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The aim of this discussion is to establish a connection between the model for sandwich beams presented in Schöftner (Acta Mech 234:2543–2560, 2023) and the so-called Krajcinovic model. Although the two models turn out to be quite similar, Krajcinovic model displays a richer kinematics and has been developed in the literature by following slightly different methodologies with respect to that adopted by Schöftner, the latter having the merit of providing equilibrium equations that allow the computation of the interfacial stresses. We also offer some remarks on the capabilities and accuracies of the models discussed. [ABSTRACT FROM AUTHOR]

This work deals with fracture mechanisms in quasi-brittle materials, focusing on the characterization of the Fracture Process Zone (FPZ) of specimens under tensile load. Particularly, paper was used as model material. Experiments were conducted on notched and unnotched specimens. Based on an image analysis of these observations, a stochastic finite element model was developed, using both a nonlocal stress-based approach and a discretized random field modeling of the Young's modulus. The proposed methodology allowed characterizing the damage zone and the size of the FPZ, analyzing the influence of the mesostructure, composed of flocs (fiber aggregates where the basis weight is larger than the average one) and antiflocs (complement of flocs). The area of the active FPZ and the normalized stress drop were linked using a surface energy dissipated in the active FPZ. The stress drop, until limiting value, increased with the width of the active FPZ. Finally, a relationship between the surface energy and the nonlocal internal length was established. [ABSTRACT FROM AUTHOR]

Transport of volatile organic compounds (VOCs) through porous media with active surfaces takes place in many important applications, such as in cellulose-based materials for packaging. Generally, it is a complex process that combines diffusion with sorption at any time. To date, the data needed to use and validate the mathematical models proposed in literature to describe the mentioned processes are scarce and have not been systematically compiled. As an extension of the model of Ramarao et al. (Dry Technol 21(10):2007–2056, 2003) for the water vapor transport through paper, we propose to describe the transport of VOCs by a nonlinear Fisher–Kolmogorov–Petrovsky–Piskunov equation coupled to a partial differential equation (PDE) for the sorption process. The proposed PDE system contains specific material parameters such as diffusion coefficients and adsorption rates as multiplication factors. Although these parameters are essential for solving the PDEs at a given time scale, not all of the required parameters can be directly deduced from experiments, particularly diffusion coefficients and sorption constants. Therefore, we propose to use experimental concentration data, obtained for the migration of dimethyl sulfoxide (DMSO) through a stack of paper sheets, to infer the sorption constant. These concentrations are considered as the outcome of a model prediction and are inserted into an inverse boundary problem. We employ Physics-Informed Neural Networks (PINNs) to find the underlying sorption constant of DMSO on paper from this inverse problem. We illustrate how to practically combine PINN-based calculations with experimental data to obtain trustworthy transport-related material parameters. Finally we verify the obtained parameter by solving the forward migration problem via PINNs and finite element methods on the relevant time scale and show the satisfactory correspondence between the simulation and experimental results. Article Highlights: A mathematical model to describe transport of polar volatile organics through paper is proposed. Based on experimental data, the deep learning method of physics-informed neural networks (PINNs) is used to solve the inverse problem of finding the sorption time constant. Solutions for the forward problem are obtained by the standard finite element method (FEM) and PINN methods. These solutions are compared with each other as well as with the experimental data to verify the model. [ABSTRACT FROM AUTHOR]

An innovative approach of using a laboratory embossing prototype was carried out to develop and optimize tissue papers, to quantify the influence of "deco" and "micro" embossing. A comparison between non-embossed and embossed tissue papers was conducted to investigate the effect of this process, on industrial and laboratory-made structures, evaluated by mechanical and softness properties. To identify the influence of the embossing patterns, the fiber composition and the creping process, a creped industrial base tissue paper, a disintegrated fibrous suspension obtained from this one, and an industrial never-dried bleached eucalyptus kraft pulp, were used as samples. These last two materials were used to produce similar industrial base tissue paper, in other words, handsheets with a grammage of 17 g/m2 and unpressed. The end-use tissue properties were evaluated on the non-embossed and embossed structures. The results indicated that the embossing process produced bulkier and more porous structures, at the expense of reduced mechanical and softness properties, more intensified in the "micro" embossing than in the "deco" embossing. The effect of fiber composition shows that the mechanical properties were increased with an adverse effect on the structures' TSA-softness. Furthermore, these properties are enhanced for the structures where creping process effects are presents. The performance of structures with and without embossing allowed to quantify the functional properties of softness and strength, combining ISO experimental methods and computational approaches that benefit from modeling strategies considering its structural hierarchy at the fiber and structure levels, and the shape pattern used in the embossing process. Finite Element Model (FEM) analysis enabled a better understanding of how the embossing patterns affect the mechanical properties during the embossing process. The experimental results were validated using FEM simulation, which proved that "micro" pattern has a higher stress field value, and consequently a lower mechanical strength. Overall, the results indicate that the embossing prototype can be used as an opportunity to investigate the embossing process at laboratory scale and to optimize the final end-use tissue properties due to the controlled process parameters implemented in this methodology. [ABSTRACT FROM AUTHOR]

The thermal response in paper has been studied by thermography. It was observed that an inhomogeneous deformation pattern arose in the paper samples during tensile testing. In the plastic regime a pattern of warmer streaks could be observed in the samples. On the same samples digital image correlation (DIC) was used to study local strain fields. It was concluded that the heat patterns observed by thermography coincided with the deformation patterns observed by DIC. Because of its fibrous network structure, paper has an inhomogeneous micro-structure, which is called formation. It could be shown that the formation was the cause of the inhomogeneous deformations in paper. Finite element simulations was used to show how papers with different degrees of heterogeneity would deform. Creped papers, where the strain at break has been increased, were analysed. For these paper it was seen that an overlaid compaction of the paper was created during the creping process. During tensile testing this was recovered as the paper network structure was strained. [ABSTRACT FROM AUTHOR]

Understanding heat transfer in corrugated fibreboard is important to the design of more effective packaging for industries which involve the freezing and chilling of food. In this work the thermal conductivity of papers which compose corrugated fibreboard were measured and used to validate finite element models of heat transfer in fibreboard. The results showed paper to be highly anisotropic, with thermal conductivity in the machine and cross machine directions being almost an order of magnitude larger than in the thickness direction. The finite element models showed good agreement with experimental results and demonstrated that the majority of heat transfer in corrugated fibreboard is though the fluted medium. Based on the finite element models, simple models for the prediction of the thermal performance of corrugated board were evaluated and shown to be very effective in reproducing the results of the more complex finite element methods. These simple methods can be used to perform corrugated fibreboard design calculations, and the models with and without radiation can be used to provide estimates of the lower and upper bounds of the thermal resistance for a given board design. [ABSTRACT FROM AUTHOR]

It is pointed out that the Levinson-Reddy beam theory should not be used as a higher-order model for the core, although it considers cross-sectional warping: this beam model is applicable for zero shear stress conditions at the core-skin-interfaces only, which is usually not the case for sandwich structures. The resulting sandwich beam model in [[2]] is a special solution from the Krajcinovic-Bardella derivation, which allows for richer kinematics because it considers zig-zag kinematics. Author's response to "Discussion on the paper by Schoeftner, J., "A verified analytical sandwich beam model for soft and hard cores: comparison to existing analytical models and finite element calculations", Acta Mech, 234, 2543-2560 (2023)" by Lorenzo Bardella. [Extracted from the article]

In this paper a three-dimensional model of a novel electronic package has been developed using Finite element analysis to evaluate the shear load, tensile, bending and thermal stresses. Simulations of a complete flexible flip chip electronic packaging method are performed to minimize stresses on the packaged electronic device to improve robustness and reliability. Three component under-fill adhesives (Loctite 4860, Loctite 480 and Loctite 4902) and three circuit substrate materials (Kapton, Mylar and PEEK) are compared and the optimal thickness of each is found by shear load, tensile load, bending test and thermal expansion simulations. A fixed die size of 3.5 mm × 8 mm × 0.53 mm has been simulated and evaluated experimentally under shear and bending load. The shear and bending experimental results show good agreement with the simulation results and verify the simulated optimal thickness of the adhesive layer. The Kapton substrate together with the Loctite 4902 adhesive were identified as the optimum in the simulation. The simulation of under-fill adhesive and substrate thickness identified an optimum configuration of a 0.045–0.052 mm thick substrate layer and a 0.042–0.045 mm thickness of the Loctite 4902 adhesive. The bending simulation has also been used to determine the neutral axis of the encapsulated electronic package in this paper, thus identifying the optimal material and thickness for the encapsulation layer of the package. [ABSTRACT FROM AUTHOR]

Paper materials are well-known to be hydrophilic unless chemical and mechanical processing treatments are undertaken. The relative humidity impacts the fiber elasticity, the interfiber joint behavior and the failure mechanism. In this work, we present a comprehensive experimental and computational study on mechanical properties of the fiber and the fiber network under humidity influence. The manually extracted cellulose fiber is exposed to different levels of humidity, and then mechanically characterized using atomic force microscopy, which delivers the humidity dependent longitudinal Young's modulus. We describe the relation and calibrate the data into an exponential function, and the obtained relationship allows calculation of fiber elastic modulus at any humidity level. Moreover, by using confoncal laser scanning microscopy, the coefficient of hygroscopic expansion of the fibers is determined. We further present a finite element model to simulate the deformation and the failure of the fiber network. The model includes the fiber anisotropy and the hygroscopic expansion using the experimentally determined constants, and further considers interfiber behavior and debonding by using a humidity dependent cohesive zone interface model. Simulations on exemplary fiber network samples are performed to demonstrate the influence of different aspects including relative humidity and fiber-fiber bonding parameters on the mechanical features, such as force-elongation curve, strength and extensibility. Finally, we provide computational insights for interfiber bond damage pattern with respect to different humidity level as further outlook. [ABSTRACT FROM AUTHOR]

Researchers often summarize their work in the form of scientific posters. Posters provide a coherent and efficient way to convey core ideas expressed in scientific papers. Generating a good scientific poster, however, is a complex and time-consuming cognitive task, since such posters need to be readable, informative, and visually aesthetic. In this paper, for the first time, we study the challenging problem of learning to generate posters from scientific papers. To this end, a data-driven framework, which utilizes graphical models, is proposed. Specifically, given content to display, the key elements of a good poster, including attributes of each panel and arrangements of graphical elements, are learned and inferred from data. During the inference stage, the maximum a posterior (MAP) estimation framework is employed to incorporate some design principles. In order to bridge the gap between panel attributes and the composition within each panel, we also propose a recursive page splitting algorithm to generate the panel layout for a poster. To learn and validate our model, we collect and release a new benchmark dataset, called NJU-Fudan Paper-Poster dataset, which consists of scientific papers and corresponding posters with exhaustively labelled panels and attributes. Qualitative and quantitative results indicate the effectiveness of our approach. [ABSTRACT FROM AUTHOR]

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A paper transport mechanism that generates tractive force in the cross direction perpendicular to the paper transport direction was developed. The mechanics of this mechanism were then investigated by using the finite element method (FEM). A pair of tapered rubber rollers is the key point of the mechanism. Each roller has two tapered surfaces that thin out in the same direction. The thin sides of both tapered rollers face each other symmetrically to form the center of the transport mechanism. A cylindrical steel roller is pressed toward the tapered roller by a spring. Paper sheets are nipped between the tapered rubber roller and the cylindrical steel roller. On being pressed, the tapered roller is bent around the mid point of the side of the roller because of it has an asymmetrical cross section. The bend first produces shear stress on the contacting area perpendicular to the transport direction. Second, it produces a bulgy deformation so the roller shape is pressed out in the same direction. These processes generate tractive force on the paper. However, the tapered roller generates not only a tractive force but also a twisting moment. Therefore, one roller has two tapered surfaces to cancel the twisting moment. FEM analysis indicates that the tractive force could be estimated within 20% error in comparison with the measured value. The advantages of the new mechanism are that rubber rollers are used in almost all paper-handling equipment and simply cutting two tapers can generate tractive force. This mechanism improves transport reliability preventing wrinkles and slack. [ABSTRACT FROM AUTHOR]

The accuracy of ultrasonic nondestructive examination is limited by the limitation of near field diffraction. With the development of nearfield optical, angular spectrum method is introduced into the acoustic field, which provides a significant direction for the ultrasonic diffraction limit resolution detection. The main research of this paper is the transmission of near field ultrasound in thin workpiece and the law of the interaction of tiny flaws. The paper establishes the relationship between the longitudinal wave signal and the structure of the workpiece and the types of flaws. A method is found that whether there are flaws can be determined near field area by analysing the acoustic field characteristics of workpiece surface. Finally, comparing the calculation results with the finite element simulation, they verify each other, the method turns out to be correct in this paper. The model can also be used to improve the ultrasonic noise reduction algorithm and the extraction of minimal defect feature. It has a greatly practical significance. [ABSTRACT FROM AUTHOR]

Capacitive and optical-based pressure sensors are considered for wide application in industries and R&D labs due to their superior performance. In general, these sensors use a diaphragm as a sensing element that needs to be designed accurately to achieve the desired level of accuracy for a higher operating range of the sensor. To design such a diaphragm, the conventional strain-based model cannot be used efficiently as the strain gradient starts dominating to introduce non-linear deformation with respect to the applied load when the diaphragm thickness reduces or the operating range increases beyond a certain value. Thus, there is a need to establish a comprehensive understanding and accurate modeling method to establish the underlying mechanism of the strain gradient. In view of this, a finite element analysis is carried out with moving-mesh to investigate the effect of the strain gradient phenomenon extensively in this paper. For the investigation, a few parameters are studied such as strain, strain gradient, bending rigidity, and deflection. It shows that the strain gradient spreads radially on the diaphragm and its zone of influence depends on the thickness as well as the applied pressure. This increases the bending rigidity significantly and the diaphragm deflection becomes non-linear as compared to the classical theory of bending. For validation of the present model, the bending rigidity and the deflection behavior are also compared with an earlier developed mathematical model as well as experimental results, and the same is discussed in this paper. The present work is useful for an accurate design and optimization of a diaphragm or a flexure for small size or/and higher operating range of pressure sensors and actuators. [ABSTRACT FROM AUTHOR]

Dry–wet cycles can cause significant deterioration of compacted loess and thus affect the safety of fill slopes. The discrete element method (DEM) can take into account the non-homogeneous, discontinuous, and anisotropic nature of the geotechnical medium, which is more capable of reflecting the mechanism and process of instability in slope stability analysis. Therefore, this paper proposes to use the DEM to analyze the stability of compacted loess slopes under dry–wet cycles. Firstly, to solve the complex calibration problem between macro and mesoscopic parameters in DEM models, an efficient parameter optimization method was proposed by introducing the chaotic particle swarm optimization with sigmoid-based acceleration coefficients algorithm (CPSOS). Secondly, during the parameter calibration, a new indicator, the bonding ratio (BR), was proposed to characterize the development of pores and cracks in compacted loess during dry–wet cycles, to reflect the impact of dry–wet action on the degradation of bonding between loess aggregates. Finally, according to the results of parameter calibration, the stability analysis model of compacted loess slope under dry–wet cycling was established. The results show that the proposed optimization calibration method can accurately reflect the trend of the stress–strain curve and strength of the actual test results under dry–wet cycles, and the BR also reflects the degradation effect of dry–wet cycles on compacted loess. The slope stability analysis shows that the DEM reflects the negative effect of dry–wet cycles on the safety factor of compacted loess slopes, as well as the trend of gradual stabilization with dry–wet cycles. The comparison with the finite element analysis results verified the accuracy of the discrete element slope stability analysis. [ABSTRACT FROM AUTHOR]

How to raise the bridge barrier with a concrete base height of only 51 cm to SS level of protection is not yet studied. In order to effectively retrofit an existing concrete barrier design to meet new crash testing criteria, the structural dimensions and concrete strength of the existing bridge barrier were investigated, and finite element simulation analysis was carried out, and simulation suggested the existing barrier was insufficient. Based on the structural dimension design principles of bridge barriers, the existing structure of bridge barrier was designed after adding lightweight and high-strength B750HL material crossbeams and posts on top of the concrete base, and the bearing capacity of the bridge barrier was calculated based on the yield line theory. Then, a finite element simulation analysis model was established to study and analyze the blocking, guiding, and cushioning functions of the improved design of bridge barrier. Finally, full-scale-vehicle crash tests were conducted with the SS-level small car, bus, and tractor-van trailer for this bridge barrier design scheme. This paper is the world's first to use B750HL steel as the material for the crossbeam and post of a bridge barrier with a concrete base height of only 51 cm. According to the research results, the B750HL bridge barrier, which was designed based on the calculation of structural dimension design and yield line theory, effectively reduces the increased constant load on the bridge deck caused by the extra crossbeams and posts. At the same time, it can reduce material costs and save engineering costs. After being verified by finite element simulation crash tests and full-scale-vehicle crash tests, the protective capacity of the B750HL bridge barrier was proven to meet the SS-level evaluation requirements of the Standard for Safety Performance Evaluation of Highway Barriers (JTG B05-01-2013). The research findings of this paper is that the finite element simulation crash tests can effectively simulate full-scale-vehicle crash test, and the finite element simulation crash tests is reliable. If the safety performance of the barrier in the finite element simulation crash tests meets the requirements, the probability of passing the full-scale-vehicle crash test is higher. Therefore, a design scheme is proposed for the B750HL bridge barrier to improve hybrid bridge barriers at a height of 51 cm or more based on various design methods. [ABSTRACT FROM AUTHOR]

In this paper a smoothing procedure is suggested for the 3D beam-to-beam contact. A smooth segment is defined basing on current position vectors of three nodes limiting two adjacent finite elements. The approximated fragment of a beam axis as a 3D curve spans between the centre points of these elements. The curve is described parametrically using three Hermite polynomials. The four boundary conditions necessary to determine the coefficients for each of these polynomials involve co-ordinates and slopes at the curve ends. The slopes are defined in terms of the element nodal co-ordinates, too. There is no dependence on nodal rotations so this formulation can be embedded in a beam analysis using any type of beam finite element. This geometric representation of the curve is incorporated into the 3D beam-to-beam frictional contact model with the penalty method used to enforce contact constraints. The residual vector and the corresponding tangent stiffness matrix are determined for the normal part of contact and for the stick or slip state of friction. A few numerical examples are presented to show the performance of the suggested smoothing procedure in the cases featuring large frictional sliding. [ABSTRACT FROM AUTHOR]

The aim of this paper is to propose an experimental procedure for determining the characteristic length of a strain gradient model. The identification problem is studied through a virtual pull-out test of a rigid bar along the symmetry axis of a cylindrical strain gradient elastic domain. To allow an accurate parameter identification based on measured data, we investigate the effect of the characteristic length on the mechanical fields for this problem. We see a significant sensitivity of the inflection point of the displacement profile evaluated on the cross section of the cylinder, with respect to the characteristic length. By adjusting the characteristic length of the strain gradient such that the theoretical models match best with experimental measurements of the surface displacement fields, the characteristic length of the strain gradient can be estimated. In order to allow for more efficient analysis and an almost real-time parameter identification, the initial three-dimensional (3D) problem is reduced to a one-dimensional (1D) problem by exploiting the cylindrical symmetry of the problem. As will be shown, an accurate 1D finite element method (FEM) strain gradient solution can be obtained for this simplified problem. Since the cylindrical symmetry is only true in an infinitely long cylinder, specific boundary conditions are constructed on a cylinder of finite length, which is then used for the comparison of the 1D and 3D problems. Results show, however, that the structural response at the inflection point is insensitive to whether the specific boundary conditions are considered or not, which is why the 1D model can be used for parameter identification. Since the proposed approach is methodological, it can be applied to any material. As a prototype problem in this paper, we consider the case of a bar embedded in Portland cement concrete. [ABSTRACT FROM AUTHOR]

The space debris in Earth's orbit has increased drastically due to the failure of spacecraft, rocket bodies, and mission-related objects. These objects in orbit increase the space waste and challenge other flying objects such as spacecraft. A hypervelocity impact of space debris on spacecraft structures can have a range of effects (mechanical damage and functional failure), raising significant concerns about spacecraft safety. This paper reviews the different studies on the performance and development of the Whipple shield against the hypervelocity impact of space debris. The study focuses on the impact mechanism, dynamic Fragmentation of materials, strength models, Equation of state, characteristics, and model of the debris cloud. The strength models (Steinberg–Guinan and Johnson–Cook) and Mie–Gruneisen equation of state, primarily used for hypervelocity impact applications, are thoroughly covered in this study. The study also reported the various experimental and numerical techniques for high and hypervelocity impact. The study concluded that mesh-based, mesh-free, and hybrid finite element methods are reliable for analyzing Whipple shield targets to resist hypervelocity impact. The study also observed that the two-stage light gas gun technique investigates most experimental analyses of hypervelocity impact on the Whipple shield. Alongside reviewing the abovementioned aspects, this paper also underlines the future scope of study in this paradigm. The authors strongly believe that this study provides more insights into the fundamentals and perceptions of the Whipple shield to protect the spacecraft against the hypervelocity impact of space debris. [ABSTRACT FROM AUTHOR]

A significant number of wind bracings in existing railway transom top bridges are numerically assessed deficient against the assessment nosing load recommended by the AS5100, where in almost all cases, there is no observed evidence of wind bracings being overloaded. This paper estimates the nosing load applied by various trains to a couple of random spans of an existing railway transom top bridge. Firstly, field testing of this bridge is conducted and the measured stresses at the mid-center of girders and wind bracings are collected during various normal train operations to validate the developed Finite Element (FE) models of this bridge. Then, the nosing loads due to different trains are estimated using the validated FE model through a two-staged validation approach, including automatic FE stress intensity optimization and rigorous manual FE model sensitivity analysis while transoms in various conditions are also incorporated in the FE model. Results demonstrate that the nosing load is significantly less than the required load in the AS5100 with magnitudes ranging between 8.6% to 9.4% of the maximum vertical axle load of the passed trains; suggesting that the AS5100 assessment nosing load should be revised to avoid unnecessary expensive upgrades of numerically assessed deficient wind bracings. [ABSTRACT FROM AUTHOR]

In order to reduce the cogging torque of a symmetrical V-type line-start permanent magnet synchronous (LSPMS) motor, this paper proposes a multi-objective optimization method based on the combination of design parameter stratification and response surface methodology (RSM). The optimal solution to the RSM model is acquired using the max–min ant algorithm. The permanent magnet width, pole opening angle, stator slot width, rotor axial length, and rotor tooth width are selected as optimization variables. The cogging torque and average torque are the optimization objectives. Finite element method (FEM) results show that the cogging torque is reduced by 71.5%, the torque ripple is reduced by 65.6%, and the average torque is improved by 12%. Finally, the effectiveness of the algorithm is verified with simulation results. [ABSTRACT FROM AUTHOR]

Structure-soil interface friction characteristics is of importance to investigate the interaction between engineering structures and soils, especially for offshore structures. The interface friction behavior between marine clay and structural materials with different roughness was studied in this paper by using 3D optical scanning tests, a modified direct shear device and numerical simulation. Relationships between the surface roughness of structures, water content and interface friction angle were presented by model tests. The increase of water contents decreased the interface friction angles. For interfaces with different roughness, the interface friction angles will be smaller than that of the soil when the water content exceeds a certain value. The roughness of the interface and the water content of the soil are mutually coupled to influence the coefficient of friction (COF). This paper proposed a Finite Element Method (FEM) to simulate the interface direct shear tests of structures with different roughness. The surface models with different roughness are established based on the structure data obtained by 3D scanning. The Coupled Eulerian-Lagrangian (CEL) approach was employed to analyse soils sheared by irregular surfaces. The interface behavior for interfaces with different roughness under cyclic shear stresses was analyzed by FEM. [ABSTRACT FROM AUTHOR]

There are limited comparative studies on modeling fluid transport in fractured porous media. Hence, this paper systematically compares the steady-state creeping flow Stokes–Brinkman and Darcy–Darcy models for computational efficiency and accuracy. Sensitivity analyses were also conducted on the effect of fracture orientations, fracture sizes, mesh resolution, and fractures with Local Grid Refinement (LGR) under the FEniCS computational framework. Both models were validated numerically, and the accuracy of their solution is compared using the R-squared metric and L2 norm estimates. Key results showed that both models have similar pressure and velocity field solutions for a given fracture orientation. The computational time required for solving the Stokes–Brinkman models for a single fracture case was unusually lower than that of the Darcy–Darcy model when the pressure and velocity terms in the Darcy–Darcy model were solved simultaneously using two equations, contrary to where only one equation solves for the pressure and the velocity is obtained by projecting the gradient of pressure onto a vector space. The Stokes–Brinkman model is more sensitive to mesh resolution, and as a result, the Darcy–Darcy model tends to be more accurate than the Stokes–Brinkman model at low resolutions. Local Grid Refinement (LGR) can improve the Stokes–Brinkman model's accuracy at low mesh resolution. Furthermore, both models showed similar results when compared for complex fracture systems such as multiple fracture cases: interconnecting and isolated fractured porous media systems under low-velocity and steady-state creeping flow conditions. The FEniCS code in this paper is shared for future researchers to reproduce results or extend the research work. [ABSTRACT FROM AUTHOR]

Objective: To study the free vibration problem of a variable curvature beam different from the conventional circular model. Methods: Based on the principle of virtual work, an analytical expression of in-plane displacement of a beam with variable curvature fixed at both ends under concentrated load is established in this paper. The flexibility matrix and stiffness matrix of curved beam are obtained by Moore integral calculation, and the mass matrix of variable curvature beam is obtained by lumped mass method. The stiffness matrix and mass matrix are transformed by static condensation method, and the natural vibration frequency of the beam with variable curvature is obtained. The finite element simulation model of the actual curved bridge and the laboratory curved arch model are established, and the simulation analysis results and laboratory measurement results are compared with the results in this paper. Conclusion: It is proved that the theory presented in this study has good engineering application and can be used as the theoretical basis for the structural research and design of the variable curvature bridge. [ABSTRACT FROM AUTHOR]

In this paper, a novel simulation-based evolutionary method is presented for designing parameter-free MEMS structures with maximum degrees of freedom. This novel design method enabled semiautomatic structure evolution by weighing the attributes of each segment of the structure and yielded an optimal design after multiple iterations. The proposed method was utilized to optimize the pressure-sensitive diaphragm of a piezoresistive pressure sensor (PPS). Finite element method (FEM) simulations revealed that, in comparison to conventional diaphragms without islands and with square islands, the optimized diaphragm increased the stress by 10% and 16% and reduced the nonlinearity by 57% and 77%, respectively. These improvements demonstrate the value of this method. Characterization of the fabricated PPS revealed a high sensitivity of 8.8 mV V−1 MPa−1 and a low nonlinearity of 0.058% FS at 20 °C, indicating excellent sensor performance. [ABSTRACT FROM AUTHOR]

When overhead ground wire (OGW) is struck by lightning, the damage or rupture accident occur. This is unacceptable for the stable operation of the power system. Therefore, the investigation on the lightning-induced damage mechanism of OGW is significant for the optimization of lightning protection measures. Combined with the structural characteristics of OGW, this paper evaluated the thermal ablation damage of OGW caused by lightning strike, which provided the data support for the damage mechanism research. Firstly, the magnetohydrodynamics (MHD) models based on OGW and plate structure were established. The current density distributions as well as the arc root radii of OGW and plate under lightning strikes were compared. The thermal ablation damage model of OGW was also established. The influence of arc root radius on thermal ablation damage evaluation of OGW under continuing component of lightning current was analyzed. The results show that the arc root radius of lightning striking OGW is reduced by at least 50% compared with that of lightning striking plate. When using arc root radius of OGW for modeling, the results of the thermal ablation damage model are consistent with the reported experimental results. The maximum error is 9.80%. While the arc root radius of plate is adopted, there is an obvious difference between the thermal ablation damage model and the experimental results. The maximum error exceeds 20%. Therefore, in the numerical modeling of thermal ablation damage of OGW, it is necessary to consider the influence of structural characteristics of OGW on arc root radius. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the mechanical behavior of corrugated board boxes, focusing attention on the strength that the boxes are able to offer in compression under stacking conditions. A preliminary design of the corrugated cardboard structures starting from the definition of each individual layer, namely the outer liners and the innermost flute, was carried out. For this purpose, three distinct types of corrugated board structures that include flutes with different characteristics, namely the high wave (C), the medium wave (B), and even the micro-wave (E), were comparatively evaluated. More specifically, the comparison is able to show the potential of the micro-wave which would eventually allow a significant saving of cellulose in the fabrication process of the boxes, thus reducing the manufacturing costs and causing a lower environmental footprint. First, experimental tests were carried out to determine the mechanical properties of the different layers of the corrugated board structures. Tensile tests were performed on samples extracted from the paper reels used as base material for the manufacturing of the liners and flutes. Instead, the edge crush test (ECT) and box compression test (BCT) were directly performed on the corrugated cardboard structures. Secondly, a parametric finite element (FE) model to allow, on a comparative basis, the study of the mechanical response of the three different types of corrugated cardboard structures was developed. Lastly, a comparison between the available experimental results and the outputs of the FE model was carried out, with the same model being also adapted to evaluate additional structures where the E micro-wave was usefully combined with the B or C wave in a double-wave configuration. [ABSTRACT FROM AUTHOR]

Experimental tests of a seven-bolted connection with an asymmetric contact area between the joined elements are presented. The research is divided into two stages. In the first one, the connection is preloaded in a three-pass cycle. In the second stage, the connection is loaded with a monotonic alternating force applied at an angle of 30 degrees to the contact surface of the joined elements to generate compressive and shear forces in the connection. The tests are carried out with the use of the INSTRON 8850 testing machine. As a result, the courses of forces in the bolts measured with the use of resistance strain gauges and the relative displacements between the joined elements measured with an extensometer are shown. In the second part, the modeling of the connection in the convention of the finite element method is presented. The joined elements are modeled with the use of spatial finite elements, and the fasteners, as the hybrid elements made of deformable beams, rigid heads, and rigid nuts. The paper is completed with a comparison of the results obtained from the measurements and calculations, based on which the conclusions important from the point of view of the FEM analysis are drawn. [ABSTRACT FROM AUTHOR]

In this paper, we consider a deformable continuous medium and its discrete representation realized by a lattice of points. The former is solved using the classical variational formulation with the finite element method. The latter, a 2D discrete "kinematic" model, instead is conceived to determine the displacements of the lattice points depending on interaction rules among them and thus provides the final configuration of the system. The kinematic model assigns the displacements of some points, so-called leaders, by solving Newton's law; the other points, namely followers, are left to rearrange themselves according to the lattice structure and the flocking rules. These rules are derived from the effort to describe the behaviour of a robot swarm as a single whole organism. The advantage of the kinematic model lies in reducing computational cost and the easiness of managing complicated structures and fracture phenomena. In addition, generalizing the discrete model to non-local interactions, such as for second gradient materials, is easier than solving partial differential equations. This paper aims to compare and discuss the deformed configurations obtained by these two approaches. The comparison between FEM and the kinematic model shows a reasonable agreement even in the case of large deformations for the standard case of the first gradient continuum. [ABSTRACT FROM AUTHOR]

The paper concerns the nonlinear behaviour of a thin platelet that is streamlined in an aerodynamic tunnel. The air velocity in the aerodynamic tunnel was at 858.9 km/h or 0.7 Ma (Ma—Mach number is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound). This experiment was numerically simulated using FSI (fluid–solid interaction) tools, namely the coupling between the strength and flow code. The strength code uses the finite element method, while the flow code is based on the finite volume method. The coupling between the codes was made by means of an interface that transmitted the relevant data and results between the two codes. The paper discusses the methodology of this coupling. The study also highlights the phenomena occurring during the interaction of flow with the plate with emphasis on their nonlinear character. [ABSTRACT FROM AUTHOR]

In electron optics, calculation of the electric field plays a major role in all computations and simulations. Accurate field calculation methods such as the finite element method (FEM), boundary element method and finite difference method, have been used for years. However, such methods are computationally very expensive and make the computer simulation challenging or even infeasible when trying to apply automated design of electrostatic lens systems with many free parameters. Hence, for years, electron optics scientists have been searching for a fast and accurate method of field calculation to tackle the aforementioned problem in the design and optimization of electrostatic electron lens systems. This paper presents a novel method for fast electric field calculation in electrostatic electron lens systems with reasonably high accuracy to enable the electron-optical designers to design and optimize an electrostatic lens system with many free parameters in a reasonably short time. The essence of the method is to express the off-axis potential in an axially symmetrical coordinate system in terms of derivatives of the axial potential up to the fourth order, and equate this to the potential of the electrode at that axial position. Doing this for a limited number of axial positions, we get a set of equations that can be solved to obtain the axial potential, necessary for calculating the lens properties. We name this method the fourth-order electrode method because we take the axial derivatives up to the fourth order. To solve the equations, a quintic spline approximation of the axial potential is calculated by solving three sets of linear equations simultaneously. The sets of equations are extracted from the Laplace equation and the fundamental equations that describe a quintic spline. The accuracy and speed of this method is compared with other field calculation methods, such as the FEM and second order electrode method (SOEM). The new field calculation method is implemented in design/optimization of electrostatic lens systems by using a genetic algorithm based optimization program for electrostatic lens systems developed by the authors. The effectiveness of this new field calculation method in optimizing optical parameters of electrostatic lens systems is compared with FEM and SOEM and the results are presented. It should be noted that the formulation is derived for general axis symmetrical electrostatic electron lens systems, however the examples shown in this paper are with cylindrical electrodes due to the simplicity of the implementation in the software. [ABSTRACT FROM AUTHOR]

Additive Manufacturing (AM) processes are known as revolutionary manufacturing processes that fabricate a part using a 3D model layer upon layer. These techniques gained more attention from various industries due to their advantages like low waste material. Also, these processes can produce any part with high degrees of complexity in a short period of time. The Fused Deposition Modeling (FDM) process is a material extrusion-based technique which works by extruding a fine molten polymeric filament through a heated nozzle on the heated platform named printer bed. In this method, some important manufacturing parameters play a crucial role in controlling the mechanical properties and quality of the final fabricated part. However, all printed specimens through the FDM process should be tested based on the standards under some critical circumstances. Thus, in the current research paper, five and three test speeds are considered in tensile and fracture testing procedures, respectively to evaluate how these speeds can affect the mechanical and mode I fracture properties. Also, as the FDM specimens present elastic–plastic behavior, the critical value of J-integral is assumed as a fracture assessment and calculated from the finite element analysis. Among the mechanical properties, ultimate tensile strength is affected significantly by the test speed. For instance, the ultimate tensile strength of FDM specimens is 39.02, 38.58, 42.33, 48.09, and 52.11 for test speeds of 2, 4, 6, 8, and 10 mm/min, respectively. But vice-versa results are detected for the mode I fracture behavior and corresponding values of J for the FDM-PLA specimens. Finally, experimental and numerical results together with comprehensive discussions about the considered speeds and obtained results are reported. [ABSTRACT FROM AUTHOR]

Purpose: In order to solve the problem that the existing models can't accurately reproduce the mechanical properties of metallic plates under complex working conditions, and the accuracy and efficiency can't be satisfied at the same time. The analysis of metallic plates by different refined finite elements is presented in this paper. The working efficiency and accuracy of the higher-order model in engineering applications are studied. Methods: The refined plate elements are based on several series expansion, and applied to the modeling and analysis of plate structures. The Carrera unified formulation is introduced to express the plate displacement field, the theoretical model of plate thickness expansion is established by using Taylor series expansion and Lagrange series expansion. The governing differential equations of metallic plate are established by using the principle of virtual displacements, the mass matrix and stiffness matrix of plate elements are deduced simultaneously. Finally, the shear locking phenomenon of the plate models is considered, tensor component mixed interpolation (MITC4) is used to revise the model. The accuracy and the reliability of the refined plate models are verified by comparing several order models and solid models generated in the commercial software ANSYS. Results and Conclusion: In this paper, the higher-order model has very low degree of freedoms (DOFs) on the premise of ensuring accuracy. And this modeling method can be used not only for thin plate analysis, but also for medium-thick plate analysis. Meanwhile, the refined plate model has high working efficiency and wide application range, which provides a new modeling method for the research of metallic plates. [ABSTRACT FROM AUTHOR]

Purpose: Considering the sudden change of the structure shape of a double-tower structure with a large podium (DTS), the mechanical properties of the structure under earthquake are extremely complex. Therefore, it is very important to evaluate the seismic fragility of new structures such as the DTS under different control schemes. This paper uses the seismic fragility analysis method based on IDA to study the seismic performance of the DTS. By comparing and analyzing the control effects of different control schemes, the advantages of composite passive control schemes are highlighted, which provides a theoretical basis for pre-earthquake disaster prevention and post-earthquake damage assessment of the DTS. Methods: With the aim of minimizing the mean–variance of the total vibration energy of the structure, the optimal control parameters of the energy dissipation damper are obtained by combining theoretical analysis with finite element simulation. Then the optimal arrangement scheme of the energy dissipation damper is determined by arrangement and combination. Considering that the previous structural performance level division methods cannot accurately reflect the results of the seismic fragility analysis of the DTS, the performance grade and damage grade of the structure were divided into five limit states and six damage degrees for the first time in this paper, and on this basis, the seismic fragility analysis of the DTS under two different control schemes was carried out based on IDA. Results: The response curves of each substructure of the equivalent single-DOF model are consistent with those of the multi-degree-of-freedom layer shear model (multi-DOF model), which indicates the validity and rationality of the equivalent single-DOF model are verified. Conclusion: The research shows that the equivalent single-DOF model of the DTS avoids a large number of iterative calculations, improves the calculation efficiency, retains the accuracy of the multi-DOF model, and has good applicability and rationality. In addition, the finite element simulation results show that the failure of the DTS under the two control schemes is caused by the failure of the isolation bearing. Compared with the LIC scheme, the CPC scheme improves the structure's seismic performance as a whole. [ABSTRACT FROM AUTHOR]

Coal mining machine drums are prone to damage and malfunction under extremely complex working conditions, which seriously affects the efficiency and safety of coal production. In this paper, based on the theory of coal rock cutting and virtual simulation technology, finite element models of drum cutting coal rock were established and then verified by physical experiments. Through simulation analysis, the dynamic reliability of the drum was studied from three aspects: load, stress and wear, and a mathematical model of drum load was established with respect to the traction speed and drum rotation speed; based on the orthogonal test, the optimal working parameters to improve the wear resistance of the drum were derived. The results of the study found that when the traction speed increases, the load on the drum increases, and when the drum rotation speed increases, the load on the drum decreases; when the traction speed is increased from 2 to 6 m/min, the stress on the pick body under different rotation speeds increases to different degrees, with an average increase rate of 27.394%; when the drum rotation speed is 90 r/min, the traction speed is 3 m/min, and the coal loading mode is projectile loading, the wear depth of the picks and spiral blades is relatively small. The research method and results of this paper can provide a reference for the selection of the drum working parameters. [ABSTRACT FROM AUTHOR]

Aiming at the requirements of strong mobility and high flexibility of rescue and relief mobile pump trucks, this paper designs a new type of mobile pump truck frame based on existing mobile vehicle frame models. The materials used for the frame are 40Cr and Q235, and the finite element method is utilized to carry out static mechanical analysis and dynamic characteristic analysis. Simultaneously utilizing topology optimization and multi-objective genetic algorithm to optimize the design of the frame structure. The results show that the optimized pump truck frame can meet the strength design requirements of four typical working conditions: full load bending, full load torsion, emergency turning and emergency braking, while avoiding resonance phenomena caused by road surface and diesel engine vibration. Compared with the original frame model, the weight of the optimized frame is reduced by 87.88 kg, with a weight reduction rate of 10.89%, realizing the lightweight design requirements. [ABSTRACT FROM AUTHOR]

As a cutting-edge additive manufacturing (AM) technology, the selective thermoplastic electrophotographic process (STEP) has opened up possibilities for mass production with its combination of real engineering plastics and potential high part quality. To improve the accuracy and fidelity of STEP for the most demanding applications, this paper proposes a novel method encompassing both pre-processing and in-process dimensional compensations. Iterative compensation before production is achieved through physics-driven simulation, resulting in input masks that better match the required dimensions at the design level. Layer-wise compensation is implemented during the production process through the laser profiler system, thereby suppressing the accumulation of surface unevenness during printing. With the compensation method proposed in this paper, the maximum distortion during simulated printing is decreased by 86.2%, and surface unevenness is effectively controlled during the printing process. [ABSTRACT FROM AUTHOR]

This paper mainly investigates linear elastic optimal control problems with two constraints: distributed load control and boundary load control. The gradient of the objective functional is derived via an adjoint problem. We obtain the H 1 -regularity for the distributed control solution. Moreover, we establish a suitable finite element interpolation to deal with the non-optimal regularity of the boundary control solution. The error estimates for the fully discretized problems is given. Then, together with the interior point method, a new numerical method for the optimal control of linear elasticity is exhibited. Finally, the effectiveness of presented scheme is demonstrated by various numerical simulations in two and three-space dimensions. [ABSTRACT FROM AUTHOR]

The catastrophic events of September 11, 2001, stand out as a major motivation for research on improving the understanding of structural behaviour in fire. These events included the first complete collapse of a tall steel framed structure solely due to fire. World Trade Center 7 (WTC7) was a 47-storey office building within the WTC complex that collapsed due to a fire initiated by debris from the collapse of WTC1. In the following years, detailed investigations were carried out by expert teams to pinpoint the cause of the progressive failure of WTC7. Each of the expert teams analysed the fire and structure and made varying conclusions with regards to the mechanisms responsible for initiating and propagating the collapse of the building. This paper revisits the collapse of WTC7 and its investigation, and then explores the hypothesis that a potential hydrocarbon fire may have compromised the large transfer structure within the mechanical space of the building. This is done via two OpenSees finite element models. The first model explores the thermomechanical response of the mechanical floors to a potential diesel fire, and the second investigates the response of the structure to a failure caused by that fire. The outcome of the analyses shows that it is feasible that a mechanical room fire could lead to a failure in the transfer structure, which would then result in the loss of support to at least two columns within the building core. The failure of these columns may unbrace the eastern-most core columns and precipitate in the failure of the structure as observed on 9/11. [ABSTRACT FROM AUTHOR]

In this paper, an efficient fully-decoupled and fully-discrete numerical scheme with second-order temporal accuracy is developed to solve the incompressible hydrodynamically coupled Cahn-Hilliard model for simulating the two-phase fluid flow system. The scheme is developed by combining the finite element method for spatial discretization and several effective time marching approaches, including the pressure-correction projection method for dealing with fluid equations and the explicit-invariant energy quadratization (explicit-IEQ) approach for dealing with coupled nonlinear terms. The obtained scheme is very efficient since it only needs to solve several decoupled, linear elliptic equations with constant coefficients at each time step. We also strictly prove the solvability and unconditional energy stability of the scheme, and verify the accuracy and stability of the scheme through plenty of numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, a two-level Newton iterative method is proposed for the stationary micropolar fluid equations. Firstly, the original equations are solved on a coarse grid based on Newton-type linearization. Then, the simplified linearized equations are solved on a fine grid. The stability and error estimates of the method are given in the theoretical part. The results of the theoretical analysis show that when the coarse mesh size H and fine mesh size h satisfy the relation h = O (H 2) , the two-level Newton iterative method can achieve an optimal convergence rate. Finally, the effectiveness and applicability of the method are verified by some numerical experiments. [ABSTRACT FROM AUTHOR]

This paper introduces a novel approach for characterizing and estimating the size of incipient cracks, employing Jensen–Shannon divergence and Wasserstein distance for precise measurement. A novel signal correction method is proposed and coupled with Finite Element Modeling can extend the experimental data. The method is verified to accurately quantify incipient cracks with areas as small as 0.02 mm 2 , with a maximum relative error of 3.5% in surface estimation, and accurately discern variations in crack sizes. This allows for more accurate predictions of crack dimensions crucial for structural health monitoring. [ABSTRACT FROM AUTHOR]

Severe pollution-induced flashovers on insulators present a pressing challenge to power system safety. The frequent failure of high-voltage insulators, particularly in the polluted environments of Pakistan, poses a critical concern. This paper investigates the impact of insulator profile on reducing pollution flashovers, testing two designs as per IEC standard 60383 and simulated using the Finite Element Method in COMSOL Multiphysics®. The test results revealed that deep under-ribs insulators exhibited a 5.008% reduction in flashover voltage, while alternating shed insulators experienced a 3.233% decrease in polluted conditions compared to clean conditions. Notably, under both clean and polluted conditions, alternating shed insulators consistently outperformed deep under-ribs insulators, with a 25.377% higher flashover voltage in clean conditions and a 27.400% superiority in polluted conditions. Computational analysis through the Finite Element Method in COMSOL Multiphysics shows a consistent pattern in potential distribution with increasing insulator count, but the presence of a pollution layer introduces spikes in the electric field distribution, validating experimental results. These findings highlight the superior performance of alternating shed insulators, especially in polluted environments. [ABSTRACT FROM AUTHOR]

Virtual reconstruction of ancient buildings often has incomplete records of the original design and construction details, and can only be reconstructed based on limited data, drawings and photography, which is different from the actual conditions. The unique overhanging structure of the corridor gable building makes it vulnerable to damage in extreme weather conditions. In order to ensure that the virtual reconstruction results can not only reproduce the original appearance of history, but also ensure that the reconstructed model maintains structural stability in the long term. This paper proposes a reconstruction method of the original appearance of the corridor gable building remains based on structural dynamics analysis. This method comprehensively uses three-dimensional reconstruction, structural engineering, dynamic analysis, and computer simulation technology to ensure the structural accuracy and historical authenticity of the virtually reconstructed corridor gable building. First, through data collection and analysis, combined with ancient architectural construction techniques, a preliminary three-dimensional model was created, which included all structural elements and details. Several groups of reconstruction schemes are determined based on material properties. Then, using finite element analysis software, perform dynamic analysis on the three-dimensional model. Evaluate the stability of the reconstructed structure and optimize the material selection plan to ensure the feasibility and accuracy of the virtual reconstruction. Taking the virtual reconstruction of the eaves in front of Leiyin Cave as an example, it shows that this method is effective and feasible to achieve the virtual reconstruction of corridor gable buildings. It provides new ideas for virtual reconstruction of ancient buildings and has important practical application value. [ABSTRACT FROM AUTHOR]

Pipe contaminant detection holds considerable importance within various industries, such as the aviation, maritime, medicine, and other pertinent fields. This capability is beneficial for forecasting equipment potential failures, ascertaining operational situations, timely maintenance, and lifespan prediction. However, the majority of existing methods operate offline, and the detectable parameters online are relatively singular. This constraint hampers real-time on-site detection and comprehensive assessments of equipment status. To address these challenges, this paper proposes a sensing method that integrates an ultrasonic unit and an electromagnetic inductive unit for the real-time detection of diverse contaminants and flow rates within a pipeline. The ultrasonic unit comprises a flexible transducer patch fabricated through micromachining technology, which can not only make installation easier but also focus the sound field. Moreover, the sensing unit incorporates three symmetrical solenoid coils. Through a comprehensive analysis of ultrasonic and induction signals, the proposed method can be used to effectively discriminate magnetic metal particles (e.g., iron), nonmagnetic metal particles (e.g., copper), nonmetallic particles (e.g., ceramics), and bubbles. This inclusive categorization encompasses nearly all types of contaminants that may be present in a pipeline. Furthermore, the fluid velocity can be determined through the ultrasonic Doppler frequency shift. The efficacy of the proposed detection principle has been validated by mathematical models and finite element simulations. Various contaminants with diverse velocities were systematically tested within a 14 mm diameter pipe. The experimental results demonstrate that the proposed sensor can effectively detect contaminants within the 0.5−3 mm range, accurately distinguish contaminant types, and measure flow velocity. [ABSTRACT FROM AUTHOR]

The rail profile milling process allows considerable thickness to be removed in a single pass. However, the residual waviness formation law after milling and its subsequent effect on rail performance remains uncertain. In this paper, the wavelength and wave height of the residual waviness are identified as the key characteristics. The relationship between milling speed and residual waviness is determined, and a numerical model of the residual waviness formed on the surface after milling is established based on the commonly used three milling speeds of 300, 600, and 1000 m/h, and its accuracy is verified using the parameters of the residual waviness detected by the milling experiments. A three-dimensional finite element analysis model of wheel-rail contact was employed to analyze the contact stresses and low fatigue cycles at a wheel load of 11.5 tons with no residual waviness on the rail profile surface and with three types of residual waviness, respectively. The results show that the residual waviness changes the wheel-rail contact position and the morphology of the contact area, reduces the maximum contact stress and increases the strain fatigue cycles. The application of elevated milling speeds reduces the wheel-rail contact stresses after milling, thereby increasing the low fatigue cycles. [ABSTRACT FROM AUTHOR]

Taper beams are widely used due to its good damping properties in vibration and noise control field. For dynamic response analysis of taper beams in the high frequency, the energy finite element analysis (EFEA) based on wave theory is the most promising method. However, there is no energy finite element model for taper beams. In this paper, energy finite element model for taper beam is built though two steps. Firstly, the approximate displacement solution of the vibration equation of the taper beam is expressed by the geometry-acoustics approximation method. The expression of the relationship between energy density and power flow of the taper beam is obtained by utilizing the displacement solution. Based on the principle of conservation of energy, the governing equation taken energy density as a variable was derived. Secondly, the stiffness matrix of taper beam element and the solution format of this governing equation are obtained using the Galerkin weighting method, which led to the energy finite element model of the taper beam. Taking a taper beam as an example, the energy finite element model presented in this paper is used to calculate the energy density distribution on the taper beam, and the calculation results are consistent with the finite element calculation results, which proving the correctness of the energy finite element model of the taper beam established in this paper. In order to show the advantages of the EFEA model presented in this paper, a comparison with approximate EFEA model based on constant cross-section elements is performed. The results shown that the EFEA model presented in this paper have higher accuracy and less time consumption, which can reflect the dynamic response characteristics of the taper beam better. [ABSTRACT FROM AUTHOR]

Topography can strongly affect ground motion, and studies of the quantification of hill surfaces' topographic effect are relatively rare. In this paper, a new quantitative seismic topographic effect prediction method based upon the BP neural network algorithm and three-dimensional finite element method (FEM) was developed. The FEM simulation results were compared with seismic records and the results show that the PGA and response spectra have a tendency to increase with increasing elevation, but the correlation between PGA amplification factors and slope is not obvious for low hills. New BP neural network models were established for the prediction of amplification factors of PGA and response spectra. Two kinds of input variables' combinations which are convenient to achieve are proposed in this paper for the prediction of amplification factors of PGA and response spectra, respectively. The absolute values of prediction errors can be mostly within 0.1 for PGA amplification factors, and they can be mostly within 0.2 for response spectra's amplification factors. One input variables' combination can achieve better prediction performance while the other one has better expandability of the predictive region. Particularly, the BP models only employ one hidden layer with about a hundred nodes, which makes it efficient for training. [ABSTRACT FROM AUTHOR]

The elastic wave bandgap (BG) properties of locally resonant phononic crystal (LRPC) make it has great potential in the research and development of damping composite material and the application of vibration control engineering. However, the number of BG of the traditional LRPC is only one, the BG frequency range is too concentrated, and the multi-frequency BGs is not opened, so the application in practical engineering is limited. In response to the above issues, this paper designs a concentric ring cement-based locally resonant phononic crystal (CRCBLRPC) composite material, and studies and analyzes its BG characteristics. Firstly, the improved plane wave expansion method (IPWEM) and finite element method (FEM) are used to calculate the band structure of the CRCBLRPC. Secondly, the transfer function and BG mechanism of CRCBLRPC are calculated using FEM. Then, the factors affecting the BG of CRCBLRPC are analyzed. Finally, an equivalent model of spring-mass system is proposed to theoretically estimate the BG range of CRCBLRPC. The results show that the CRCBLRPC opens multi-frequency and low frequency BGs within the 200 Hz frequency band, and the number of BGs is more than that of the traditional LRPC. Within the BG frequency range, the CRCBLRPC has a good inhibition effect on vibration. Among them, the density of the scatterer and the elastic modulus of the coating layer are the main factors affecting the BG of the CRCBLRPC. The established spring-mass system equivalent model can accurately calculate the BG range of the CRCBLRPC. The research content and related conclusions of this paper provide new perspectives and insights for the study and design of LRPC composite materials with multi-frequency and low frequency BGs, and can also provide new ideas and methods for solving low frequency vibration in practical engineering. [ABSTRACT FROM AUTHOR]

With the development of virtual reality, the projection design of the head-mounted display (HMD) requires improvement as well. The surface relief grating (SRG) is one of the popular diffraction elements to achieve light guiding through the waveguide. Using the SRG as the coupler, incoming information light can be coupled into the waveguide by the 1-order diffraction. To increase possible design options for the HMD, SRG with complex geometry has been designed to fit more diffraction conditions. In this paper, a 2D SRG is proposed to form by periodically arranging slanted glass pillars on the surface of a glass waveguide, just like a photonic crystal. The structure can suppress all the other diffraction orders except the 0-order and the [1, 0] order. The best diffraction efficiency of the [1, 0] order can be obtained when the incident light is incident with not only an incident angle but also an azimuth angle. The geometric parameters of the pillars are investigated and optimized with the diffraction efficiency by the finite element method, and the relationship between the incident angles and the diffraction efficiency will also be discussed. The proposed structure has the potential in both the in-coupler and the out-coupler, respectively, for integrating light coming from different azimuth angles or for outputting light to different azimuth angles. [ABSTRACT FROM AUTHOR]