Linear Elements Research Articles

Can neural networks learn finite elements?

The aim of this note is to construct a neural network for which the linear finite element approximation of a simple one dimensional boundary value problem is a minimum of the cost function to find out if the neural network is able to reproduce the finite element approximation. The deepest goal is to shed some light on the problems one encounters when trying to use neural networks to approximate partial differential equations.

Predictive Maintenance Planning Using a Hybrid ARIMA-ANN Model

Predicting machine faults is crucial for maintaining operational efficiency in industrial settings, minimizing unplanned downtime, and ensuring customer satisfaction. Fault prediction helps identify faults and create maintenance schedules. Maintenance planning involves strategically scheduling activities to ensure the continuous operational efficiency of systems. This study focuses on reducing unplanned downtime in a food company by developing a predictive maintenance plan through machine fault prediction. Artificial Neural Networks (ANNs) are excellent in handling non-linear models, while the ARIMA model is adequate for linear models. However, real-world data often contains linear and non-linear elements, requiring hybrid models for improved accuracy. This study employs ARIMA, ANNs, and a Hybrid ARIMA-ANN model. The dataset is individually modelled using each approach. Using a 3-month machine fault dataset, predictive values for machine fault times are generated and statistically evaluated using metrics such as Mean Absolute Error (MAE), Mean Squared Error (MSE), Mean Absolute Percentage Error (MAPE), and Root Mean Squared Error (RMSE). The findings indicate that the hybrid model outperforms both ARIMA and ANN models. The food company can significantly reduce unplanned downtime and ensure operational efficiency using a hybrid model. Predictive maintenance planning can help the food company save costs and maintain a competitive edge in the market.

Experimental, numerical, and theoretical analysis of tapered belleville spring

Uniform thickness belleville springs(UBS) are a suitable replacement for coil springs in many applications due to their ability to take higher loads and their relatively small and compact size. This paper presents an experimental, numerical and theoretical analysis of the taper belleville spring(TBS). Experimental results on a normal taper belleville spring (NTBS), fabricated from stainless steel alloy (SS304), are presented. Non linear elastic-plastic finite element simulations support the experimental behaviour reasonably well. A correction factor based on Timoshenko’s theory of plates, to match the finite element analysis(FEA) results for NTBS, is presented. Reverse taper belleville spring (RTBS) analysis shows that it can store more elastic strain energy than UBS and NTBS. An optimisation study on TBS geometrical parameters is performed to attain maximum energy absorption for the null stiffness region.

Condition of linear landscape elements improves with contiguity to protected habitats: Empirical evidence useful for agroecosystem accounting and restoration

In Mediterranean Europe, both intensification and abandonment of traditional cultural practices represent main drivers for the loss of natural and semi-natural elements in agricultural settings. Once common in rural landscapes, these habitats have to be conserved or restored to ensure resilience and resistance of agroecosystems against biodiversity loss and socio-ecological changes. In particular, linear landscape elements (LE) fall among the high-biodiversity landscape features that require to be increased in agricultural lands to facilitate species mobility and provide a wide range of ecosystem services. However, within the framework of environmental accounting procedures, there is still a need for a thorough methodology to assess conditions of LE and, subsequently, of the hosting agroecosystems. The present research is therefore aimed at (i) proposing a method for a thorough assessment of LE conditions, with a special focus on biodiversity support capacity, (ii) investigating the potential effect of extrinsic determinants on LE conditions, such as contiguity to protected habitats and governance framework, and (iii) identifying useful parameters to guide LE ecological restoration actions. Based on different structural, compositional and landscape indicators, the proposed assessment method was tested in eight administrative units of two Mediterranean Europe countries. In the study sites, favorable LE conditions were found to be strongly associated with contiguity to protected habitats, by showing marked structural continuity, dominance of trees, active dynamics, and good quality of the surrounding landscape mosaic. Potential applications of the results have been finally explored in both ecosystem accounting and ecological restoration processes.

Error estimates of unilateral piezoelectric contact problem in a curved and smooth boundary domain

We study the linear finite element approximation of piezoelectric unilateral contact problem in a curved and smooth boundary domain. The unilateral contact conditions will be weakly imposed by the penalty method. We derive error estimates which depend on the penalty parameter and the mesh size. In fact, under regularity of the solution, we prove some convergence rate results.

Robust Containment Queries over Collections of Rational Parametric Curves via Generalized Winding Numbers

Point containment queries for regions bound by watertight geometric surfaces, i.e., closed and without self-intersections, can be evaluated straightforwardly with a number of well-studied algorithms. When this assumption on domain geometry is not met, such methods are either unusable, or prone to misclassifications that can lead to cascading errors in downstream applications. More robust point classification schemes based on generalized winding numbers have been proposed, as they are indifferent to these imperfections. However, existing algorithms are limited to point clouds and collections of linear elements. We extend this methodology to encompass more general curved shapes with an algorithm that evaluates the winding number scalar field over unstructured collections of rational parametric curves. In particular, we evaluate the winding number for each curve independently, making the derived containment query robust to how the curves are arranged. We ensure geometric fidelity in our queries by treating each curve as equivalent to an adaptively constructed polyline that provably has the same generalized winding number at the point of interest. Our algorithm is numerically stable for points that are arbitrarily close to the model, and explicitly treats points that are coincident with curves. We demonstrate the improvements in computational performance granted by this method over conventional techniques as well as the robustness induced by its application.

The role of the foundation flexibility on the seismic response of a modern tall building: Vertically incident plane waves

The soil-structure interaction (SSI) is an integral part of the seismic response of structures. The knowledge about its effects is based largely on numerical simulations involving simplified models. In this paper, we examine the consequence of several assumptions in SSI models of buildings, with emphasis on the rigid foundation assumption. To this end, we analyze several variants of a linear three-dimensional finite element model of the structure and soil corresponding to a uniquely instrumented 50-story skyscraper, with a basement on a pile foundation, located in southwest China. The models are excited by triaxial motion due to a vertically incident plane wave. The most realistic model (with basement and piles, both with bond contact with the soil), predicted an 8 % reduction of the apparent frequency and a 30 %–50 % increase in the apparent damping ratio of the 1st mode of vibration, relative to the model with fixed basement. The model with a rigid foundation (basement) embedded in the soil underestimated the reduction in apparent frequency by a factor of two. The SSI effects were the most pronounced for the model with flexible basement and no piles (16 %–19 % reduction in apparent frequency and 73 %–86 % increase in apparent damping ratio). The basement-structure interaction reduced the apparent frequency by 5 %–8 % depending on the direction. It is concluded that, for such a building, a detailed model of the structure and its foundation is needed to predict reliably the SSI effects.

Fatigue crack propagation life analysis of propeller

Fatigue crack fracture is a common failure mode in structures. For the propeller with initial crack, the hydrodynamic effect cannot be ignored when studying the fatigue crack propagation behavior. Taking the full-size KP505 propeller as the research object, its hydrodynamic performance is simulated and verified. By using the fluid-structure interaction (FSI), the pressure distribution and stress distribution of propeller under different working conditions are analyzed comprehensively, and the position of propeller hot spot stress is obtained. According to the principal stress and its direction of the hot spot stress, the location and orientation of possible macroscopic crack initiation are determined. By using the linear elastic fracture mechanics and finite element method (FEM), the propeller fatigue crack propagation law and life are calculated. The analysis results show that the Forman-Newman-de Koning (FNK) model predicts more complete fatigue crack propagation life than Paris model. The fatigue crack propagation of propeller has two stages, steady propagation stage, and accelerated propagation stage. The crack breaking blade thickness is the dividing point between the two stages. In addition, the effects of the advance coefficient, stress ratio, and initial crack size on the computed results are also analyzed, which provide reference for ship driving and propeller maintenance.

ON THE PECULIARITIES OF REFLECTION OF SHEAR WAVES WITH LINEAR POLARIZATION FROM THE ROUGH SURFACE OF A CRACK

The reflection coefficient of shear waves with SV- and SH-linear polarization from a statistically inhomogeneous surface consisting of scattering linear elements with a feature of their height distribution according to the normal law in a two-dimensional approximation is estimated. The estimation of the reflection coefficients in the reverse and forward directions is based on the calculation of the reflected wave energy flow propagating from an inhomogeneous surface averaged over the possible values of the height of the reflecting elements. It is theoretically shown and confirmed experimentally that the ratio of the coefficients of the reverse reflection of SH- and SV-polarization waves is significantly greater than 1, which provides better detection of cracks by SH-waves. The peculiarity of the behavior of the dependence of the coefficients of the reverse and direct reflected signal of the SV-polarization waves on the mean square deviation corresponds to the results of theoretical estimates. The coefficient of variation of the ratio of reflection coefficients shows the statistical stability of the direct reflected signal, which determines the feasibility of using such a signal to measure the equivalent area of the reflector.

A computational study for simulating MHD duct flows at high Hartmann numbers using a stabilized finite element formulation with shock-capturing

The concern of this manuscript is stabilized finite element simulations of two-dimensional incompressible and viscous magnetohydrodynamic (MHD) duct flows governed by a coupled system of partial differential equations of the convection–diffusion type. In such flows, the high values of the Hartmann numbers (Ha) indicate that the convection process dominates the flow field. As is typical trouble encountered in convection-dominated flow simulations, classical discretization methods fail to function properly for MHD flows at high Hartmann numbers, yielding several numerical instabilities. In this study, the core computational tool we employ in order to overcome such challenges is the streamline-upwind/Petrov–Galerkin (SUPG) formulation. Beyond that, since the SUPG-stabilized formulation requires additional treatment where solutions experience rapid changes, we also enhance the SUPG-stabilized finite element formulation with a shock-capturing operator for achieving better solution profiles around sharp layers. The formulations are derived for both steady-state and time-dependent models. The proposed method, the so-called SUPG-YZβ formulation, techniques used, and in-house-developed finite element solvers are evaluated on a comprehensive set of numerical experiments. The test computations reveal that the SUPG-YZβ formulation yields quite good solution profiles near strong gradients without any significant numerical instabilities, even for quite challenging values of Ha, whereas the SUPG usually fails alone. Furthermore, by using only linear elements on relatively coarser meshes, the proposed formulation achieves this without the need for any adaptive mesh strategy, in contrast to most previously reported studies.

A second-order in time, BGN-based parametric finite element method for geometric flows of curves

Over the last two decades, the field of geometric curve evolutions has attracted significant attention from scientific computing. One of the most popular numerical methods for solving geometric flows is the so-called BGN scheme, which was proposed by Barrett et al. (2007) [8], due to its favorable properties (e.g., its computational efficiency and the good mesh property). However, the BGN scheme is limited to first-order accuracy in time, and how to develop a higher-order numerical scheme is challenging. In this paper, we propose a fully discrete, temporal second-order parametric finite element method, which integrates with two different mesh regularization techniques, for solving geometric flows of curves. The scheme is constructed based on the BGN formulation and a semi-implicit Crank-Nicolson leap-frog time stepping discretization as well as a linear finite element approximation in space. More importantly, we point out that the shape metrics, such as manifold distance and Hausdorff distance, instead of function norms, should be employed to measure numerical errors. Extensive numerical experiments demonstrate that the proposed BGN-based scheme is second-order accurate in time in terms of shape metrics. Moreover, by employing the classical BGN scheme as mesh regularization techniques, our proposed second-order schemes exhibit good properties with respect to the mesh distribution. In addition, an unconditional interlaced energy stability property is obtained for one of the mesh regularization techniques.

Investigation of Lateral and Longitudinal Deformation of Submarine Nuclear Power Plant Water-Intake Tunnel on Non-Uniform Soft Soil during Earthquake

The safety-grade water-intake immersed tunnel plays a vital role in the nuclear power cooling system, and its seismic safety is crucial. This paper employs the response displacement method and dynamic time-history analysis using the finite element software ANSYS to construct a beam–spring model and a 3D finite element model of a shield tunnel and foundation. It also develops equivalent linear dynamic constitutive and viscoelastic boundary element subprograms. This study focuses on the weak joint sections of immersed tunnels, conducting a seismic performance analysis under extreme safety earthquake conditions (SL-2). The results indicate that the joint stiffness of immersed tunnels and the increase in seismic peak values do not affect the trend of joint opening variation with longitudinal position. The change in joint opening is primarily located where the thickness of the cover layer changes abruptly or where the soil hardness is unevenly distributed. The joint opening is mainly influenced by seismic forces when considering static and dynamic superposition. When the stiffness of the joint GINA water stop exceeds a certain value, the correlation between stiffness change and joint compression–tension variation gradually weakens. This research can provide a reference for the seismic design of similar projects.

Pressure-robust finite element scheme for the time-dependent fully coupled Stokes–Darcy-transport problem

We present a pressure-robust mixed finite element scheme for the time-dependent fully coupled Stokes–Darcy-transport problem. The P1c⊕RT0 discretization and Raviart–Thomas mixed elements are used to discretize the velocity in the free flow region and the porous medium region, respectively. We approximate the pressure with piecewise constant finite elements and the concentration with piecewise linear finite elements. We perform a divergence-free reconstruction of the velocity in the Stokes domain. Our scheme preserves local mass conservation in the sense of projection and has pressure-robust property. The stability and error analysis of the method are obtained. The errors of velocity and concentration are independent of pressure, and our method works well even with small viscosity. The theoretical results are validated with numerical examples.

Goal-based angular adaptivity with contributon theory for the discrete ordinates transport equation

A goal-based angular adaptivity has been described for solving the discrete ordinates transport equation. This method uses the linear discontinuous finite element quadrature sets, allowing for local angular refinement across space-energy dimensions. Anisotropy quantified factor derived by contributon theory is introduced in this adaptivity to locate spatial regions that require more angular unknowns in every energy group for a given goal region. The goal-based error metric is considered to trigger local refinement in angle, which requires the solutions of the contributon transport equation to determine the importance to a user-defined functional. Several problems that include both one-group and multi-group transport calculations are displayed to demonstrate the effectiveness of this method. Results indicate that our goal-based adaptivity can significantly reduce computational expenses in terms of angular unknowns and computational times for a similar accuracy, as compared to uniform quadrature sets. It is expected that this adaptivity has the potential to enhance the efficiency of an even wider range of transport problems.

Phase field modeling of ductile fracture with isotropic hardening and radius return method

Phase field model has been investigated for brittle fracture in many static and dynamic scenarios, but its applications to ductile fracture is not as common as brittle fracture, especially implementing in software LS-DYNA with explicit scheme. In this study, an efficient LS-DYNA implementation of the phase field modeling of ductile fracture is presented and both with and without the split of elastic strain energy have been considered for the damage evolution. In more detail, plasticity formulation of ductile material with isotropic hardening is briefly presented first and then the governing equations of the classical phase field model are derived, which gives the displacement-phase coupled problem. For with the split of elastic strain energy, the shear component of elastic strain energy is considered for the damage evolution. The influence of degradation function on stress–strain curve is also investigated by using three kinds of function (polynomial function, algebraic fraction function and sigmoid function), which leads to linear and nonlinear finite element method (FEM) formulation of the phase field model and Newton–Raphson method is used to solve the nonlinear FEM formulation of the phase field model. A tensile bar test shows the influence of critical energy release rate and degradation function on stress–strain curve. Mode Ⅰ failure of three-point bending test, Mode Ⅱ failure of single-edge notched plate and mixed-mode failure of asymmetrical double-notched plate verify the proposed model in this study. From these simulations, with the split of elastic strain energy shows improvements on plastic deformation than without the split of elastic strain energy.

SPICE-Compatible Circuit Models of Multiports Described by Scattering Parameters with Arbitrary Reference Impedances

New SPICE-compatible circuit models of a multiport are presented here that are suitable for the frequency-domain and time-domain analyses of hybrid systems containing linear distributed elements and possibly non-linear lumped elements. Distributed elements models are based on scattering parameters with potentially complex reference impedances, which are not necessarily equal for all ports. Both exact and approximated (lumped) models are proposed. The scattering parameters are directly taken as the model element values in the former case. In the latter case, the model element values are equal to the real and imaginary parts of the poles and residues of the rational approximation. The models comprise a multiport (with an admittance matrix numerically equal to the modeled scattering matrix or approximating it) equipped with a pair of coupled impedances at each port. A few examples validate the proposed approach and prove its efficiency in terms of matrix size and analysis time compared to some selected commercial counterparts.

Complete analysis of hyperentangled Bell state in three degrees of freedom using Kerr effect and self-assisted mechanism

We present an efficient scheme for the complete hyperentangled Bell state analysis (HBSA) of photon system with polarization and two longitudinal momentum degrees of freedom (DOFs), resorting to weak cross-Kerr nonlinearity, linear optical elements and single photon detectors. In the process of distinguishing the 64 hyperentangled Bell states in three DOFs, the self-assisted mechanism is embedded, which makes our scheme simple and realizable. Moreover, we have discussed the applications of this complete HBSA scheme for high-capacity quantum communication protocols that are based on photonic hyperentanglement in three DOFs.

Hacking coherent-one-way quantum key distribution with present-day technology

Recent results have shown that the secret-key rate of coherent-one-way (COW) quantum key distribution (QKD) scales quadratically with the system’s transmittance, thus rendering this protocol unsuitable for long-distance transmission. This was proven by using a so-called zero-error attack, which relies on an unambiguous state discrimination (USD) measurement. This type of attack allows the eavesdropper to learn the whole secret key without introducing any error. Here, we investigate the feasibility and effectiveness of zero-error attacks against COW QKD with present-day technology. For this, we introduce two practical USD receivers that can be realized with linear passive optical elements, phase-space displacement operations and threshold single-photon detectors. The first receiver is optimal with respect to its success probability, while the second one can impose stronger restrictions on the protocol’s performance with faulty eavesdropping equipment. Our findings suggest that zero-error attacks could break the security of COW QKD even assuming realistic experimental conditions.

Complete four-dimensional Bell state measurement using weak cross-Kerr nonlinearity

In this paper, we present an efficient scheme for the complete analysis of the four-dimensional Bell state of the photon system in the path degree of freedom, resorting to the weak cross-Kerr nonlinearity and linear optics. In our scheme, the measurements on two probe coherent states are used for obtaining the bit information of high-dimensional entanglement, and the linear optical elements and single-photon detectors are used for obtaining the relative phase information of high-dimensional entanglement. With these two independent processes, the 16 orthogonal four-dimensional path Bell states can be completely distinguished from each other. This simple and realizable scheme may have useful applications in the quantum information technology based on high-dimensional entanglement.

Increasing quantum communication rates using hyperentangled photonic states

Quantum communication is based on the generation of quantum states and exploitation of quantum resources for communication protocols. Currently, photons are considered as the optimal carriers of information, because they enable long-distance transition with resilience to decoherence and they are relatively easy to create and detect. Entanglement is a fundamental resource for quantum communication and information processing, and it is of particular importance for quantum repeaters. Hyperentanglement, a state where parties are entangled with two or more degrees of freedom (DoFs) simultaneously, provides an important additional resource because it increases data rates and enhances error resilience. However, in photonics, the channel capacity, i.e., the ultimate throughput, is fundamentally limited when dealing with linear elements. We propose a technique for achieving higher transmission rates for quantum communication by using hyperentangled states, based on multiplexing multiple DoFs on a single photon, transmitting the photon, and eventually demultiplexing the DoFs to different photons at the destination, using Bell state measurements. Following our scheme, one can generate two entangled qubit pairs by sending only a single photon. The proposed transmission scheme lays the groundwork for novel quantum communication protocols with higher transmission rates and refined control over scalable quantum technologies.