitude. Finally, case studies are presented to investigate the effects of geometric ratios, boundary condition, material distribution, layup, characteristics of flow and geometric nonlinearity on the response quantities. Findings indicate that the large deformation term in the developed impermeability condition has significant effect on the pressure distribution and its effect is more pronounced for thicker plates with larger mode number in the flow direction. Therefore, the novel nonlinear fluid-structure interaction model should be considered to study flow-induced dynamic behavior of sandwich plates with different boundary conditions. In addition, the snap-through behavior is seen in the nonlinear frequency-upstream speed curves and the incipient points of dynamic instability can vary remarkably with the fluid boundary conditions.

Stable and accurate representation of species diffusion in multilayer composite electrodes using physics-informed neural networks

Stable and accurate reconstruction of species diffusion in Li-ion cell electrodes is a crucial problem, especially in modeling emerging composite electrode materials. Lithium-ion batteries are typically modeled using electrode theory coupled with various transport mechanisms that the solid-phase diffusion equation represents the main computational burden. In this paper, a computationally efficient representation for species transport in multilayer electrode is proposed based on the physics-informed neural networks (PINNs). A multi-objective loss function is constructed to obtain an accurate representation of field variables. It consists of the residual of solid-phase diffusion equation, associated initial/boundary conditions together with interface conditions. To deal with the problem of distinct material properties, the whole computational domain is divided into several subdomains where different neural networks for PINN are adopted. By using continuity conditions at interfaces, a whole network is established by combining subnetworks. By this way, the field variables can be obtained accurately by training and learning the neural networks. Li-ion concentrations in electrodes with single-layer and multilayer plate under the galvanostatic, potentiostatic, time-dependent flux, as well as time-dependent concentration charging are analyzed, and the results are validated against solutions obtained from finite element and analytical analysis. In terms of practical application, the galvanostatic voltage profiles of bi-layer (graphite-Si/SiOx) and tri-layer (graphite-Si/SiOx-graphite) electrodes are obtained using the Butler–Volmer kinetic equation and the performance is validated through good agreement with past experimental data. This study demonstrates for the first time the usefulness of the PINN to an electrochemical energy problem for designing multilayer electrode materials.

Natural Frequency Characteristics of Stiffened FG Multilayer Graphene-Reinforced Composite Plate with Circular Cutout Resting on Elastic Foundation

In this research, natural frequency response of functionally-graded multilayer graphene-reinforced composite plate with circular cutout reinforced by orthogonal stiffeners is investigated for the first time. The structure is surrounded by Winkler-type elastic support. The plate is composed of polymethyl methacrylate (PMMA) as matrix material and reinforced by graphene platelets (GPLs). The material of the orthogonal stiffeners is the same as that for the matrix. Rule of mixtures and Halpin–Tsai approach are applied to estimate the effective material properties of the composite plate. Third-order shear deformation plate theory and finite element procedure is employed to obtain the element matrices of the structure. Natural frequencies and mode shapes of the stiffened plate are reported for different variables such as nanofillers dispersion patterns, width and height of the stiffeners, aspect ratio of plate, plate thickness ratio, weight fraction of nanofillers, number of stiffeners, boundary conditions, elastic foundation stiffness parameter and size of circular cutout. The obtained results denote that with the addition of a set of stiffeners, fundamental frequency enhanced up to 32.3% with just about 10% increase of mass.

Axisymmetric vibration of multilayered electroactive circular plates in contact with fluid

Soft electroactive materials (SEAMs), which possess significant advantages over conventional hard materials, have attracted great attention in recent years. They have been widely used in automotive, aerospace, and biomedical industries, where they frequently come into contact with fluid. However, few analytical studies on the SEAM structures interacting with fluid have been reported. Based on the nonlinear electroelasticity and its relevant incremental theory, this paper investigates the linearized axisymmetric vibration of SEAM plates in contact with a fluid medium and subjected to electromechanical biasing fields. The state-space method and Hankel transform technique are adopted to solve the fully coupled partial differential equations. The numerical examples of a homogeneous plate, a two-layer plate, and a functionally graded plate are considered. We find various interesting phenomena and results, such as the complex competition mechanism, the difference between dry and wet high-order modes, and the influence of electromechanical biasing fields, fluid, and material heterogeneity on the natural frequency and buckling threshold. Our numerical findings provide helpful guidance for the design of dynamic devices made of SEAMs working in a fluid environment.

A assembled plate column bioreactor for adherent cell culture

The ideal bioreactor should be highly efficient, cost-effective and able to promote cells adhesion growth. In this study, we constructed a plate-tower bioreactor with S-loop in each layer based on multilayer plate bioreactor and plate column theory. Human hepatocellular carcinomas(HepG2) and human normal liver cell L02 (L02) cells were employed evaluation of bioreactor performance. The results show that cells were able to adhere to the plates and the density reached to 1～1.2 × 105/cm2. When circulating flow rate of the reactor is 8 ml/min and the oxygen supply concentration is 40 %, the sufficient material and gas exchange in bioreactor, the amount of albumin, urea and cytochrome P450(CYP450) content in the hyperoxia group were 3.31, 2.58 and 2.6 times higher than that of the control group, there was no obvious cell damage. This condition up the regulation of genes in more metabolic pathways and improved the metabolic capacity of hepatocytes. The single-layer area and the number of bioreactors can be flexibly adjusted, and the manufacturing cost of single-layer is close to that of ordinary plastic cell culture dishes. Either batch or continuous mode can be used in the bioreactor. In view of the above characteristics, the bioreactor is more conducive to practical application.

Enhancing laser-driven flyer velocity by optimizing of modulation period of Al/Ti reactive multilayer films

Reactive multilayer films (RMFs), a type of nanostructured energetic material, are recognized as an indispensable component for laser-driven flyer plate initiator systems. In this work, Al/Ti-RMF with three different modulation periods (600, 300, and 150 nm) were prepared and integrated into multilayer flyer plates, and energetic material with optimized performance for laser-driven flyers was obtained. Cross-sectional observations demonstrate that the modulation periods of the RMF are precisely regulated, with thickness errors falling within 3.4%. The velocity of the flyer plates was significantly higher with a modulation period of 150 nm, reaching 2174.16 m/s. Molecular dynamics simulation results show that as the modulation period decreases, the diffusion rate of atoms increases, enabling the reaction between the RMF to be completed in a shorter time span, which makes for higher velocity of the flyer. The energy coupling efficiency results indicate that the kinetic energy coupling efficiency of the RMF with a modulation period of 150 nm is 145.6% and 29.8% higher compared to those with modulation periods of 600 and 300 nm, respectively. It is proved that Al/Ti-RMF have high-energy output performance and can be a novel candidate for laser-driven flyer plates, which will play a critical role in complex electromagnetic interference environments in the future.

Nonlinear free vibration analysis of internal thickness-tapered multi-layered composite rectangular plates undergoing moderately large deflections

Thickness-tapering in multi-layered composites is achieved by terminating the plies at discrete locations. This allows for effective material utilization and significant weight savings and is adopted in applications involving multi-layered composites that demand variation in thickness such as helicopter yokes, flexbeams and rotor blades, aircraft wing-skin structures and turbine blades. In the present work, the nonlinear free vibration of such tapered composites undergoing moderately large deflections is investigated for the first time. A general nonlinear finite element formulation for tapered multi-layered composite plates based on Reddy's higher-order shear deformation theory and considering Von Karman nonlinearity is developed. Newton–Raphson scheme in conjunction with Newmark time-integration technique is employed to obtain the time response. The developed model is validated against available results in the literature and through experimentally obtained linear natural frequencies of a honeycomb sandwich plate with tapered face sheets. Parametric studies are conducted to deeply understand the nonlinear dynamic behaviour of tapered composite structures. The investigation reveals that tapered multi-layered composite plates exhibit higher nonlinearity compared to uniform plates thus necessitating the consideration of nonlinear effects in the analysis of such structures.

Solver‐free classical computational homogenization for nonlinear periodic heterogeneous media

AbstractModeling the behavior of composite materials is an important application of computational homogenization methods. Classical computational homogenization (CCH), based on asymptotic analysis, is such a method. In CCH, equilibrium equations are separated into two length scales and solved numerically. Solving the fine‐scale equilibrium equations at every coarse‐scale Gauss point, in every iteration of a Newton–Raphson loop, is often too computationally expensive for real engineering applications. In this study, we propose a modified CCH approach that avoids solving the fine‐scale equilibrium equations. The proposed method, which we call solver‐free CCH, works by pre‐computing a set of eigenstrain influence function tensors based on data from a small number of numerical experiments. Then, during the online stage of the computation, these eigenstrain influence tensors are used in the fine‐scale problem to evaluate and homogenize strains and stresses. This article begins by formulating the solver‐free CCH approach for small‐deformation problems involving composites with nonlinear constituent phase material models, including computation of the eigenstrain influence tensors and their application within the online stage. To verify the proposed approach, we consider loading cases outside the training set used to derive the eigenstrain influence tensors. The combinational efficiency and accuracy of the solver‐free CCH in comparison to the conventional CCH is studied on a multilayer composite plate in three point bending (3pt‐bend) and open hole tension.

Buckling response of functionally graded multilayer graphene platelet-reinforced composite plates with circular/elliptical cutouts supporting on an elastic foundation under normal and shear loads

The present article deals with the buckling response of functionally graded multilayer graphene platelet-reinforced composite (FG-GPL RC) rectangular plates with circular/elliptical cutouts resting on a Winkler-type elastic foundation under uniaxial and biaxial normal and shear loads. Rule of mixtures and the Halpin–Tsai approach are applied to obtain the effective Poisson’s ratio, mass density, and elastic modulus of the reinforced composite. The governing equations are developed by applying the third-order shear deformation plate theory. Then, the finite element procedure is used to solve the problem. Four different types of graphene platelet distributions, namely, UD, FG-X, FG-V, and FG-O, are considered. A broad range of factors such as plate aspect ratio, plate slenderness ratio, applying uniaxial and biaxial normal and shear loads to the plate, several Winkler elastic foundation stiffness parameters, different displacement boundary conditions, the effect of size of the circular cutout and orientation of the elliptical cutout, and the influence of GPL weight fraction are discussed in several tabular and graphical data in detail.

Ballistic response of additively manufactured AA6061/AA7075 multistack plate for armor-piercing projectile

The current ballistics research study focuses heavily on substituting heavy metals with lightweight materials to make mobility more accessible and effective for all armor applications. To do so, the researchers found that aluminum alloys are the better alternative to substitute steel armor due to their high strength-to-weight ratio. Therefore, this research conducted ballistic studies on aluminum alloys using the Finite Element Analysis (FEM) methodologies and associated mathematical analysis. This Research primarily focuses on the damage factor, ballistic limit, and residual velocity of the bullet following penetration of target plates. In this investigation, the Johnson-Cook fracture and Recht-Ipson models were implemented on materials AA6061-T6 and AA7075-T6. The main objective of these models is to establish the damage factor and verify whether it is less than unity; if the factor is less than unity, it is eligible to study the residual velocity of the bullet after penetration into the target armor plate. The target plate was impacted with a 7.62 mm armor-piercing projectile with an impact velocity of 500 m/s. Monolithic plates of 18 mm thickness were evaluated initially. After that, the multilayered stack of each 3 mm thick plate was analyzed, and studied the effectiveness of using a multilayered stack armor plate.

Computer Simulation of Bending of a Rectangular Multi-Layered Plate Using a Numerical Approach

Computer simulation of the bending of a rectangular multilayer plate using a numerical approach is carried out on the basis of differential equations of a variant of the refined theory of multilayer plates, which take into account: transverse shear, pressure of layers against each other, normal deformations, layer orthotropy, asymmetry of the structure. The general order of the system is 12. Three functions of the coordinate surface are unknown: the function of effort, deflection, and shear. The boundary conditions for various cases of fixing the edges of the plate are obtained from the contour integral of the variational equation. Discretization of the system of resolving equations and the corresponding contour conditions for a computer simulation of the bending of a rectangular multilayer plate was performed by the finite difference method. According to the proposed numerical technique on the basis of a two-dimensional model, computer simulation of the problem of bending three-layer articulated support symmetrical in thickness square plates with orthotropic carbon fiber layers in a wide range of changes was carried out.

Dynamic Analysis of Multilayered Piezoelectric Quasicrystal Three-Dimensional Sector Plates with Imperfect Interfaces

Piezoelectric quasicrystals have attracted extensive attention due to their unique physical and mechanical properties. This paper studies the dynamic response of multilayered two-dimensional decagonal piezoelectric quasicrystal sector plates with imperfect interfaces. Based on the quasicrystal linear elasticity, partial differential state equations along the thickness direction are derived by using the state-space method. Then, by virtue of the differential quadrature method and the Fourier series expansions, this boundary-value problem with mixed boundary conditions and imperfect interfaces is solved. In addition, via the joint coupling matrix, the field quantities in the interior of the structure are connected to those on the external surfaces with numerical instability. Finally, parameter studies on the effects of angular spans, imperfect interfaces, and mixed boundary conditions are numerically investigated where the dimensionless frequencies and modes are exhibited.