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Very recently, an innovative mesh-free method, the so-called line element-less method (LEM), has been proposed to determine the response of plates under uniformly distributed edge moments. However, the previous formulations do not solve the problem related to plates with reentrant angles. In this paper, an innovative formulation is introduced to evaluate the deflection function of a simply supported plate possessing reentrant angles at the boundary and loaded by uniformly distributed edge moments. Framed in the LEM, this formulation consents to obtain a plate deflection function, implementing a simple algorithm within Mathematica software. Compelling savings in terms of time and computational costs are achieved, since there is no need to discretize the domain or the contour. Finally, the accuracy of the proposed results is highlighted by a good match with those achieved by classical methods and the finite-element method. [ABSTRACT FROM AUTHOR]

This paper develops two-step methods for solving contact problems with uncertainties. In the first step, we propose stochastic Lagrangian multiplier/penalty methods to compute a set of reduced basis. In the stochastic Lagrangian multiplier method, the stochastic solution is represented as a sum of products of a set of random variables and deterministic vectors. In the stochastic penalty method, the problem is divided into the solutions of non-contact and possible contact nodes, which are represented as sums of the products of two different sets of random variables and deterministic vectors, respectively. The original problems are then transformed into deterministic finite element equations and one-dimensional (corresponding to stochastic Lagrangian multiplier method)/two-dimensional (corresponding to stochastic penalty method) stochastic algebraic equations. The deterministic finite element equations are solved by existing numerical techniques, and the one-/two-dimensional stochastic algebraic equations are solved by a sampling method. Since the computational cost for solving stochastic algebraic equations does not increase dramatically as the stochastic dimension increases, the proposed methods avoid the curse of dimensionality in high-dimensional problems. Based on the reduced basis, we propose semi-reduced order Lagrangian multiplier/penalty equations with two components in the second step. One component is a reduced order equation obtained by smooth solutions of the reduced basis and the other is the full order equation for the nonsmooth solutions. A significant amount of computational cost is saved since the sizes of the semi-reduced order equations are usually small. Numerical examples of up to 100 dimensions demonstrate the good performance of the proposed methods. [ABSTRACT FROM AUTHOR]

To solve the problem of fast convergence in large aperture plane optics continuous polishing, the concept of vibration-assisted polishing is proposed in this paper. The paper first builds a low-frequency short-range vibration processing platform based on large-size polishing tools. Then, the kinematics and polishing pressure of the optics without vibration and vibration are analyzed. Furthermore, the pressure distribution under the element is simulated based on the finite element method. Finally, the material removal rate (MRR) is calculated based on Preston equation, which proves that the removal rate of optics under vibration condition is higher. In this paper, the problem of optics removal efficiency in continuous polishing is solved and the material enhanced removal mechanism is revealed. [ABSTRACT FROM AUTHOR]

Physics-informed neural networks (PINNs) provide a new approach to solving partial differential equations (PDEs), while the properties of coupled physical laws present potential in surrogate modeling. However, the accuracy of PINNs in solving forward problems needs to be enhanced, and solving inverse problems relies on data samples. The smoothed finite element method (S-FEM) can obtain high-fidelity numerical solutions, which are easy to solve for the forward problems of PDEs, but difficult to solve for the inverse problems. To the best of the authors' knowledge, there has been no prior research on coupling S-FEM and PINN. In this paper, a novel approach that couples S-FEM and PINN is proposed. The proposed approach utilizes S-FEM to synthesize high-fidelity datasets required for PINN inversion, while also improving the accuracy of data-independent PINN in solving forward problems. The proposed approach is applied to solve linear elastic and elastoplastic forward and inverse problems. The computational results demonstrate that the coupling of the S-FEM and PINN exhibits high precision and convergence when solving inverse problems, achieving a maximum relative error of 0.2% in linear elasticity and 5.69% in elastoplastic inversion by using approximately 10,000 data points. The coupling approach also enhances the accuracy of solving forward problems, reducing relative errors by approximately 2–10 times. The proposed coupling of the S-FEM and PINN offers a novel surrogate modeling approach that incorporates knowledge and data-driven techniques, enabling it to solve both forward and inverse problems associated with PDEs with high levels of accuracy and convergence. [ABSTRACT FROM AUTHOR]

Positive displacement motor is a widely used downhole power drilling tool. In order to solve the problems of short life of conventional positive displacement motors and difficulty in processing micro-sized positive displacement motors with equal wall thickness, this paper proposes to use the liquid filling and external extrusion composite forming process to process the tiny size spiral tube with equal wall thickness. Based on the tensile test of 304 stainless steel and the liquid-filled and external extrusion composite forming process, a finite element model of the 5LZ54 type equal-wall spiral tube by liquid-filled and external extrusion composite forming was established. We use the finite element method to study the composite forming of liquid-filled and externally extruded metal spiral pipes with equal wall thickness. The reasonable process parameters are that the outer diameter of the tube is 51 mm, the wall thickness of the tube is 5.5 mm, the friction coefficient is 0.125, the hydraulic pressure is 700 MPa, the extrusion speed of die is 0.167 m/s, and the hydraulic pressure loading path is path 5. The spiral tube completely fits the die. The variance of the wall thickness is 0.00846, and the wall thickness is more concentrated. The minimum wall thickness is 4.948 mm, the design wall thickness is 5 mm, the maximum wall thickness is 5.353 mm, and the average wall thickness is 5.15 mm. The maximum wall thickness error of the spiral section is 0.275 mm. The wall thickness at the convex arc is larger, and the wall thickness at the concave arc is smaller. Studies have shown that it is feasible to form a spiral tube with a small size and equal wall thickness by liquid filling and external extrusion forming process. [ABSTRACT FROM AUTHOR]

Double-Sided Linear Flux-Switching Permanent Magnet (DSLFSPM) motor has the merits of high efficiency, high power factor and low-cost stator structure. But the speed range of DSLFSPM is limited due to its adoption of permanent magnets. Double-Sided High Temperature Superconducting Linear Flux-Switching Motor (DSHTS-LFSM) adopts HTS coils to replace the permanent magnets, thus obtaining better power density and wider speed range. However, when the magnetic field gets much stronger, the iron core is easily saturated and flux leakage gets serious, which threatens the reliability of HTS coils and lowers the utilization of iron core. To solve this problem, a novel Double-Sided High Temperature Superconducting Linear Modular Flux-Switching Motor (DSHTS-LMFSM) is proposed. The armature windings are designed different from existing DSHTS-LFSMs to reduce flux leakage. Furthermore, by sealing the HTS coils together in a Dewar away from armature windings, the reliability is improved. In this paper, the structure and working principle of the proposed DSHTS-LMFSM is explained. The electromagnetic performance of it is calculated using Finite Element Method (FEM). As evaluation, its performance is compared against a traditional DSHTS-LFSM. [ABSTRACT FROM AUTHOR]

In this paper, we propose to compare three a posteriori error estimators namely equilibrated, star-based and residual based for the Poisson problem and the Stokes problem with lowest-order Crouzeix-Raviart finite element discretization. The numerical results are presented to compare the performance of the three estimators in an adaptive refinement strategy. [ABSTRACT FROM AUTHOR]

In this paper, a stabilized reduced-order model based on the gappy proper orthogonal decomposition (POD) technique is applied to an eddy-current problem with the non-linear material property. A classical magnetodynamic finite element formulation based on the magnetic vector potential is used as reference and starting point to build up the reduced models. The computational complexity of the non-linear problem might be reduced by the discrete empirical interpolation method-POD technique, but the eddy current effects may make this method unstable. In this paper, we propose an approach which is similar to the gappy method to successfully overcome this instability problem, while keeping the computational cost (time and memory) low. [ABSTRACT FROM AUTHOR]

A computational technique is presented in this paper which improves finite element method (FEM) in solving inverse problems. Subregion method is used to select and isolate the area of interest where design parameters for defect shape are updated. An elastic mesh generator is developed in this paper to generate optimal meshes in the selected area to save connectivity matrix until having the most accurate design parameters. Using subregion FEM in solving inverse problems will help in minimizing processing time and memory usage in addition of reducing solution complexity. A 2-D eddy current testing (ECT) problem of detecting and characterizing the location and shape of a defect by separating the defect from entire domain is used to validate the presented subregion FEM algorithm. The elastic mesh generator is investigated to update the preselected design parameters of the defect in each iteration. This meshing technique adds the specialty of using subregion method in inverse problems where elements and nodes numberings are saved inside and outside the defect region. Both the genetic algorithm and simulated annealing optimization techniques are developed to get the accurate defect parameters. The presented subregion FEM results have been verified computationally using conventional FEM. Excellent results of signals agreement and processing time minimization with a factor of 90% with an accuracy of 98% have been achieved. In addition, the presented subregion FEM algorithm has been verified experimentally using aluminum (T6061-T6) and mild steel plate (0.15%–0.30% carbon and Fe) samples. This experiment is carried using an elongated excitation coil in a fixed position mounted on the top of the sample and tunneling magnetoresistive sensor to measure magnetic field. The measured magnetic fields were used as input to the inverse subregion FEM solver and the machined artificial defects were characterized with excellent accuracy. [ABSTRACT FROM AUTHOR]

A novel linear flux switching motor (LFSM) with simple passive segmented secondary (SSLFSM) is presented in this paper. In this motor, the armature and field winding concentrated coils are wound around mover (primary) teeth alternatively. The structure of this linear motor is different from other types of LFSMs presented in previous research. All LFSMs are suffering from unbalanced back electromotive force (EMF) waveform. The same problem appears in SSLFSM. In this paper, the influence of secondary segments number on back EMF waveform of designed SSLFSM is derived analytically. It is found that the secondary segment numbers have a strong effect on generated back EMF waveform harmonic contents and phase balances. These effects are evaluated by finite-element analysis for different configurations of SSLFSM as well. With analytical and numerical evaluations, a suitable number of secondary segments for minimum harmonic contents and phase unbalances is obtained. [ABSTRACT FROM PUBLISHER]

This paper is a review of applications and possibilities offered by performing Finite Element Method computations in real time. Real time means obtaining results every certain time interval so that online reactions to some dynamic environment changes are possible. Real time processing is most commonly used in control systems which do not use computationally demanding methods, like the finite element method. However, there are some papers that discuss the real time processing of data. At the present state, there are not many examples of applied Real Time Finite Element Method (RTFEM) in the literature. The greatest problem with RTFEM is a conflict between accuracy and simulation time. It is because accurate FEM simulations are time-consuming and fast simulations are not precise enough. Due to those computational performance problems, papers concentrate mainly on simple analysis. Solutions found in the literature involve either RTFEM simulations, returning very roughly estimated results, for applications which do not require precise results, or a model that is built on the basis of results obtained from pre-calculated FEM analysis of possible load cases. This paper also discusses possibilities of performing RTFEM computations on different resources from embedded systems, personal computers, to computers with GPU (Graphics Processing Unit) acceleration. [ABSTRACT FROM AUTHOR]

Metal bulk forming is widely used because of its own advantages. In order to improve the production efficiency and reduce the cost, numerical simulation is often used to analyze the volume forming process. Because of the large deformation and non-linearity of the forming process, the finite element method (FEM) has the problem of element distortion, which will affect the accuracy and even lead to the failure of the analysis process. In this paper, an adaptive finite element method (AFEM) is proposed to solve this problem. Firstly, the finite element model is established, and grids are roughly divided. After the analysis, according to the error calculation model, the area with large error is determined by the standard deviation of nominal strain energy of nodes. Then, the grids are refined by dichotomy method, and the calculation is continued, repeating this step until the error meets the requirement. Finally, the numerical analysis of the forging process of the bulge formed joint is taken as an example to prove the accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

This paper presents a contribution to the field of numerical solutions for contact problems, which pose significant challenges in engineering and simulations. Specifically, we address the intricate task of connecting bodies that have been discretized using non-conforming and non-overlapping meshes. Our primary focus lies in investigating the efficacy of the mortar method with a segment-to-segment approach. In this context, we provide a concise overview of the underlying theoretical framework and present our implementation in the MATLAB programming environment. To ascertain the reliability and accuracy of our proposed methodology, we conduct a rigorous validation study by comparing the outcomes obtained from our implementation with those derived from the widely adopted commercial software, ANSYS. To enable a comprehensive evaluation, we select specific benchmark problems that involve the interaction of two elastic bodies. Through a meticulous analysis and comparison of results, we demonstrate the effectiveness and robustness of our approach. The findings of this study contribute substantively to the advancement of numerical techniques for solving contact problems. The validated methodology not only establishes a solid foundation for future research endeavors but also offers a reliable framework for conducting simulations in this domain. Furthermore, the insights gained from this study can potentially facilitate the development of more efficient and accurate computational algorithms for addressing contact problems encountered in various engineering applications. [ABSTRACT FROM AUTHOR]

The so-called material distribution methods for topology optimization cast the governing equation as an extended or fictitious domain problem, in which a coefficient field represents the design. In practice, the finite element method is typically used to approximate that kind of governing equations by using a large number of elements to discretize the design domain, and an element-wise constant function approximates the coefficient field in that domain. This paper presents a spectral analysis of the coefficient matrices associated with the linear systems stemming from the finite element discretization of a linearly elastic problem for an arbitrary coefficient field in three spatial dimensions. The given theoretical analysis is used for designing and studying an optimal multigrid method in the sense that the (arithmetic) cost for solving the problem, up to a fixed desired accuracy, is linear in the corresponding matrix size. Few selected numerical examples are presented and discussed in connection with the theoretical findings. [ABSTRACT FROM AUTHOR]

This paper presents an analytical method for estimating the maximum angular operation range (MAOR) in a permanent-magnet slotted limited-angle torque motor (LATM). The operating principle of three topologies is analyzed and discussed, including a toroidal LATM, a slotted LATM with common pole/slot combination, and a slotted LATM with special pole/slot combination. The analysis indicates that no effective methods have been proposed to estimate the MAOR for a slotted LATM with special pole/slot combination. Hence, this paper is focused on solving this problem. The results obtained from the analytical method are validated by a finite-element (FE) method. The average time of the proposed method takes far less than that of an FE method, so that the design cycle of LATMs can be shortened. Finally, two prototype machines are manufactured, and their experimental results are presented and discussed. The FE and experimental results validate the accuracy of an analytical method. [ABSTRACT FROM AUTHOR]

This paper develops an error estimator for a known multiscale method, which is used to solve the eddy-current problem using the time-harmonic single component current vector potential in 2-D. The multiscale method allows for the solution of the problem in a laminated domain without needing to resolve each laminate in the mesh, which would require a prohibitively large number of degrees of freedom in the finite-element system. The error estimator is based on a flux equilibration technique, which has so far been presented for a more restricted class of problems and has the advantage of being efficient as well as reliable with a generic constant equal to 1. It can be shown to be extendable to the equations arising in the used multiscale method. Its local nature allows for the construction of an efficient adaptive mesh refinement. Using these findings, the multiscale method can be improved to obtain a better rate of convergence with respect to the number of degrees of freedom. [ABSTRACT FROM AUTHOR]

In the domain of field computation with the finite-element method, choosing the mesh refinement is an important step to obtain an accurate solution. In order to evaluate the quality of the mesh, a posteriori error estimators are frequently used. In this paper, we propose to analyze and to compare residual and equilibrated error estimators for eddy-current problems in the case of A- $\varphi $ and T- $\Omega $ formulations. The different properties of the estimators will be discussed. [ABSTRACT FROM AUTHOR]

The main aim of the paper is to study the impact of delay times in a poro-elastic medium using the finite element approach and the three-phase lag thermo-elastic theory. The governing equations were obtained for a three-phase lag model with six delay times. Consideration was given to a one-dimensional application of a poro-elastic half-space. Because of the complex form of the basic equations, the finite element approach was used to solve this problem. Asymmetric and symmetric tensors were used to represent all of the physical quantities. The numerical results were presented in graphical form. The effects of porosity and delays were introduced. Finally, the results were plotted to show the difference between the three-phase delay (TPL) and the Green−Naghdi with and without energy dissipation (GNIII) models. [ABSTRACT FROM AUTHOR]

The interpretation of three-dimensional (3-D) magnetotelluric (MT) data is usually based on the isotropic assumption of the subsurface structures, and this assumption could lead to erroneous interpretation in the area with considerable electrical anisotropy. Although arbitrary anisotropy is much closer to the ground truth, it is generally more challenging to recover full anisotropy parameters from 3-D inversion. In this paper, we present a 3-D triaxial anisotropic inversion framework using the edge-based finite element method with a tetrahedral mesh. The 3-D inverse problem is solved by the Gauss-Newton (GN) method which shows fast convergence behavior. The computation cost of the data-space method depends on the size of data, which is usually smaller than the size of model; therefore, we transform the inversion algorithm from the model space to the data space for memory efficiency. We validate the effectiveness and applicability of the developed algorithm using several synthetic model studies. [ABSTRACT FROM AUTHOR]

Although demand for the multi-segmented and multi-layered (MSML) interior permanent magnet (IPM) motor is high, the analytic method for this motor has not yet been proposed. The finite element method has been used in the analysis and design of the MSML IPM motor, even though it takes much time to perform. To solve this problem, the correct and rapid analytic analysis method for the MSML IPM motor is proposed in this paper. This method is called the MCC method because it is the combination of the Magnetic equivalent circuit, Conformal mapping to consider slotting effect, and Concentration flux of IPM. Furthermore, the feasibility of the optimization of the MSML motor by using the proposed MCC method is verified in this paper. [ABSTRACT FROM AUTHOR]

Native application of finite-element method (FEM) to the analysis of skin and proximity effects in multi-turn coils results in large equation systems, whose solution needs long computational time. This paper proposes a semi-analytical approach to overcome this problem. For the analysis of the proximity effect, the complex permeability of a round conducting wire immersed in uniform time-harmonic magnetic fields is represented in a closed form. Then, the homogenized complex permeability over the cross section of the multi-turn coil is analytically evaluated using the Ollendorff formula. The magnetoquasistatic problem is thus replaced by the magnetostatic one, in which the multi-turn coil is treated as a uniform material with the homogenized complex permeability. The skin effect is taken into consideration by introducing the corresponding impedance in the circuit equation. The proposed method is shown to give the impedance of multi-turn coils, which is in good agreement with that obtained by the conventional FEM as well as experiments. [ABSTRACT FROM AUTHOR]

The fruit fly optimization algorithm-general regression neural network (FOA-GRNN) coupled model and the Finite Element Method-Smoothed Particle Hydrodynamics (FEM-SPH) numerical calculation method are comprehensively used. The control problem of blasting vibration in the process of mining hidden resources under complex environmental conditions has been studied. Taking a lead-zinc mine as the engineering background, the development of hidden resources in the collapse area due to unreasonable mining was studied. Based on the establishment of the first mining stope and its mining method in this area, biosimulation and generalized neural networks were introduced to solve this problem, the coupling of blasting parameters was analyzed, and the 3D nonlinear dynamic coupling model was constructed for numerical simulation. The results show that the blasting parameters of deep-hole mining were optimized, including the values of six output quantities: hole distance, row spacing, side hole distance, explosive unit consumption, minimum resistance line, and interval ratio (the Root Mean Squared Error value is only 0.051). The error between the network optimization parameters and the empirically obtained values was controlled to within 0.05; five possible edge-hole charge structures were designed (the interval ratio is 0.696), and the vibration velocity peak and pressure peak variations with time after detonation are reflected by the simulation results. The dynamic evolution law of the rock mass velocity vector and the damage of the rock damage was revealed. According to the analysis in this paper, the smallest and optimal edge-hole charge structure of the surrounding rock was obtained. [ABSTRACT FROM AUTHOR]

The soil in Iraq has a low load carrying or bearing capacity and high deflections or settlement because of the applied loads. The use of strip footing as a foundation to support different kinds of heavy structures has become necessary nowadays through solving such problems by using geogrid. This soil improvement technique is widely used all over the world. In this paper, the bearing capacity and settlements were calculated using finite elements and analytical models for strip footing resting on different kinds of soil. The study parameters are footing rigidity, the number of layers in a geogrid, the dimension of geogrid, and spacing of geogrid layers. According to the findings, the geogrid improved the bearing ability of the footing and reduced settlement. The optimum geogrid dimension was three times the footing width, and three geogrid layers were optimum. The changing in footing rigidity also affects the stress and settlement behavior. [ABSTRACT FROM AUTHOR]

Elliptic interface problems have wide applications in engineering and science. Non-body-fitted grid has the advantage of saving the cost of mesh generation. In this paper, we propose a Petrov-Galerkin formulation using non-body-fitted grid for solving elliptic interface problems. In this method, adaptive mesh refinement is employed for cells with large errors. The new mesh still has all triangles being right triangles of the same shape. Numerical experiments show side-by-side comparison that to obtain the same accuracy, our new method has much less overall CPU time compared with the previous method even with some cost on mesh generation. [ABSTRACT FROM AUTHOR]

The goal of the paper is to correlate real brain deflection with its numerical model as the 3D model of a fragment of the brain and suction pipe. The model is analyzed with the Finite Element Method with use of Ansys software. The brain tissue can undergo large strains, which is why it is described by a hyperelastic material. The Mooney-Rivlin material model is used for numerical analyzes. The inverse problem is solved with use of optimization Non-Linear Programming by Quadratic Lagrangian (NLPQL). [ABSTRACT FROM AUTHOR]

Perforated composite laminates are frequently encountered in multiple engineering applications as sub-components of complicated structures. In many of these applications, the primary objective of using the panel is to resist buckling under diverse environmental and loading conditions. This paper is mainly focused on the vibration and buckling responses of composite laminates with elliptical cutouts subjected to localized edge loads under different hygrothermal environments. Toward this, a nine-noded heterosis plate element has been utilized to discretize the plate by adopting a refined meshing pattern around the elliptical cutout. The geometric nonlinearity has been incorporated to predict free vibrations under the hygrothermal environment. Considering the plethora of applications of composite laminates in hygrothermal conditions, a new temperature/moisture-dependent model is presented by taking into consideration various mechanical loadings. For a given environmental and loading condition, the stress distribution within the perforated panel is highly non-uniform in nature and hence, a novel dynamic approach has been proposed to solve buckling problems by adopting two sets of boundary conditions. A MATLAB program has been developed to investigate the effect of various parameters such as elliptical cutout size, elliptical orientation, elliptical cutout eccentricity, thickness and boundary conditions of the laminated composite plate under diverse hygrothermomechanical loading conditions. A notable difference in the critical buckling load is observed when the locally prestressed perforated panels are subjected to complex hygrothermal environments, especially at larger elliptical cutouts and hence the importance of localized edge loads under hygrothermal environment is emphasized. [ABSTRACT FROM AUTHOR]

In this paper, an efficient multiscale finite element method via local defect-correction technique is developed. This method is used to solve the Schrödinger eigenvalue problem with three-dimensional domain. First, this paper considers a three-dimensional bounded spherical region, which is the truncation of a three-dimensional unbounded region. Using polar coordinate transformation, we successfully transform the three-dimensional problem into a series of one-dimensional eigenvalue problems. These one-dimensional eigenvalue problems also bring singularity. Second, using local refinement technique, we establish a new multiscale finite element discretization method. The scheme can correct the defects repeatedly on the local refinement grid, which can solve the singularity problem efficiently. Finally, the error estimates of eigenvalues and eigenfunctions are also proved. Numerical examples show that our numerical method can significantly improve the accuracy of eigenvalues. [ABSTRACT FROM AUTHOR]

In multi-degree-of-freedom (multi-DOF) systems, a number of motors are used to achieve a multi-DOF motion. However, these systems have problems, such as heavy weight, large size, and no back drivability due to the large number of motors. In order to solve these problems, there has been much work on multi-DOF motion using one actuator. In this paper, a novel 2-DOF differentially coupled magnetic actuator is proposed, and its structure and operating principle are described. A 2-D motion can be realized with the conventional motor control circuits. [ABSTRACT FROM AUTHOR]

The paper deals with an examination of the behaviour of glued Ti-Al column under compression at elevated temperature. The tests of compressed columns with initial load were performed at different temperatures to obtain their characteristics and the load-carrying capacity. The deformations of columns during tests were registered by employing non-contact Digital Image Correlation Aramis® System. The numerical computations based on finite element method by using two different discrete models were carried out to validate the empirical results. To solve the problems, true stress-logarithmic strain curves of one-directional tensile tests dependent on temperature both for considered metals and glue were implemented to software. Numerical estimations based on Green–Lagrange equations for large deflections and strains were conducted. The paper reveals the influence of temperature on the behaviour of compressed C-profile Ti-Al columns. It was verified how the load-carrying capacity of glued bi-metal column decreases with an increase in the temperature increment. The achieved maximum loads at temperature 200 °C dropped by 2.5 times related to maximum loads at ambient temperature. [ABSTRACT FROM AUTHOR]

This paper analyzes the transverse vibration laws of 5000 m ladder-shaped mining pipe under different towing velocities and accelerations in the ocean, thinking of the pipe as the beam model, discretized based on the FEM. The algorithm is used to solve the problem to obtain the transverse vibration law. The research shows that the mining pipe overall transverse vibration trend decreases first and then increases, the minimum vibration value occurs at 3000 m, and the maximum occurs at the top. Increasing the towing velocity, acceleration, and ore bin weight will increase the transverse vibration value. The vibration intensity produced by the same acceleration in the constant acceleration and deceleration stages is different, and the damping effect after adding the same damping is also different. In the range of 0.01 m/s2–0.1 m/s2, the vibration reduction effect after adding damping in the constant deceleration stage is more significant, and in the range of 0.1 m/s2-0.2 m/s2, the vibration reduction effect after adding damping in the constant acceleration stage is more significant. In the stage of the constant acceleration or deceleration, when adding the same damping, the vibration intensity generated by the large acceleration is still far greater than the vibration intensity generated by the small acceleration, so the mining ship should keep the small acceleration for towing motion. [ABSTRACT FROM AUTHOR]

In this paper, some of the displacement-based plate theories are used to investigate the elastic-plastic analysis of plates in the framework of the finite element method including the buckling and postbuckling effects with the focus on the general third-order plate theory (GTPT). The plate calculation results were compared with the results obtained using 64-nodes solid elements involving Lobatto integration scheme. The problem is solved using the Newton–Raphson method applying modified Crisfield constant arc-length procedure. The results show good agreement of results and the GTPT can be acknowledged to fulfill essential criteria for application to the elastic-plastic analysis of thin and thick plates. [ABSTRACT FROM AUTHOR]

Accurate and efficient source analysis in electro- and magnetoencephalography using sophisticated realistic head geometries requires advanced numerical approaches. This paper presents DUNEuro, a free and open-source C++ software toolbox for the numerical computation of forward solutions in bioelectromagnetism. Building upon the DUNE framework, it provides implementations of modern fitted and unfitted finite element methods to efficiently solve the forward problems of electro- and magnetoencephalography. The user can choose between a variety of different source models that are implemented. The software's aim is to provide interfaces that are extendable and easy-to-use. In order to enable a closer integration into existing analysis pipelines, interfaces to Python and MATLAB are provided. The practical use is demonstrated by a source analysis example of somatosensory evoked potentials using a realistic six-compartment head model. Detailed installation instructions and example scripts using spherical and realistic head models are appended. [ABSTRACT FROM AUTHOR]

High temperature superconducting (HTS) cables have advantages of low loss and large capacity transmission. In order to analyze and protect the HTS cable, especially in the transient process, this paper develops a new method to analyze its thermal properties. Based on the structure parameters and actual working conditions of three-phase coaxial (tri-axial) HTS cable a two-dimensional (2-D) axisymmetric finite element simulation model along the axis was built in COMSOL. By coupling first and then decoupling, the temperature distribution was studied under the conditions of cooling, rated current, cryogenic system failure, local hot spot and short circuit fault. This method solves the problem that non-isothermal flow (nitf) is hard to converge under transient conditions, and has the advantages of simple and accurate. [ABSTRACT FROM AUTHOR]

In this paper, an efficient finite element (FE) solution of regular and near-regular systems is presented using graph product rules. Such systems can be observed in an FE solution of differential equations or direct construction of the stiffness matrix in a structural/mechanical problem. Graph product rules are developed to decompose a regular pattern to its preliminary generating components, solving the problem using efficient divide and conquer approaches. Regularity is regarded as a specific condition mathematically; however, due to natural repetition of elements in FE models, regular/near-regular patterns are very common in these models. In this paper, graph product mathematical formulations for FE models are developed, and the efficiency of the method is demonstrated using computational complexity. Comprehensiveness of the method is shown using diverse complementary examples. [ABSTRACT FROM AUTHOR]

The problem of determining the electromagnetic scattering of arbitrary structures consisting of both dielectric and conducting materials are analyzed in this paper by the natural-element method coupled with the absorbing boundary condition (NEM-ABC). By this method, the target is first enclosed by a fictitious boundary. Maxwell’s equations are then solved by NEM inside and ABC is applied on the fictitious boundary. The results are compared with analytical and finite-element method-ABC ones which show the robustness, applicability and relevance of the method. [ABSTRACT FROM PUBLISHER]

This paper addresses the generalized finite-element method enriched by plane waves for the 2-D Helmholtz equation. The enrichment function is modified to reduce the effect of numerical dispersion from coarse meshes and to make it possible to treat essential boundary conditions in a straightforward way. Two numerical examples, the free space propagation problem and the plane wave scattering by a cylinder, demonstrate the effectiveness of the new enrichment function. [ABSTRACT FROM PUBLISHER]

The element energy projection (EEP) method for computation of superconvergent resulting in a one-dimensional finite element method (FEM) is successfully used to self-adaptive FEM analysis of various linear problems, based on which this paper presents a substantial extension of the whole set of technology to nonlinear problems. The main idea behind the technology transfer from linear analysis to nonlinear analysis is to use Newton's method to linearize nonlinear problems into a series of linear problems so that the EEP formulation and the corresponding adaptive strategy can be directly used without the need for specific super-convergence formulation for nonlinear FEM. As a result, a unified and general self-adaptive algorithm for nonlinear FEM analysis is formed. The proposed algorithm is found to be able to produce satisfactory finite element results with accuracy satisfying the user-preset error tolerances by maximum norm anywhere on the mesh. Taking the nonlinear ordinary differential equation of second-order as the model problem, this paper describes the related fundamental idea, the implementation strategy, and the computational algorithm. Representative numerical examples are given to show the efficiency, stability, versatility, and reliability of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper presents a superconvergence result based on projection method for stabilized finite element approximation of the Stokes eigenvalue problem. The projection method is a postprocessing procedure that constructs a new approximation by using the least squares method. The paper complements the work of Li et al. (2012), which establishes the superconvergence result of the Stokes equations by the stabilized finite element method. Moreover, numerical tests confirm the theoretical analysis. [ABSTRACT FROM AUTHOR]

In the electrostatic field computations, second-order elliptic interface problems with nonhomogeneous interface jump conditions need to be solved. In realistic applications, often the total electric quantity on the interface is given. However, the charge distribution on the interface corresponding to the nonhomogeneous interface jump condition is unknown. This paper proposes a Cartesian grid method for solving the interface problem with the given total electric quantity on the interface. The proposed method employs both the immersed finite element with the nonhomogeneous interface jump condition and the augmented technique. Numerical experiments are presented to show the accuracy and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

In recent decades, bearingless switched reluctance motors (BSRMs) have been proposed. However, few researchers focused on the optimal design of the BSRMs. In this paper, the multi-objective optimal design of BSRMs is investigated. At first, an analytical design model is derived from the mathematical model of the BSRMs. An initial design is calculated by the analytical design model. The electromagnetic performance is compared with calculation results from the finite-element method (FEM). Then, the objective functions, constraints, and decision variables are also determined. Corresponding sensitivity analysis of the decision variables is implemented. Besides, aiming at solving the optimization problem with disconnected, non-uniformly distributed Pareto front and multiple local optimums, a novel multi-objective genetic particle swarm optimizer (MOGPSO) is presented. The algorithm performance of the proposed MOGPSO is validated by solving the standard test functions. Then the proposed MOGPSO is applied for the optimal design of BSRMs. Optimization results solved by MOGPSO, conventional multi-objective particle swarm optimizer, and non-dominated sorting genetic algorithm II are compared and analyzed. Comparison results reveal that the proposed MOGPSO can achieve more non-dominated solutions in Pareto front and is particularly suitable for optimization of BSRMs. The final optimal design is selected from the obtained Pareto front. The electromagnetic performance is compared with the initial design and verified by the FEM. Verification results show that the optimal design of BSRMs based on the analytical design model and the proposed MOGPSO is feasible and effective. [ABSTRACT FROM PUBLISHER]

In this work, we develop an a posteriori error analysis of a conforming mixed finite element method for solving the coupled problem arising in the interaction between a free fluid and a fluid in a poroelastic medium on isotropic meshes in ℝ d , d ∈ 2 , 3 . The approach utilizes a Lagrange multiplier method to impose weakly the interface conditions [Ilona Ambartsumyan et al., Numerische Mathematik, 140 (2): 513-553, 2018]. The a posteriori error estimate is based on a suitable evaluation on the residual of the finite element solution. It is proven that the a posteriori error estimate provided in this paper is both reliable and efficient. The proof of reliability makes use of suitable auxiliary problems, diverse continuous inf-sup conditions satisfied by the bilinear forms involved, Helmholtz decomposition, and local approximation properties of the Clément interpolant. On the other hand, inverse inequalities and the localization technique based on simplexe-bubble and face-bubble functions are the main tools for proving the efficiency of the estimator. Up to minor modifications, our analysis can be extended to other finite element subspaces yielding a stable Galerkin scheme. [ABSTRACT FROM AUTHOR]

The paper presents the numerical modeling of large deflections of a flat textile structure subjected to a constant force acting on the free end. It was assumed that the examined structure is inextensible. The effect of the structure's own weight was also taken into account. In order to solve the problem, the flat textile structure was modeled using the heavy elastica theory. An important element of the analysis involves taking into account the variable bending rigidity of the examined textile structure along its length, which is often found in this type of products. The function of variable bending rigidity was assumed in advance. Numerical calculations were carried out in the Mathematica environment using the shooting method for the boundary value problem. The obtained results were verified using the finite element method. [ABSTRACT FROM AUTHOR]

Mine rock slope stability rating is the process of assessing its stability probability, analyzing its failure mode, and then determining its stability rating by location matching principle and scale matching principle, having important theoretical and practical significance in putting forward reasonable restoration suggestions. In recent years, rapidly developing artificial intelligence methods not only have the characteristics of highly nonlinear mapping, self-organization, and self-adaptation but also mostly apply probability optimal strategy and, hence, bypass the problem of solving function derivatives, having higher efficiency and feasibility in solving the problems of global optimal solution and local optimal solution. On the basis of summarizing and analyzing previous research works, this paper expounded the current research status and significance of mine rock slope stability rating, elaborated the development background, current status, and future challenges of artificial intelligence methods, introduced the principles of the limit equilibrium method and finite element method, constructed an artificial intelligence-based mine rock slope stability calculation model, performed slope stability influencing factors' analysis and optimization model parameter selection, proposed a mine rock slope stability rating algorithm based on artificial intelligence, analyzed the rating algorithm design and rating algorithm implementation, and finally conducted a case analysis and its discussion. The study results show that the artificial intelligence-based mine rock slope stability rating method can make full use of computer advantages to have larger capacity and faster calculation speed and solve to the greatest extent the randomness, timeliness, ambiguity, and other uncertain characteristics of mine rock slope stability by a large number of random sampling for finding the optimal value of the objective function. The study results of this paper provide a reference for further research studies on the stability rating of mine rock slopes based on artificial intelligence. [ABSTRACT FROM AUTHOR]

A modified meshless local Petrov–Galerkin for an electromagnetic axisymmetric problem is presented in this paper. The method uses the shape functions generated by the radial point interpolation method with a modified T-scheme to select the support nodes, and also a new and malleable strategy to determine the test domains. The convergence of the method is evaluated using a coaxial cavity problem and it is compared with the finite-element method for two different meshes: one with a good quality mesh and another partially composed to bad quality elements. The total execution time using both methods is also compared. [ABSTRACT FROM AUTHOR]

To solve stochastic static field problems, a discretization by the finite-element method can be used. A system of equations is obtained with the unknowns (scalar potential at nodes, for example) being random variables. To solve this stochastic system, the random variables can be approximated in a finite-dimension functional space—a truncated polynomial chaos expansion. The error between the exact solution and the approximated one depends not only on the spatial mesh, but also on the discretization along the stochastic dimension. In this paper, we propose an a posteriori estimation of the error due to the discretization along the stochastic dimension. [ABSTRACT FROM AUTHOR]

In this paper, a method is proposed to estimate the detailed muscular strength of a human limb. The detailed muscular strength discussed in this paper is not the strength produced by coordinated muscle actions but the joint torque generated by each muscle group classified according to its function. It is assumed that a human limb is modeled as a two-link manipulator actuated by three pairs of six muscle groups. Although the model theoretically derives the output force distribution at an end effector from the joint torques, the joint torques are not calculated directly from the distribution. The antagonistic ratios of the output forces at the end effector are introduced to solve this problem. However, the estimation results cannot be compared with actual values in a real environment because it is impossible to measure the output of only a certain muscle in a noninvasive way. Instead, simulations and experiments using a robotic arm demonstrate that the proposed method estimates the output ratios of muscle groups with a satisfactory accuracy. [ABSTRACT FROM AUTHOR]

A novel and general method to quickly obtain frequency-domain solutions based on one or a few time-domain solutions is presented. The time-domain solution of electromagnetic field is found by using either two-dimensional (2-D) or three-dimensional (3-D) finite-element methods (FEM). The time-domain FEM is first used to obtain a solution for step function excitations by taking into account all the necessary initial conditions. Then, based on time-domain convolution theorem and the principle of integration by parts, a numerical algorithm to find the solutions of any excitations, without additional FEM computation, is deduced. A typical, interesting and meaningful application is to obtain the frequency-domain solutions when sweeping the operating frequency over a wide range. In this paper, a problem involving the finding of the resonant frequency of a copper loop connected with a pair of parallel plates using 3-D FEM is used as an illustrative example. The numerical experiment shows that the proposed method can reduce the computing time effectively and readily as it is easy to adjust the time step size in time-domain FEM. [ABSTRACT FROM AUTHOR]

In this paper, numerical computation of the modified equal width equation (MEW), which is one of the equations used to model nonlinear events, will be carried out. For this equation, numerical computations have been obtained by many researchers using different methods. The goal of the new approach is to check how well it performs with respect to the numerical calculations the researchers found. For this, the proposed study presents a Lie-Trotter splitting algorithm in accordance with the time-splitting technical rules combined with Lumped Galerkin FEM based on the basis function of the cubic B-spline. Two valid test examples are given to determine the validity and effectiveness of the current technique. The results obtained in a new way with the Matlab computational software are compared with the studies of other authors in the literature and are shown graphically. Based on these new results, it can clearly be stated that the benefit of the proposed approach is to demonstrate that reliability is achieved in obtaining approximate computations. [ABSTRACT FROM AUTHOR]

This paper proposes interface and polynomial enrichments using the generalized finite element method (IGFEM) for the material interface in composite materials without matching the finite element mesh to the boundaries of different materials. Applications in structural members such as laminated beams and heterogeneous composites (matrix and inclusions) employing coarse and fine meshes are employed. The results were compared with conventional GFEM and analytical solutions. Verification and simulations proved the efficiency of the suggested framework for solving problems with discontinuous gradients resulting from a material interface. The proposed method allows flexibility in mesh generation for composite materials by letting the interface be embedded in an element without the need to match the mesh to the material interface. This improves the computational efficiency over conventional methods. [ABSTRACT FROM AUTHOR]

In this paper, we present a new approach to model the steady-state heat transfer in heterogeneous materials. The multiscale finite element method (MsFEM) is improved and used to solve this problem. MsFEM is a fast and flexible method for upscaling. Its numerical efficiency is based on the natural parallelization of the main computations and their further simplifications due to the numerical nature of the problem. The approach does not require the distinct separation of scales, which makes its applicability to the numerical modeling of the composites very broad. Our novelty relies on modifications to the standard higher-order shape functions, which are then applied to the steady-state heat transfer problem. To the best of our knowledge, MsFEM (based on the special shape function assessment) has not been previously used for an approximation order higher than p = 2, with the hierarchical shape functions applied and non-periodic domains, in this problem. Some numerical results are presented and compared with the standard direct finite-element solutions. The first test shows the performance of higher-order MsFEM for the asphalt concrete sample which is subject to heating. The second test is the challenging problem of metal foam analysis. The thermal conductivity of air and aluminum differ by several orders of magnitude, which is typically very difficult for the upscaling methods. A very good agreement between our upscaled and reference results was observed, together with a significant reduction in the number of degrees of freedom. The error analysis and the p-convergence of the method are also presented. The latter is studied in terms of both the number of degrees of freedom and the computational time. [ABSTRACT FROM AUTHOR]