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The coupling process between the loading mechanism and the tank car mouth is a crucial step in the tank car loading process. The purpose of this paper is to design a method to accurately measure the pose of the tanker car.

The collected image is first subjected to a gray enhancement operation, and the black parts of the image are extracted using Otsu’s threshold segmentation and morphological processing. The edge pixels are then filtered to remove outliers and noise, and the remaining effective points are used to fit the contour information of the tank car mouth. Using the successfully extracted contour information, the pose information of the tank car mouth in the camera coordinate system is obtained by establishing a binocular projection elliptical cone model, and the pixel position of the real circle center is obtained through the projection section. Finally, the binocular triangulation method is used to determine the position information of the tank car mouth in space.

Experimental results have shown that this method for measuring the position and orientation of the tank car mouth is highly accurate and can meet the requirements for industrial loading accuracy.

A method for extracting the contours of various types of complex tanker mouth is proposed. This method can accurately extract the contour of the tanker mouth when the contour is occluded or disturbed. Based on the binocular elliptic conical model and perspective projection theory, an innovative method for measuring the pose of the tanker mouth is proposed, and according to the space characteristics of the tanker mouth itself, the ambiguity of understanding is removed. This provides a new idea for the automatic loading of ash tank cars.

This study aims to derive a novel spatial numerical method based on multidimensional local Taylor series representations for solving high-order advection-diffusion (AD) equations.

The parabolic AD equations are reduced to the nonhomogeneous elliptic system of partial differential equations by utilizing the Chebyshev spectral collocation method (ChSCM) in the temporal variable. The implicit-explicit local differential transform method (IELDTM) is constructed over two- and three-dimensional meshes using continuity equations of the neighbor representations with either explicit or implicit forms in related directions. The IELDTM yields an overdetermined or underdetermined system of algebraic equations solved in the least square sense.

The IELDTM has proven to have excellent convergence properties by experimentally illustrating both h-refinement and p-refinement outcomes. A distinctive feature of the IELDTM over the existing numerical techniques is optimizing the local spatial degrees of freedom. It has been proven that the IELDTM provides more accurate results with far fewer degrees of freedom than the finite difference, finite element and spectral methods.

This study shows the derivation, applicability and performance of the IELDTM for solving 2D and 3D advection-diffusion equations. It has been demonstrated that the IELDTM can be a competitive numerical method for addressing high-space dimensional-parabolic partial differential equations (PDEs) arising in various fields of science and engineering. The novel ChSCM-IELDTM hybridization has been proven to have distinct advantages, such as continuous utilization of time integration and optimized formulation of spatial approximations. Furthermore, the novel ChSCM-IELDTM hybridization can be adapted to address various other types of PDEs by modifying the theoretical derivation accordingly.

This paper focuses on the unconditionally optimal error estimates of a linearized second-order scheme for a nonlocal nonlinear parabolic problem. The first step of the scheme is based on Crank–Nicholson method while the second step is the second-order BDF method.

A rigorous error analysis is done, and optimal L² error estimates are derived using the error splitting technique. Some numerical simulations are presented to confirm the study’s theoretical analysis.

Optimal L² error estimates and energy norm.

The goal of this research article is to present and establish the unconditionally optimal error estimates of a linearized second-order BDF finite element scheme for the reaction-diffusion problem. An optimal error estimate for the proposed methods is derived by using the temporal-spatial error splitting techniques, which split the error between the exact solution and the numerical solution into two parts, that is, the temporal error and the spatial error. Since the spatial error is not dependent on the time step, the boundedness of the numerical solution in L∞-norm follows an inverse inequality immediately without any restriction on the grid mesh.

This study aims to propose and numerically assess different ways of discretising a very weak formulation of the Poisson problem.

We use integration by parts twice to shift smoothness requirements to the test functions, thereby allowing low-regularity data and solutions.

Various conforming discretisations are presented and tested, with numerical results indicating good accuracy and stability in different types of problems.

This is one of the first articles to propose and test concrete discretisations for very weak variational formulations in primal form. The numerical results, which include a problem based on real MRI data, indicate the potential of very weak finite element methods for tackling problems with low regularity.

The ability to characterise highly conducting objects, that may also be highly magnetic, by the complex symmetric rank–2 magnetic polarizability tensor (MPT) is important for metal detection applications including discriminating between threat and non-threat objects in security screening, identifying unexploded anti-personnel landmines and ordnance and identifying metals of high commercial value in scrap sorting. Many everyday non-threat items have both a large electrical conductivity and a magnetic behaviour, which, for sufficiently weak fields and the frequencies of interest, can be modelled by a high relative magnetic permeability. This paper aims to discuss the aforementioned idea.

The numerical simulation of the MPT for everyday non-threat highly conducting magnetic objects over a broad range of frequencies is challenging due to the resulting thin skin depths. The authors address this by employing higher order edge finite element discretisations based on unstructured meshes of tetrahedral elements with the addition of thin layers of prismatic elements. Furthermore, computer aided design (CAD) geometrical models of the non-threat and threat object are often not available and, instead, the authors extract the geometrical features of an object from an imaging procedure.

The authors obtain accurate numerical MPT characterisations that are in close agreement with experimental measurements for realistic physical objects. The assessment of uncertainty shows the impact of geometrical and material parameter uncertainties on the computational results.

The authors present novel computations and measurements of MPT characterisations of realistic objects made of magnetic materials. A novel assessment of uncertainty in the numerical predictions of MPT characterisations for uncertain geometry and material parameters is included.

Topology optimization of structures under self-weight loading is a challenging problem which has received increasing attention in the past years. The use of standard formulations based on compliance minimization under volume constraint suffers from numerous difficulties for self-weight dominant scenarios, such as non-monotonic behaviour of the compliance, possible unconstrained character of the optimum and parasitic effects for low densities in density-based approaches. This paper aims to propose an alternative approach for dealing with topology design optimization of structures into three spatial dimensions subject to self-weight loading.

In order to overcome the above first two issues, a regularized formulation of the classical compliance minimization problem under volume constraint is adopted, which enjoys two important features: (a) it allows for imposing any feasible volume constraint and (b) the standard (original) formulation is recovered once the regularizing parameter vanishes. The resulting topology optimization problem is solved with the help of the topological derivative method, which naturally overcomes the above last issue since no intermediate densities (grey-scale) approach is necessary.

A novel and simple approach for dealing with topology design optimization of structures into three spatial dimensions subject to self-weight loading is proposed. A set of benchmark examples is presented, showing not only the effectiveness of the proposed approach but also highlighting the role of the self-weight loading in the final design, which are: (1) a bridge structure is subject to pure self-weight loading; (2) a truss-like structure is submitted to an external horizontal force (free of self-weight loading) and also to the combination of self-weight and the external horizontal loading; and (3) a tower structure is under dominant self-weight loading.

An alternative regularized formulation of the compliance minimization problem that naturally overcomes the difficulties of dealing with self-weight dominant scenarios; a rigorous derivation of the associated topological derivative; computational aspects of a simple FreeFEM implementation; and three-dimensional numerical benchmarks of bridge, truss-like and tower structures.

This study aims to assess the robustness and accuracy of the face-centred finite volume (FCFV) method for the simulation of compressible laminar flows in different regimes, using numerical benchmarks.

The work presents a detailed comparison with reference solutions published in the literature –when available– and numerical results computed using a commercial cell-centred finite volume software.

The FCFV scheme provides first-order accurate approximations of the viscous stress tensor and the heat flux, insensitively to cell distortion or stretching. The strategy demonstrates its efficiency in inviscid and viscous flows, for a wide range of Mach numbers, also in the incompressible limit. In purely inviscid flows, non-oscillatory approximations are obtained in the presence of shock waves. In the incompressible limit, accurate solutions are computed without pressure correction algorithms. The method shows its superior performance for viscous high Mach number flows, achieving physically admissible solutions without carbuncle effect and predictions of quantities of interest with errors below 5%.

The FCFV method accurately evaluates, for a wide range of compressible laminar flows, quantities of engineering interest, such as drag, lift and heat transfer coefficients, on unstructured meshes featuring distorted and highly stretched cells, with an aspect ratio up to ten thousand. The method is suitable to simulate industrial flows on complex geometries, relaxing the requirements on mesh quality introduced by existing finite volume solvers and alleviating the need for time-consuming manual procedures for mesh generation to be performed by specialised technicians.

Due to high speeds, heavy loads, large slide-to-roll ratios (SRR) and other variable operating conditions, some rolling bearings that have been working in harsh conditions may experience flash temperatures in the contact area, which may result in early damage like smearing and then affect service life. This study aims to investigate the flash temperature phenomenon of rolling bearings through theoretical and experimental analysis.

A technology for measuring temperature distribution in rolling ball on disk contact under lubrication was developed. The test-rig can simulate the ball bearing contact. The effects of working conditions such as entrainment speed, load, SRR and lubricating oil viscosity on the flash temperature were investigated.

The results of the theoretical calculation and experiments indicate that the parameters promoting the reduction of film thickness in elastohydrodynamic lubrication are always related with the number of flash points, even film thickness reduced to mixed lubrication. The flash temperature is easier to happen in conditions of high SRR, heavy load, slow entrainment speed and low viscosity oil.

This work conducts an experimental study on the flash temperature phenomenon, providing a test technology for bearing lubrication and failure investigation.

This author has opted into Transparent Peer Review available at: https://publons.com/publon/10.1108/ILT-04-2023-0104

The main purpose of this paper is to introduce the gradient discretisation method (GDM) to a system of reaction diffusion equations subject to non-homogeneous Dirichlet boundary conditions. Then, the authors show that the GDM provides a comprehensive convergence analysis of several numerical methods for the considered model. The convergence is established without non-physical regularity assumptions on the solutions.

In this paper, the authors use the GDM to discretise a system of reaction diffusion equations with non-homogeneous Dirichlet boundary conditions.

The authors provide a generic convergence analysis of a system of reaction diffusion equations. The authors introduce a specific example of numerical scheme that fits in the gradient discretisation method. The authors conduct a numerical test to measure the efficiency of the proposed method.

This work provides a unified convergence analysis of several numerical methods for a system of reaction diffusion equations. The generic convergence is proved under the classical assumptions on the solutions.

To predict the real behavior of the full-scale model using a scale model, optimized simulation should be achieved. In reinforced concrete (RC) models, scaling can be substantially more critical than in single-material models because of multiple reasons such as insufficient bonding strength between small-diameter steel bars and concrete, and excessive aggregate size. Overall, there is a shortfall of laboratory and field-testing studies on the behavior of secant pile walls under lateral and axial loads. Accordingly, the purpose of this study is to investigate the validity and the performance of the 1/10th scaled RC secant pile wall under the influence of different types of loading.

The structural performance of the examined models was evaluated using two types of tests: bending and axial compression. A self-compacting concrete mix was suggested, which provided the best concrete mix workability and appropriate compressive strength.

Under axial and bending loads, the failure modes were typical. Where the plain and reinforced concrete piles worked in tandem to support the load throughout the loading process, even when they failed. The experimental results were relatively consistent with some empirical equations for calculating the modulus of elasticity and critical buckling load. This confirmed the validity of the proposed model.

According to the analysis and verification of experimental tests, the proposed 1/10th scaled RC secant pile model can be used for future laboratory purposes, especially in the field of geotechnical engineering.