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.

Analytical and Experimental Research on Wave Scattering by an Open-Type Rectangular Breakwater with Horizontal Perforated Plates

This study proposes a novel open-type rectangular breakwater combined with horizontal perforated plates on both sides to enhance the sheltering effect of the rectangular box-type breakwaters against longer waves.The hydrodynamic characteristics of this breakwater are analyzed through analytical potential solutions and experimental tests.The quadratic pressure drop conditions are exerted on the horizontal perforated plates to facilitate assessing the effect of wave height on the dissipated wave energy of breakwater through the analytical solution.The hydrodynamic quantities of the breakwater,including the reflection,transmission,and energyloss coefficients,together with vertical and horizontal wave forces,are calculated using the velocity potential decomposition method as well as an iterative algorithm.Furthermore,the reflection and transmission coefficients of the breakwater are measured by conducting experimental tests at various wave periods,wave heights,and both porosities and widths of the horizontal perforated plates.The analytical predicted results demonstrate good agreement with the iterative boundary element method solution and measured data.The influences of variable incident waves and structure parameters on the hydrodynamic characteristics of the breakwater are investigated through further calculations based on analytical solutions.Results indicate that horizontal perforated plates placed on the water surface for both sides of the rectangular breakwater can enhance the wave dissipation ability of the breakwater while effectively decreasing the transmission and reflection coefficients.

Presentation of the Berry-Tabor conjecture in Levy plates

The Berry-Tabor(BT)conjecture is a famous statistical inference in quantum chaos,which not only establishes the spectral fluctuations of quantum systems whose classical counterparts are integrable but can also be used to describe other wave phenomena.In this paper,the BT conjecture has been extended to Lévy plates.As predicted by the BT conjecture,level clustering is present in the spectra of Lévy plates.The consequence of level clustering is studied by introducing the distribution of nearest neighbor frequency level spacing ratios P(r),which is calculated through the analytical solution obtained by the Hamiltonian approach.Our work investigates the impact of varying foundation parameters,rotary inertia,and boundary conditions on the frequency spectra,and we find that P(r)conforms to a Poisson distribution in all cases.The reason for the occurrence of the Poisson distribution in the Lévy plates is the independence between modal frequencies,which can be understood through mode functions.

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.

Study on the application of optical interferometry in the measurement of the coating thickness of color-coated plates

The principle and application of optical interferometry to measure the coating thickness of color-coated plates were introduced in this paper.Additionally,several factors affecting the test results,including coating refractive index,wavelength range,and film thickness range setting,were analyzed.Among these,the refractive index of the color coating,which cannot be measured directly,was identified as the key factor.A solution to this problem was proposed.Finally,the optical interference method and the current detection methods,including the micrometer method and the magnetic eddy current method,were analyzed and compared.The results show that optical interferometry has better repeatability and reproducibility than the current methods and show no significant difference from the current methods through statistical tests.Therefore,the method can be applied to the detection of the coating thickness of color-coated plates.

Generative optimization of bistable plates with deep learning

Bistate plates have found extensive applications in the domains of smart structures and energy harvesting devices.Most bistable curved plates are characterized by a constant thickness profile.Regrettably,due to the inherent complexity of this problem,relatively little attention has been devoted to this area.In this study,we demonstrate how deep learning can facilitate the discovery of novel plate profiles that cater to multiple objectives,including maximizing stiffness,forward snapping force,and backward snapping force.Our proposed approach is distinguished by its efficiency in terms of low computational energy consumption and high effectiveness.It holds promise for future applications in the design and optimization of multistable structures with diverse objectives,addressing the requirements of various fields.

A theory for three-dimensional response of micropolar plates

Through combined applications of the transfer-matrix method and asymptotic expansion technique,we formulate a theory to predict the three-dimensional response of micropolar plates.No ad hoc assumptions regarding through-thickness assumptions of the field variables are made,and the governing equations are two-dimensional,with the displacements and microrotations of the mid-plane as the unknowns.Once the deformation of the mid-plane is solved,a three-dimensional micropolar elastic field within the plate is generated,which is exact up to the second order except in the boundary region close to the plate edge.As an illustrative example,the bending of a clamped infinitely long plate caused by a uniformly distributed transverse force is analyzed and discussed in detail.

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.

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.

Bonding enhancement of cold rolling TA1 P-Ti/AA6061 composite plates via surface oxidation treatment

TA1 P-Ti/AA6061 composite plate was produced by oxidizing the surface of the titanium plate and adopting a cold roll bonding process.The results revealed that the oxide film(Ti6O)prepared on the surface of TA1 pure titanium was easy to crack during the cold roll bonding,thereby promoting the formation of an effective mechanical interlock at the interface,which can effectively reduce the minimum reduction rate of the composite plates produced by cold rolling of titanium and aluminium plates.Moreover,the composite plate subjected to oxidation treatment exhibited high shear strength,particularly at a 43%reduction rate,achieving a commendable value of 117 MPa.Based on oxidation treatment and different reduction rates,the annealed composite plates at temperatures of 400,450,and 500°C displayed favorable resistance to interface delamination,highlighting their remarkable strength-plasticity compatibility as evidenced by a maximum elongation of 31.845%.

Improved YOLOv8n Model for Detecting Helmets and License Plates on Electric Bicycles

Wearing helmetswhile riding electric bicycles can significantly reduce head injuries resulting fromtraffic accidents.To effectively monitor compliance,the utilization of target detection algorithms through traffic cameras plays a vital role in identifying helmet usage by electric bicycle riders and recognizing license plates on electric bicycles.However,manual enforcement by traffic police is time-consuming and labor-intensive.Traditional methods face challenges in accurately identifying small targets such as helmets and license plates using deep learning techniques.This paper proposes an enhanced model for detecting helmets and license plates on electric bicycles,addressing these challenges.The proposedmodel improves uponYOLOv8n by deepening the network structure,incorporating weighted connections,and introducing lightweight convolutional modules.These modifications aim to enhance the precision of small target recognition while reducing the model’s parameters,making it suitable for deployment on low-performance devices in real traffic scenarios.Experimental results demonstrate that the model achieves an mAP@0.5 of 91.8%,showing an 11.5%improvement over the baselinemodel,with a 16.2%reduction in parameters.Additionally,themodel achieves a frames per second(FPS)rate of 58,meeting the accuracy and speed requirements for detection in actual traffic scenarios.

External Factors Influencing the Motion of Tectonic Plates

The investigation aims to understand how external forces influence tectonic plate movement, causing earthquakes and volcanic eruptions. Our emphasis was on calculating perigee forces at various moon-Earth distances. Our initial concern is the fluctuating perigee distance between the Moon and Earth. Later, we will cover Earth’s mass fluctuations caused by crustal inhomogeneity. Gravitational force depends on distance and Earth’s mass variations. Wobbling’s Earth and translation around Sun are additional factors. Tidal variations from the Moon trigger subduction zone earthquakes. Volcanoes in the Ring of Fire are influenced by plate movement on fractures and faults.

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.

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.

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.

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.

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.

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.