Modeling Geometrically Nonlinear FG Plates: A Fast and Accurate Alternative to IGA Method Based on Deep Learning

Isogeometric analysis (IGA) is known to showadvanced features compared to traditional finite element approaches.Using IGA one may accurately obtain the geometrically nonlinear bending behavior of plates with functionalgrading (FG). However, the procedure is usually complex and often is time-consuming. We thus put forward adeep learning method to model the geometrically nonlinear bending behavior of FG plates, bypassing the complexIGA simulation process. A long bidirectional short-term memory (BLSTM) recurrent neural network is trainedusing the load and gradient index as inputs and the displacement responses as outputs. The nonlinear relationshipbetween the outputs and the inputs is constructed usingmachine learning so that the displacements can be directlyestimated by the deep learning network. To provide enough training data, we use S-FSDT Von-Karman IGA andobtain the displacement responses for different loads and gradient indexes. Results show that the recognition erroris low, and demonstrate the feasibility of deep learning technique as a fast and accurate alternative to IGA formodeling the geometrically nonlinear bending behavior of FG plates.

Performance analysis of single-focus phase singularity based on elliptical reflective annulus quadrangle-element coded spiral zone plates

Optical vortices generated by the conventional vortex lens are usually disturbed by the undesired higher-order foci,which may lead to additional artifacts and thus degrade the contrast sensitivity. In this work, we propose an efficient methodology to combine the merit of elliptical reflective zone plates(ERZPs) and the advantage of spiral zone plates(SZPs) in establishing a specific single optical element, termed elliptical reflective annulus quadrangle-element coded spiral zone plates(ERAQSZPs) to generate single-focus phase singularity. Differing from the abrupt reflectance of the ERZPs, a series of randomly distributed nanometer apertures are adopted to realize the sinusoidal reflectance. Typically, according to our physical design, the ERAQSZPs are fabricated on a bulk substrate;therefore, the new idea can significantly reduce the difficulty in the fabrication process. Based on the Kirchhoff diffraction theory and convolution theorem, the focusing performance of ERAQSZPs is calculated. The results reveal that apart from the capability of generating optical vortices,ERAQSZPs can also integrate the function of focusing, energy selection, higher-order foci elimination, as well as high spectral resolution together. In addition, the focusing properties can be further improved by appropriately adjusting the parameters, such as zone number and the size of the consisted primitives. These findings are expected to direct a new direction toward improving the performance of optical capture, x-ray fluorescence spectra, and forbidden transition.

Dirac method for nonlinear and non-homogenous boundary value problems of plates

The boundary value problem plays a crucial role in the analytical investigation of continuum dynamics. In this paper, an analytical method based on the Dirac operator to solve the nonlinear and non-homogeneous boundary value problem of rectangular plates is proposed. The key concept behind this method is to transform the nonlinear or non-homogeneous part on the boundary into a lateral force within the governing function by the Dirac operator, which linearizes and homogenizes the original boundary, allowing one to employ the modal superposition method for obtaining solutions to reconstructive governing equations. Once projected into the modal space, the harmonic balance method(HBM) is utilized to solve coupled ordinary differential equations(ODEs)of truncated systems with nonlinearity. To validate the convergence and accuracy of the proposed Dirac method, the results of typical examples, involving nonlinearly restricted boundaries, moment excitation, and displacement excitation, are compared with those of the differential quadrature element method(DQEM). The results demonstrate that when dealing with nonlinear boundaries, the Dirac method exhibits more excellent accuracy and convergence compared with the DQEM. However, when facing displacement excitation, there exist some discrepancies between the proposed approach and simulations;nevertheless, the proposed method still accurately predicts resonant frequencies while being uniquely capable of handling nonuniform displacement excitations. Overall, this methodology offers a convenient way for addressing nonlinear and non-homogenous plate boundaries.

Love wave propagation in one-dimensional piezoelectric quasicrystal multilayered nanoplates with surface effects

The exact solutions for the propagation of Love waves in one-dimensional(1D)hexagonal piezoelectric quasicrystal(PQC)nanoplates with surface effects are derived.An electro-elastic model is developed to investigate the anti-plane strain problem of Love wave propagation.By introducing three shape functions,the wave equations and electric balance equations are decoupled into three uncorrelated problems.Satisfying the boundary conditions of the top surface on the covering layer,the interlayer interface,and the matrix,a dispersive equation with the influence of multi-physical field coupling is provided.A surface PQC model is developed to investigate the surface effects on the propagation behaviors of Love waves in quasicrystal(QC)multilayered structures with nanoscale thicknesses.A novel dispersion relation for the PQC structure is derived in an explicit closed form according to the non-classical mechanical and electric boundary conditions.Numerical examples are given to reveal the effects of the boundary conditions,stacking sequence,characteristic scale,and phason fluctuation characteristics on the dispersion curves of Love waves propagating in PQC nanoplates with surface effects.

Review of Computational Approaches to Optimization Problems in Inhomogeneous Rods and Plates

In this paper,we review computational approaches to optimization problems of inhomogeneous rods and plates.We consider both the optimization of eigenvalues and the localization of eigenfunctions.These problems are motivated by physical problems including the determination of the extremum of the fundamental vibration frequency and the localization of the vibration displacement.We demonstrate how an iterative rearrangement approach and a gradient descent approach with projection can successfully solve these optimization problems under different boundary conditions with different densities given.

Exact solution for thermal vibration of multi-directional functionally graded porous plates submerged in fluid medium

An analytical method for analyzing the thermal vibration of multi-directional functionally graded porous rectangular plates in fluid media with novel porosity patterns is developed in this study.Mechanical properties of MFG porous plates change according to the length,width,and thickness directions for various materials and the porosity distribution which can be widely applied in many fields of engineering and defence technology.Especially,new porous rules that depend on spatial coordinates and grading indexes are proposed in the present work.Applying Hamilton's principle and the refined higher-order shear deformation plate theory,the governing equation of motion of an MFG porous rectangular plate in a fluid medium(the fluid-plate system)is obtained.The fluid velocity potential is derived from the boundary conditions of the fluid-plate system and is used to compute the extra mass.The GalerkinVlasov solution is used to solve and give natural frequencies of MFG porous plates with various boundary conditions in a fluid medium.The validity and reliability of the suggested method are confirmed by comparing numerical results of the present work with those from available works in the literature.The effects of different parameters on the thermal vibration response of MFG porous rectangular plates are studied in detail.These findings demonstrate that the behavior of the structure within a liquid medium differs significantly from that within a vacuum medium.Thereby,they offer appropriate operational approaches for the structure when employed in various mediums.

Least Square Finite Element Model for Analysis of Multilayered Composite Plates under Arbitrary Boundary Conditions

Laminated composites are widely used in many engineering industries such as aircraft, spacecraft, boat hulls, racing car bodies, and storage tanks. We analyze the 3D deformations of a multilayered, linear elastic, anisotropic rectangular plate subjected to arbitrary boundary conditions on one edge and simply supported on other edge. The rectangular laminate consists of anisotropic and homogeneous laminae of arbitrary thicknesses. This study presents the elastic analysis of laminated composite plates subjected to sinusoidal mechanical loading under arbitrary boundary conditions. Least square finite element solutions for displacements and stresses are investigated using a mathematical model, called a state-space model, which allows us to simultaneously solve for these field variables in the composite structure’s domain and ensure that continuity conditions are satisfied at layer interfaces. The governing equations are derived from this model using a numerical technique called the least-squares finite element method (LSFEM). These LSFEMs seek to minimize the squares of the governing equations and the associated side conditions residuals over the computational domain. The model is comprised of layerwise variables such as displacements, out-of-plane stresses, and in- plane strains, treated as independent variables. Numerical results are presented to demonstrate the response of the laminated composite plates under various arbitrary boundary conditions using LSFEM and compared with the 3D elasticity solution available in the literature.

无界域上具有记忆的非自治Plate方程随机吸引子的存在性

研究无界域上一类具有衰退记忆和加性噪声的非自治Plate方程解的长时间行为.利用一致估计验证了解的拉回渐近紧性,获得了其随机吸引子的存在性.

Relationships between distribution characteristics of ceramic fragments and anti-penetration performance of ceramic composite bulletproof insert plates

Through quantitative statistics and morphological characterization of ceramic fragments for ceramic composite bulletproof insert plates(CCBIPs),distribution characteristics of ceramic fragments within a specific size range were analyzed for different Armor Piercing Incendiary(API)and shot times.To quantitatively evaluate the effect of energy absorption for ceramic plates,a model of energy absorption during penetration for CCBIPs was established based on statistics of the size distribution of ceramic fragments(SDCF).Variation in the SDCF and its influence on energy absorption for CCBIPs were investigated.The results indicate that the distribution feature of ceramic fragments in the range of 0.25-2.25 mm is Gaussian distribution.Compared with Type 56 of API(56-API),ceramic fragments formed by 53-API with higher kinetic energy possess more quantity and more concentrated distribution,whose average equivalence size decreases by 6.5%,corresponding to increasing by 83.9%of estimated energy absorption.Besides,the ability of CCBIPs to resist the third shot is significantly weakened,whose estimated energy absorption decreases by 58.8%compared with the first shot.More concentrated distribution and fewer fragments are formed after the third shot,the average equivalence size of ceramic fragments increases by 6.9%,which may attribute to the micro-cracks induced by the previous two shots.

Locking plates for distal fibula fractures in young and elderly patients:A retrospective study

BACKGROUND Ankle fractures are common injuries in the young and elderly populations.To prevent post-traumatic arthritis,an anatomic reconstruction of the ankle structure is mandatory.Open reduction and internal fixation is the treatment of choice among orthopaedics.Conventional plates allow stability of the fracture if bone quality is present.Locking plates might offer an advantage for the treatment of lateral malleolar fracture in patients with comminution,severe instability,distal fractures,or osteoporotic bone.Our hospital introduced a new locking plate for fracture of the distal fibula.AIM To evaluate locking plates in terms of outcomes and complications in young and elderly patients.METHODS We retrospectively reviewed a total of 67 patients treated for displaced distal fibula fractures.Demographic data,number of comorbidities,use of inter fragmentary screw,complication,time of fracture healing,partial or full weight bearing,and reoperation were recorded for all patients.Clinical outcome was assessed by the American Orthopedic Foot and Ankle Society clinical scoring system.Radiographs were obtained at 4,8,12,16,20,and 24 wk until radiographic union was obtained.RESULTS All patients displayed complete bony union on radiographic assessment,and no patients developed any serious complications.We observed two superficial infections,one delayed wound healing,and two plate intolerances.Significant differences were observed between the two age groups in terms of radiographic healing(11.9 wk in younger patients vs 13.7 wk in older patients;P=0.011)and in the American Orthopedic Foot and Ankle Society score at 6 mo after surgery(88.2 in younger patients vs 86.0 in older patients;P=0.001)and at 12 mo after surgery(92.6 in younger patients vs 90.0 in older patients;P=0.000).CONCLUSION Locking plates provide a stable and rigid fixation in multifragmentary and comminuted fractures or in the presence of poor bone quality.

Time-sequenced damage behavior of reactive projectile impacting double-layer plates

The time-sequenced damage behavior of the reactive projectile impacting double-layer plates is discussed.The analytical model considering the combined effect of kinetic and chemical energy is developed to reveal the damage mechanism.The influences of impact velocity and reactive projectile chemical characteristics on the damage effect are decoupled analyzed based on this model.These analyses indicate that the high energy releasing efficiency and fast reaction propagation velocity of the reactive projectile are conducive to enhancing the damage effect.The experiments with various reactive projectiles impact velocity increasing from 702 to 1385 m/s were conducted to verify this model.The experimental results presented that,the damage hole radius of the rear-plate increases with the increase of impact velocity.At the impact velocity of 1350 m/s,the radius of damage hole formed by PTFE/Al/Bi_(2)O_(3),PTFE/Al/MoO_(3),PTFE/Al/Fe_(2)O_(3)projectile on the rear-plate become smaller in sequence.These results are consistent with the analytical model prediction,demonstrating that this model can predict the damage effect quantitatively.This work is of constructive significance to the application of reactive projectiles.

Residual Stresses and Forming Quality of Metal Bipolar Plates for PEMFC During the Stamping Process

Stamping is a critical step in the manufacture of metallic bipolar plates.Typically,residual stress and a spring back effect appear on the bipolar plate after the stamping process,which impacts on the performance and lifetime of the proton exchange membrane fuel cell(PEMFC).The residual stress and spring back behavior which occur as a result of stamping a bipolar plate are investigated in this study.The effects of the punch radius,the die radius,the channel depth,and the clearance between the punch and the die on the residual stress and forming quality of the bipolar plate are examined.The stamping process can be divided into three stages.The high stress area and the middle section residual stress area were selected to study the formation process and to obtain the composition of the residual stress regions.Spring back was mainly related to the position of the fixed end of the sheet and the degree of plastic deformation,and the sheet thickness have increased by 2μm after spring back.Based on the results of finite element analysis,as described by the distribution of residual stress,the formation,the thickness of the middle cross section and the equivalent plastic strain,it was found that all the tool parameters affected the distribution of the residual stress.This research can provide a design reference for the manufacture of metallic bipolar plates based on the stamping process.

Sound absorbing properties of spiral metasurfaces inspired by micro-perforated plates

As a kind of classical low-frequency sound-absorbing material,the microperforated plate(MPP)has been widely used.Here,we inspired by the sound absorption mechanism of the MPP,a spiral metasurface(SM)is designed and the analytical solution of acoustic impedance and sound absorption coefficient are obtained.The relationship between the sound absorption properties of the MPP and the SM with their own structures is systematically studied,and the analytical solutions are used to optimise the structure.It is concluded that the MPP and the SM of the same thickness achieve effective absorption in the frequency range between 390-900 Hz and 1920-4266 Hz,with a total thickness less than 1/6 of the wavelength.Meanwhile,the numerical calculation shows that the MPP and SM can match well with the background medium in the effective rang.Our study provides new insights into the design methods of sound-absorbing materials and is potentially suitable for many acoustic engineering applications.

Blast disruption using 3D grids/perforated plates for vehicle protection

In this work, blast disruption and mitigation using 3D grids/perforated plates were tested for underbelly and side protection of vehicles. Two vehicle simulants were used: a small-scale one for side vehicle protection assessment and a true-to-scale simulant for underbelly protection testing. The deformation of target plates was assessed. These were either unprotected or protected by three different types of disruptors. The first disruptor was made of a sandwich structure of two perforated plates filled with a thin aluminum structure allowing the air to pass through. The two other disruptors were made of pieces of cast metallic foam. Two different kinds of foams were used: one with large cells and the second one with small cells. Beforehand, the mitigation efficiency of the disruptors was evaluated using an explosivedriven shock tube(EDST). The experiments showed that blast disruption/mitigation by 3D grid/perforated plate structures was not suitable for vehicle side protection. However, 3D grids/perforated structures proved to be relatively effective for underbelly protection compared to an equivalent mass of steel.

Copper Ions Removal from Wastewater by Electrocoagulation Using Cement-based Cathode Plates

The present work uses PEO solution to well disperse carbon fiber and identifies percolation thresholds of carbon fiber and carbon black which are used as conductive fillers.The resultant cathode plates have an average compressive strength of 27.3 MPa and flexural strength of 29.09 MPa,which demonstrate excellent mechanical properties.The Cu^(2+)removal efficiency was measured at different current densities in EC process with cement-based cathode plate,while the voltage changes were recorded.The results showed that the cement-based cathode plate operated stably and achieved 99.7%removal of 1 L of simulated wastewater with a Cu^(2+)concentration of 200 ppm at a current density of 8 m A/cm^(2)for 1 h.Characterization of floc and tested cathode plates,SEM and EDS analyses,and repeatability testing of the tested plates demonstrate the reusability of the plates,proving that cement-based plates can effectively replace metal cathode plates,reduce the cost of EC and improve the applicability of EC devices.

Anisotropy of mechanical properties of 2297-T87 Al–Li alloy thick plates

The tensile properties of 2297-T87 Al–Li alloy thick plates at different thickness position and in different direction were analyzed via tensile testing,optical microscopy(OM),X-ray diffraction(XRD),scanning electron microscopy(SEM),energy dispersive spectrometry(EDS),and transmission electron microscopy(TEM).Results indicated that the ultimate tensile strength(UTS)and yield strength(YS)of the alloy decreased firstly and then increased from the 1/8T position to the 1/2T position,whereas elongation to failure(Ef)decreased gradually such that its value along the rolling direction(RD)was higher than those along the transverse direction(TD)at the same thickness position.From the 1/8T position to the 3/8T position of the alloy,the UTS and YS along the TD were higher than those along the RD.At the 1/2T position of the alloy,the UTS,YS,and Ef along the RD were the highest,whereas those along the normal direction(ND)were the lowest.Microstructural observations further revealed that the anisotropy of tensile properties was related to grain morphology,crystal texture,second-phase particles,and Li atom segregation.

High-Velocity Projectile Impact Behaviour of Friction Stir Welded AA7075 Thick Plates

In this study, high velocity impact behaviour of friction stir welded AA7075-T651 25 mm thick plates were investigated using a 7.62 mm × 51 mm lead core and 7.62 mm × 39 mm steel core projectiles. Prior to ballistic trails, mechanical and metallurgical properties of friction stir welded AA 7075-T651 25 mm thick plates were studied. Microstructural and hardness studies revealed that friction stir welds constituted three distinct regions namely Weld Nugget(WN), Thermo-Mechanically Affected Zone(TMAZ) and Heat Affected Zone(HAZ). Base Material(BM) and all three weld regions were ballistically tested as per military standard NIJ.0108.01 using lead and steel core bullets at maximum permissible velocities of 830 ± 20 and 700 ± 30 m/s, respectively. It has been found that base material(AA7075-T651)and all three weld regions of 25 mm thick plates were able to resist perforation by both types of projectiles used. However depth of penetration has been found to increase from BM to WN, HAZ and TMAZ for both types of projectiles. In all cases steel core projectiles caused higher depth of penetration compared to those caused by lead core projectiles. TMAZs of the friction stir welds were found to be the weakest zone. The fracture that occurred in the base material was spall fragmentation indicating brittle failure, whereas all zones of friction stir welded AA7075-T651 targets with a front petalling, indicating ductile failure. The post-ballistic tested samples showed no significant change in the microstructure of the BM and WN. On the other hand, TMAZ and HAZ showed severe grain deformation in the direction of projectile penetration, and the formation of adiabatic shear bands(ASB). This work showed that 25 mm thick friction stir welded AA7075-T651 joints responded well to ballistic impact loads, making them a good choice for light combat vehicles.

Multiresolution method for bending of plates with complex shapes

A high-accuracy multiresolution method is proposed to solve mechanics problems subject to complex shapes or irregular domains.To realize this method,we design a new wavelet basis function,by which we construct a fifth-order numerical scheme for the approximation of multi-dimensional functions and their multiple integrals defined in complex domains.In the solution of differential equations,various derivatives of the unknown function are denoted as new functions.Then,the integral relations between these functions are applied in terms of wavelet approximation of multiple integrals.Therefore,the original equation with derivatives of various orders can be converted to a system of algebraic equations with discrete nodal values of the highest-order derivative.During the application of the proposed method,boundary conditions can be automatically included in the integration operations,and relevant matrices can be assured to exhibit perfect sparse patterns.As examples,we consider several second-order mathematics problems defined on regular and irregular domains and the fourth-order bending problems of plates with various shapes.By comparing the solutions obtained by the proposed method with the exact solutions,the new multiresolution method is found to have a convergence rate of fifth order.The solution accuracy of this method with only a few hundreds of nodes can be much higher than that of the finite element method(FEM)with tens of thousands of elements.In addition,because the accuracy order for direct approximation of a function using the proposed basis function is also fifth order,we may conclude that the accuracy of the proposed method is almost independent of the equation order and domain complexity.

Vibration characteristics of sandwich plates with an auxetic honeycomb core and laminated three-phase skin layers under blast load

In this article,vibration characteristics of sandwich plates with an auxetic honeycomb core and laminated three-phase skin layers subjected to blast load are studied.Higher-order ES-MITC3 element based on higher-order shear deformation theory(HSDT)to achieve the governing equations.The sandwich plates with the ultra-light feature of the auxetic honeycomb core layer(negative Poisson’s ratio)and reinforced by two laminated three-phase skin layers.The obtained results in our work are compared with other previously published to confirm accuracy and reliability.In addition,the effects of parameters such as geometrical and material parameters on the vibration characteristics of sandwich plates with an auxetic honeycomb core and laminated three-phase skin layers are fully investigated.

Statics, vibration, and buckling of sandwich plates with metamaterial cores characterized by negative thermal expansion and negative Poisson's ratio

This paper proposes a three-dimensional(3D)Maltese cross metamaterial with negative Poisson’s ratio(NPR)and negative thermal expansion(NTE)adopted as the core layers in sandwich plates,and aims to explore the relations between the mechanical responses of sandwich composites and the NPR or NTE of the metamaterial.First,the NPR and NTE of the metamaterial are derived analytically based on energy conservation.The effective elastic modulus and mass density of the 3D metamaterial are obtained and validated by the finite element method(FEM).Subsequently,the general governing equation of the 3D sandwich plate under thermal environments is established based on Hamilton’s principle with the consideration of the von Kármán nonlinearity.The differential quadrature(DQ)FEM(DQFEM)is utilized to obtain the numerical solutions.It is shown that NPR and NTE can enhance the global stiffness of sandwich structures.The geometric parameters of the Maltese cross metamaterial significantly affect the responses of the thermal stress,natural frequency,and critical buckling load.