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In traditional methods, a one-directional distance transformation is employed to eliminate the near-singularity in the radial direction. However, when the projection point of the source point is near the boundary of the integral element, the near-singularity in the circumferential direction still exists, resulting in large errors in the numerical results. The purpose of this paper is to propose a bi-directional distance transformation for the elimination of near-singularities in two directions arising from the irregular integral element.

The sources of the circumferential near-singularity caused by irregular sub-triangular element are analyzed in this paper. A bi-directional distance transformation based on the (a, β) transformation is proposed to eliminate the near-singularities in the two directions. The (a, β) transformation is initially introduced to separate the integral variables and streamline the implementation of subsequent transformations. In the transformed (a, β) coordinate system, a new distance transformation applied in the circumferential direction is constructed.

With the proposed method, the radial and circumferential near-singularities are eliminated using two different distance transformations, respectively. Thus, accurate calculations of the nearly singular integrals can be achieved, irrespective of the shape of the integral element.

Numerical examples are presented to calculate the nearly singular integrals of different orders over both the linear integral element and the quadratic integral element. Comparative studies demonstrate that the proposed method significantly improves the accuracy of these calculations.

Buried pipelines under various soil embankment heights are cost-effective alternatives to transporting liquid products. This paper aims to assist pipeline architects and professionals in selecting the most cost-effective buried reinforced concrete pipelines under deep embankment soil with minor structural reinforcement while meeting shear stress requirements, safety and reliability constraints.

It is unfeasible to experimentally assess pipeline efficiency with high soil fill depth. Thus, to fill this gap, this research uses a dependable finite element analysis (FEA) to conduct a parametric study and carry out such an issue. This research considered reinforced concrete pipes with diameters of 25, 50, 75, 100, 125 and 150 cm at depths of 5, 10, 15 and 20 m.

According to this research, the proposed best pipeline diameter-to-thickness (D/T) proportions for soil embankment heights 5, 10, 15 and 20 m are 8.75, 4.8, 3.5 and 3.1, correspondingly. The cost-effective reinforced concrete (RC) pipeline thickness dramatically rises if the soil embankment reaches 20 m, indicating that the soil embankment depth highly influences it. Most of the analyzed reinforced concrete pipelines had a maximum deflection value of less than 1 cm, telling that the FEA accurately identified the pipeline width, needed flexural steel reinforcement, and concrete crack width while avoiding significant distortion.

The cost-effective thickness for the analyzed structured concrete pipes was calculated by considering the lowest required value of steel reinforcement. An algorithm was developed based on the parametric scientific findings to predict the ideal pipeline D/T ratio. A construction case study was also shown to assist architects and professionals in determining the best reinforced concrete pipeline geometry for a specific soil embankment height.

The purpose of this paper is to propose a new combined finite-discrete element method (FDEM) to analyze the mechanical properties, failure behavior and slope stability of soil rock mixtures (SRM), in which the rocks within the SRM model have shape randomness, size randomness and spatial distribution randomness.

Based on the modeling method of heterogeneous rocks, the SRM numerical model can be built and by adjusting the boundary between soil and rock, an SRM numerical model with any rock content can be obtained. The reliability and robustness of the new modeling method can be verified by uniaxial compression simulation. In addition, this paper investigates the effects of rock topology, rock content, slope height and slope inclination on the stability of SRM slopes.

Investigations of the influences of rock content, slope height and slope inclination of SRM slopes showed that the slope height had little effect on the failure mode. The influences of rock content and slope inclination on the slope failure mode were significant. With increasing rock content and slope dip angle, SRM slopes gradually transitioned from a single shear failure mode to a multi-shear fracture failure mode, and shear fractures showed irregular and bifurcated characteristics in which the cut-off values of rock content and slope inclination were 20% and 80°, respectively.

This paper proposed a new modeling method for SRMs based on FDEM, with rocks having random shapes, sizes and spatial distributions.

The purpose of this paper is to propose a compact model to represent the magnetic field outside the sources. This model provides the multipolar ordering of a spherical harmonic expansion far from the source while being valid in its close proximity.

The authors investigate equivalent surface sources that enable to compute the field very close to any chosen surface that encloses the source. Then the authors present a method to find an appropriate initial basis and its associated inner product that allow to construct multipolar harmonic bases for these equivalent sources, where any vector of order k produces a field that decreases at least as fast as the field produced by a multipole of order k. Finally, those bases are numerically implemented to demonstrate their performances, both far from the source and in its close proximity.

The charge distribution and normal dipole distribution are well-suited to construct multipolar harmonic bases of equivalent sources. These bases can be described by as few parameters as the decreasing spherical harmonic expansion. Comparison with other numerical models shows its ability to compute the field both far from the source and close to it.

A basis for normal dipole distribution has already been described in the literature. This paper presents a general method to construct a multipolar basis for equivalent sources and uses it to construct a basis for single-layer potential.

This paper aims to apply the novel numerical model to analyze the effect of pillar material on the response of compound quartz crystal resonator (QCR) with an array of pillars. The performance of the proposed device compared to conventional QCR method was also investigated.

A finite element method model was developed to analyze the behavior of QCR coupled with an array of pillars. The model was composed of an elastic pillar, a solution and a perfectly matched layer. The validation of the model was performed through a comparison between its predictions and previous experimental measurements. Notably, a good agreement was observed between the predicted results and the experimental data.

The effect of pillar Young’s modulus on the coupled QCR and pillars with a diameter of 20 µm, a center-to-center spacing of 40 µm and a density of 2,500 kg/m³ was investigated. The results indicate that multiple vibration modes can be obtained based on Young’s modulus. Notably, in the case of the QCR–pillar in air, the second vibration mode occurred at a critical Young’s modulus of 0.2 MPa, whereas the first mode was observed at 3.75 Mpa. The vibration phase analysis revealed phase-veering behavior at the critical Young’s modulus, which resulted in a sudden jump-and-drop frequency shift. In addition, the results show that the critical Young’s modulus is dependent on the surrounding environment of the pillar. For instance, the critical Young’s modulus for the first mode of the pillar is approximately 3.75 Mpa in air, whereas it increases to 6.5 Mpa in water.

It was concluded that the performance of coupled QCR–pillar devices significantly depends on the pillar material. Therefore, choosing pillar material at critical Young’s modulus can lead to the maximum frequency shift of coupled QCR–pillar devices. The model developed in this work helps the researchers design pillars to achieve maximum frequency shift in their measurements using coupled QCR–pillar.

The phase-field method of interfacial damage is used to simulate the damage in composite structures containing the brittle orthotropic materials and their interface.

In the brittle fracture modeling, the strain tensor is decomposed into positive and negative parts characterizing tension and compression behaviors. By requiring an elastic energy preserving transformation involving the elastic stiffness tensor, these two strain parts must satisfy the orthogonality condition in the sense that the elastic stiffness tensor responds as a metric. However, most of the recent phase-field methods for brittle fracture do not verify this orthogonality condition. Additionally, to describe the damage in structures with anisotropic phases, recent studies have used multiple phase-field variables, with each preferential orientation represented by a phase-field variable to describe the bulk damage of component materials. This approach increases the complexity of simulation procedure. These disadvantages motivate the present study aimed at enhancing the simulation method.

The present study improves the phase-field method of interfacial damage by (1) incorporating the strain orthogonality condition into the phase-field method; (2) using only one phase-field variable instead of multiple phase-field variables to simulate damage in component orthotropic phases; and (3) investigating the interaction between interfacial damage and bulk damage as well as the effect of orientation tensor of preferential orientation in each orthotropic phase and the interfacial parameters on crack branching in composite structures.

Through several simulation examples, the present simulation method is proven to be accurate, effective, and helps the simulation process simpler than previous relevant methods.

This paper aims to numerically examine the impact of gyrotactic microorganisms and radiation on heat transport features of magnetic nanoliquid within a closed cavity. Thermophoresis, chemical reaction and Brownian motion are also considered in flow geometry for the moment of nanoparticles.

Finite element method (FEM) was depleted to numerically approximate the temperature, momentum, concentration and microorganisms concentration of the nanoliquid. The present simulation was unsteady state, and the resulting transformed equations are simulated by FEM-based Mathematica algorithm.

It has been found that isotherm patterns get larger with increasing values of the magnetic field parameter. Additionally, numerical codes for rate of heat transport impedance inside the cavity with an increasing Brownian motion parameter values.

To the best of the authors’ knowledge, the research work carried out in this paper is new, and no part is copied from others’ works.

The purpose of this study is to present a novel extended hybrid analytical method (HAM) that leverages a two-dimensional (2-D) coupling between the semi-analytical Maxwell–Fourier analysis and the finite element method (FEM) in Cartesian coordinates.

The proposed model is applied to flat permanent-magnet linear electrical machines with rotor-dual. The magnetic field solution across the entire machine is established by coupling an exact analytical model (AM), designed for regions with relative magnetic permeability equal to unity, with a FEM in ferromagnetic regions. The coupling between AM and FEM occurs bidirectionally (x, y) along the edges separating teeth regions and their adjacent regions through applied boundary conditions.

The developed HAM yields accurate results concerning the magnetic flux density distribution, cogging force and induced voltage under various operating conditions, including magnetic or geometric parameters. A comparison with hybrid finite-difference and hybrid reluctance network methods demonstrates very satisfactory agreement with 2-D FEM.

The original contribution of this paper lies in establishing a direct coupling between the semi-analytical Maxwell–Fourier analysis and the FEM, particularly at the interface between adjacent regions with differing magnetic parameters.

This study aims to focuse on the flow behavior of a specific nanofluid composed of blood-based iron oxide nanoparticles, combined with motile gyrotactic microorganisms, in a ciliated channel with electroosmosis.

This study applies a powerful mathematical model to examine the combined impacts of bio convection and electrokinetic forces on nanofluid flow. The presence of cilia, which are described as wave-like motions on the channel walls, promotes fluid propulsion, which improves mixing and mass transport. The velocity and dispersion of nanoparticles and microbes are modified by the inclusion of electroosmosis, which is stimulated by an applied electric field. This adds a significant level of complexity.

To ascertain their impact on flow characteristics, important factors such as bio convection Rayleigh number, Grashoff number, Peclet number and Lewis number are varied. The results demonstrate that while the gyrotactic activity of microorganisms contributes to the stability and homogeneity of the nanofluid distribution, electroosmotic forces significantly enhance fluid mixing and nanoparticle dispersion. This thorough study clarifies how to take advantage of electroosmosis and bio convection in ciliated micro channels to optimize nanofluid-based biomedical applications, such as targeted drug administration and improved diagnostic processes.

First paper discussed “Numerical Computation of Cilia Transport of Prandtl Nanofluid (Blood-Fe₃O₄) Enhancing Convective Heat Transfer along Micro Organisms under Electroosmotic effects in Wavy Capillaries”.

This study aims to use regression Least-Square Support Vector Machine (LS-SVM) as a probabilistic model to determine the factor of safety (FS) and probability of failure (PF) of anisotropic soil slopes.

This research uses machine learning (ML) techniques to predict soil slope failure. Due to the lack of analytical solutions for measuring FS and PF, it is more convenient to use surrogate models like probabilistic modeling, which is suitable for performing repetitive calculations to compute the effect of uncertainty on the anisotropic soil slope stability. The study first uses the Limit Equilibrium Method (LEM) based on a probabilistic evaluation over the Latin Hypercube Sampling (LHS) technique for two anisotropic soil slope profiles to assess FS and PF. Then, using one of the supervised methods of ML named LS-SVM, the outcomes (FS and PF) were compared to evaluate the efficiency of the LS-SVM method in predicting the stability of such complex soil slope profiles.

This method increases the computational performance of low-probability analysis significantly. The compared results by FS-PF plots show that the proposed method is valuable for analyzing complex slopes under different probabilistic distributions. Accordingly, to obtain a precise estimate of slope stability, all layers must be included in the probabilistic modeling in the LS-SVM method.

Combining LS-SVM and LEM offers a unique and innovative approach to address the anisotropic behavior of soil slope stability analysis. The initiative part of this paper is to evaluate the stability of an anisotropic soil slope based on one ML method, the Least-Square Support Vector Machine (LS-SVM). The soil slope is defined as complex because there are uncertainties in the slope profile characteristics transformed to LS-SVM. Consequently, several input parameters are effective in finding FS and PF as output parameters.