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The paper deals with an application of the artificial immune system (AIS) and the particle swarm optimizer (PSO) to the optimization of composites with thin rigid fibers. The boundary value problem is solved using the boundary element method (BEM). The numerical examples demonstrate the optimization of the distribution and orientation of fibers in a composite. The objective functions depend on effective elastic properties. Two separate independent optimization methods are used to confirm the correctness of the obtained results (AIS and PSO). The bioinspired approach shows that the method based on the artificial immune system or particle swarm optimizer is an efficient technique for solving computer-aided optimal design problems (maximalization of the Young's modulus or Poisson's ratio) and allows for the development of new materials. [ABSTRACT FROM AUTHOR]

The novelty of this work is the development of a new fractional boundary element model based on the Caputo derivative to investigate anomalous thermal stress effects on cement-based materials. To obtain the BEM integral equations for the proposed formulation, we employ the weighted residuals technique, with the anisotropic fundamental solution serving as the weighting function in the anomalous heat governing equation. The Caputo fractional derivative was employed as an integrand for the domain integral of the proposed formulation. The time step selection is less dependent on the time derivative order. This allows the approach to overcome the non-locality of the fractional operators. The key benefit provided by the suggested formulation is the ability to analyze situations with tiny values of the fractional time derivative. The current BEM methodology proves that it is a useful tool for solving fractional calculus problems. [ABSTRACT FROM AUTHOR]

A numerical study was carried out to analyze the phenomenon of natural convection in a porous medium saturated with nanofluid. In the study, the boundary element method was used for computational modeling. The fluid flow through a porous matrix is described using the Darcy–Brinkman–Forchheimer momentum equation. In addition, a mathematical model for nanofluids was used, which follows a single-phase approach and assumes that the nanoparticles within a fluid can be treated as an independent fluid with effective properties. A combination of single- and sub-domain boundary element methods was used to solve the relevant set of partial differential equations. The method was originally developed for pure flow scenarios, but also proves to be effective in the context of fluid flow through porous media. The results are calculated for the case of two- and three-dimensional square cavities. In addition to various values of dimensionless control parameters, including the porous Rayleigh number (Rap), Darcy number (Da), porosity (ϕ) and nanoparticle volume fractions (φ), the effects of the inclination angle of the cavity on the overall heat transfer (expressed by the Nusselt number (Nu)) and fluid flow characteristics were investigated. The results indicate a pronounced dependence of the overall heat transfer on the introduction of nanoparticles and inclination angle. The heat transfer in a two-dimensional cavity is increased for higher values of Darcy number in the conduction flow regime, while it is suppressed for lower values of Darcy number in the Darcy flow regime. In the case of a three-dimensional cavity, increasing the volume fraction of nanoparticles leads to a decrease in heat transfer, and furthermore, increasing the inclination angle of the cavity considerably weakens the buoyancy flow. [ABSTRACT FROM AUTHOR]

As one of the main numerical methods, the boundary element method boasts the advantages of fast computation speed and high accuracy. Based on the considerations of the influence of pressure drop, perforation height, skin coefficient, reservoir coefficient, and reservoir radius on the seepage law, a novel three-dimensional seepage model for vertical wells was established using the Laplace transform method and Stehfest numerical inversion method. The model was utilized to examine the velocity of pressure propagation and drop amplitude, revealing that the near-well area experienced faster propagation and drop than the far-well area. During dimensional analysis, it was observed that neglecting the effects of formation pressure change could lead to a substantial increase in the dimensional error of bottom hole pressure, with a maximum error of 9.45% recorded in this study. Additionally, a sensitivity analysis was conducted on perforation length, wellbore reservoir coefficient, skin coefficient, and reservoir radius to further elucidate the seepage law of vertical wells. This study provides theoretical guidance for oil and gas production. The original contribution of this research lies in the incorporation of formation pressure changes into the three-dimensional seepage model of vertical wells for the first time, which significantly enhances the model's accuracy and practicality. [ABSTRACT FROM AUTHOR]

For problems with very fine surface meshes, typically the most time-consuming step of a boundary element method (BEM, also called a panel method) is solving the final linear system of equations. Many have already studied how to efficiently solve the dense, asymmetric systems which arise in elliptic BEMs. However, this has not been studied for a supersonic aerodynamic BEM, for which the governing PDE is hyperbolic. Due to this hyperbolic character, the matrix equation which arises from a supersonic BEM has a large number of identically zero elements. But the resulting linear system of equations is also not sparse in the standard sense. Hence, the efficient solution of the linear system of equations arising in a supersonic BEM is here considered. A novel sorting algorithm is developed whereby the non-zero elements may be arranged into a useful structure with minimal cost. A novel direct solution method is developed here based on fast Givens rotations and the QR decomposition. This novel solver leverages the unique matrix structure to solve the supersonic system of equations more quickly than traditional direct methods. This novel method is then compared to other direct and iterative matrix solvers and is shown to be more robust than iterative solvers and more efficient than other direct solvers, with a computational time complexity of approximately O (N 2.5) . [ABSTRACT FROM AUTHOR]

This paper investigates the forces generated by axially magnetized ring permanent magnets with trapezoidal cross-sections when placed near a soft magnetic cylinder. Utilizing the Hybrid Boundary Element Method (HBEM), this study models interactions in magnetic configurations, aiming to improve force calculation efficiency and accuracy compared to traditional finite element methods (FEMM 4.2 software program). The influence of the permanent magnet and the soft magnetic cylinder is approximated with a system of thin toroidal sources on the surfaces of the magnet and the cylinder, which significantly reduces the computation time for the force calculation. The approach is validated by comparing results with FEM solutions, revealing high precision with a much faster computation. Additionally, this study explores the influence of various parameters, including magnet size, separation distance, and magnetic permeability of the cylinder, on the magnetic force. The results demonstrate that the HBEM approach is effective for analyzing complex magnetic configurations, particularly in applications requiring efficient parametric studies. This approach can be adapted for other geometries, such as truncated cones or rectangular cross-section ring magnets. The findings contribute valuable insights into designing efficient magnetic systems and optimizing force calculations for varied magnet geometries and configurations, including the atypical ones. [ABSTRACT FROM AUTHOR]

Electroencephalographic (EEG) source localization is a fundamental tool for clinical diagnoses and brain-computer interfaces. We investigate the impact of model complexity on reconstruction accuracy by comparing the widely used three-layer boundary element method (BEM) as an inverse method against a five-layer BEM accelerated by the fast multipole method (BEM-FMM) and coupled with adaptive mesh refinement (AMR) as forward solver. Modern BEM-FMM with AMR can solve high-resolution multi-tissue models efficiently and accurately. We generated noiseless 256-channel EEG data from 15 subjects in the Connectome Young Adult dataset, using four anatomically relevant dipole positions, three conductivity sets, and two head segmentations; we mapped localization errors across the entire grey matter from 4000 dipole positions. The average location error among our four selected dipoles is ∼5 m m (±2 m m) with an orientation error of ∼ 12 ∘ (± 7 ∘ ). The average source localization error across the entire grey matter is ∼9 m m (±4 m m), with a tendency for smaller errors on the occipital lobe. Our findings indicate that while three-layer models are robust under noiseless conditions, substantial localization errors (10–20 m m) are common. Therefore, models of five or more layers may be needed for accurate source reconstruction in critical applications involving noisy EEG data. [ABSTRACT FROM AUTHOR]

This study investigated the possibility of quantum effects arising from defects resulting from the use of textronic electroconductive thin films and evaluated their impact on control characteristics. A hybrid model, where the classical approach to determine stationary fields based on the boundary element method was combined with a quantum mechanical approach using nonequilibrium Green's functions, was created. The results of conductance and transmission coefficient simulations for different types of defects in the studied structure and a wide range of temperatures assuming two different control modes are presented. Based on the results, the conditions for the occurrence of quantum effects on the surface of conducting paths containing defects were specified, and their impact on conductance in the quantum mechanical approach was estimated. [ABSTRACT FROM AUTHOR]

As surface wear is one of the major failure mechanisms in many applications that include polymer gears, lifetime prediction of polymer gears often requires time-consuming and expensive experimental testing. This study introduces a contact mechanics model for the surface wear prediction of polymer gears. The developed model, which is based on an iterative numerical procedure, employs a boundary element method (BEM) in conjunction with Archard's wear equation to predict wear depth on contacting tooth surfaces. The wear coefficients, necessary for the model development, have been determined experimentally for Polyoxymethylene (POM) and Polyvinylidene fluoride (PVDF) polymer gear samples by employing an abrasive wear model by the VDI 2736 guidelines for polymer gear design. To fully describe the complex changes in contact topography as the gears wear, the prediction model employs Winkler's surface formulation used for the computation of the contact pressure distribution and Weber's model for the computation of wear-induced changes in stiffness components as well as the alterations in the load-sharing factors with corresponding effects on the normal load distribution. The developed contact mechanics model has been validated through experimental testing of steel/polymer engagements after an arbitrary number of load cycles. Based on the comparison of the simulated and experimental results, it can be concluded that the developed model can be used to predict the surface wear of polymer gears, therefore reducing the need to perform experimental testing. One of the major benefits of the developed model is the possibility of assessing and visualizing the numerous contact parameters that simultaneously affect the wear behavior, which can be used to determine the wear patterns of contacting tooth surfaces after a certain number of load cycles, i.e., different lifetime stages of polymer gears. [ABSTRACT FROM AUTHOR]

A novel Boundary Element Method (BEM) is presented for predicting the hydrodynamic behavior of twin-hull vessels, traveling at low speeds, aiming to quantify the benefits of integrating solar technology onboard. In particular, the power requirements of an electric 33 m long twin-hull ship are examined. The study discusses the placement of solar panels on deck and assesses their utilization in terms of real-time energy generation, aiming to extend the autonomy range while also reducing carbon emissions. The discussed methodology predicts the power needs by considering various operational variables, design specifications and hydrodynamic principles. In addition, it addresses the viability and possible advantages of integrating solar technology onboard and provides preliminary estimates regarding the extent to which solar energy may compensate for power needs, based on several factors, including the velocity, the prevailing sea state and the incident solar irradiance. The results provide useful information regarding the utilization of solar energy in the shipping sector, in addition to advancing sustainable maritime propulsion. [ABSTRACT FROM AUTHOR]

The water exit problem, which is ubiquitous in ocean engineering, is a significant research topics in the interaction between navigators and water. The study of the water exit problem can help to improve the structural design of marine ships and underwater weapons, allowing for better strength and movement status. However, the water exit problem involves complex processes such as three-phase gas–liquid–solid coupling, cavitation, water separation, liquid surface deformation, and fragmentation, making it challenging to study. Following work carried out by many researchers on this issue, we summarize recent developments from three aspects: theoretical research, numerical simulation, and experimental results. In theoretical research, the improved von Karman model and linearized water exit model are introduced. Several classical experimental devices, data acquisition means, and cavitation approaches are introduced in the context of experimental development. Three numerical simulation methods, namely, the BEM (Boundary Element Method), VOF (Volume of Fluid), and FVM (Finite Volume Method) with LES (Large Eddy Simulation) are presented, and the respective limitations and shortcomings of these three aspects are analyzed. Finally, an outlook on future research improvements and developments of the water exit problem is provided. [ABSTRACT FROM AUTHOR]

The primary objective of this paper is to identify the critical components of the acoustic field for a piston-type pressure reducing valve (PRV) with a high pressure reduction ratio, as well as to predict unfavorable noise both experimentally and numerically. The numerical calculations were conducted using a hybrid approach that combines computational fluid dynamics (CFD) and computational aeroacoustics (CAA). Flow-induced pressure fluctuation from unsteady turbulent flow extracted by the throttling cone, the valve body and the baffle in the low-pressure chamber were considered as individual dipole acoustic sources during calculation of the internal acoustic field. The results indicated that the selected three dipole acoustic sources always played a vital role in the response of the acoustic field, and none of them could be ignored. In comparison, the throttling cone had the most salient contribution to acoustic field distribution, the valve body took second place, and the baffle had the least salient contribution. The radiated noise of interest was predicted using the indirect boundary element method (IBEM), incorporating all three components as dipole acoustic sources simultaneously; the numerical noise values showed strong validation against the experimental data. Furthermore, the distribution of sound pressure levels, as well as directional and planar field points, is also presented. This paper provides new insights into the role of each component in flow-induced noise, and offers technical support for noise reduction design and optimization of pressure reducing valves. [ABSTRACT FROM AUTHOR]

The study of the dynamic response characteristics of "W"-type deep canyon terrain to double-span concrete arch bridges under earthquake action holds great practical significance. In this research, a bridge in Sichuan Province is taken as the object of study. The boundary-integral equation method and peak frequency shift method are combined to apply an embedded linear time–history analysis algorithm to the finite element spatial dynamic calculation model of the entire bridge, resulting in an improved model. By comparing these two methods with model test results, the seismic response characteristics of the middle part of a "W" concrete arch bridge under different foundation depths and seismic intensities are examined. The boundary integral equation method was utilized to calculate ground motion response at any point on site, revealing a significant amplifying effect of increased seismic wave intensity on acceleration response at the top of the arch bridge. When input seismic wave intensity increased from 0.1 g to 0.3 g, maximum acceleration at buried depths of 3 m and 8 m in the middle of the arch bridge foundation increased by 102.63% and 79.16%, respectively, indicating that shallow buried depth structures are more sensitive to seismic wave intensity. Furthermore, using peak frequency shift rules for analyzing seismic wave propagation characteristics in "W"-type deep canyon topography confirms the sensitivity of shallow buried depth structures to seismic wave intensity and reveals the mechanism through which topography influences seismic wave propagation. This study provides a helpful method for understanding the propagation law and energy distribution characteristics of seismic waves in complex terrain. It was observed that the displacement at the top of the arch bridge increased significantly with an increase in seismic intensity. When subjected to 0.1 g, 0.2 g, and 0.3 g EI-Centro seismic waves, the maximum displacement at the top of the arch bridge model with a foundation buried depth of 3 m was 8 mm, 32 mm, and 142 mm, respectively. For arch bridge models with an 8-m foundation buried depth, these displacements were measured at 6.2 mm, 21 mm, and 68 mm, respectively. The results from model tests verified that increasing the depth of foundation burial effectively reduces the displacement at the top of the structure. Furthermore, by combining a boundary-integral equation method and peak-frequency shift method, this study accurately predicted significant influences on W-shaped double deep canyon topography from seismic response, and successfully captured stress concentration and seismic wave amplification/focusing effects on arch foot structures. The calculated results from both methods align well with model test data which confirm their effectiveness and complementarity when analyzing seismic responses under complex terrain conditions for bridge structures. [ABSTRACT FROM AUTHOR]

This paper investigates wrinkling dynamics of two-dimensional multicomponent vesicles subjected to time-dependent extensional flow. By employing a non-stiff, pseudo-spectral boundary integral approach, we inspect the wrinkling patterns that arise due to negative surface tension and differential bending within a two-phase system. We focus on the formation and evolution of the wrinkling behaviors under diverse phase concentrations, extensional rates, and vesicle sphericity. Our findings demonstrate that for slightly perturbed circular vesicles, the numerical simulations align well with perturbation theory. For elongated vesicles, the wrinkling patterns vary significantly between phases, primarily influenced by their respective bending moduli. In weak flows, buckling behaviors are observed for elongated vesicles, where the membrane bends inward in regions with lower bending modulus. [ABSTRACT FROM AUTHOR]

The paper is concerned with using boundary element methods (BEM) for the accurate evaluation of fields in structures with clusters. For large-scale problems, the BEM system is solved iteratively by speeding up matrix-to-vector multiplications by applying a kernel-independent fast multipole method. Multiplication starts with source-to-multipole (S2M) translations, whose accuracy predefines the overall accuracy. We aim to increase the accuracy of these translations. The intensities of sources are assembled into clusters by an algorithm suggested. Each of them is characterized by its representative source, whose intensity equals the sum of the intensities of cluster sources. Thus, with growing distance, its field tends toward the field of the cluster. The accuracy of S2M translations is increased by subtracting from and adding to the far field of the cluster the far field of its representative source, and by using the proposed modified kernel to evaluate the difference of the fields, which decreases faster than the field of the cluster itself. Numerical results for typical kernels show a notable increase in the accuracy provided by the modified S2M translations. Keeping in them merely the added field is acceptable for many practical applications. This simplifies the modified S2M translations by avoiding calculation and storing matrices specific to each of the clusters. The improved translations may be also used for multipole-to-multipole translations, performed on next, after leaves, levels in upward running a hierarchical tree. [ABSTRACT FROM AUTHOR]

Soil–structure interaction (SSI) leads to a modification in the dynamic properties of structure, but due to the complexity of analysis, it is traditionally assumed in seismic designs that the structure is fixed-supported on the ground, which brings about potential risks to the seismic performances of structure. The study works on the possibility of SSI having detrimental effects by comparing the dynamic responses of the SSI system to a fixed-base structure, and presents charts for an evaluation of the system frequency of SSI for the purpose of engineering practice. In order to reveal the physical nature, the SSI model is reduced to its simplest form, consisting of a SDOF oscillator, a three-dimensional rectangular foundation, and a multi-layered half-space. The energy dissipation in the soil is achieved by foundation impedances and the substructure method. Previously, the foundation impedances are usually acquired by two-dimensional or axisymmetric three-dimensional models in uniform half-space to avoid the high cost of the more realistic, fully 3D models, while a high-precision indirect boundary element method is employed, combined with the non-singular Green's functions of distributed loads to calculate the foundation impedances. Although SSI dampens the peak amplitude of structure response in the frequency domain, case studies on four buildings' responses to 42 earthquakes in the time history show a possibility of 15–20% that SSI amplifies the dynamic responses of structures, such as the maximum and the mean values in the time history, depending on the properties of the structures and the site, as well as the frequency component of incident waves. [ABSTRACT FROM AUTHOR]

This study introduces an innovative model-order reduction (MOR) technique that integrates boundary element and finite element methodologies, streamlining the analysis of wideband vibro-acoustic interactions within aquatic and aerial environments. The external acoustic phenomena are efficiently simulated via the boundary element method (BEM), while the finite element method (FEM) adeptly captures the dynamics of vibrating thin-walled structures. Furthermore, the integration of isogeometric analysis within the finite element/boundary element framework ensures geometric integrity and maintains high-order continuity for Kirchhoff–Love shell models, all without the intermediary step of meshing. Foundational to our reduced-order model is the application of the second-order Arnoldi method coupled with Taylor expansions, effectively eliminating the frequency dependence of system matrices. The proposed technique significantly enhances the computational efficiency of wideband vibro-acoustic coupling analyses, as demonstrated through numerical simulations. [ABSTRACT FROM AUTHOR]

When the time-dependent boundary element method, also termed the pseudo-initial condition method, is employed for solving transient heat conduction problems, the numerical evaluation of domain integrals is necessitated. Consequently, the accurate calculation of the domain integrals is of crucial importance for analyzing transient heat conduction. However, as the time step decreases progressively and approaches zero, the integrand of the domain integrals is close to singular, resulting in large errors when employing standard Gaussian quadrature directly. To solve the problem and further improve the calculation accuracy of the domain integrals, an (α, β) distance transformation is presented. Distance transformation is a simple and efficient method for eliminating near-singularity, typically applied to nearly singular integrals. Firstly, the (α, β) coordinate transformation is introduced. Then, a new distance transformation for the domain integrals is constructed by replacing the shortest distance with the time step. With the new method, the integrand of the domain integrals is substantially smoothed, and the singularity arising from small time steps in the domain integrals is effectively eliminated. Thus, more accurate results can be obtained by the (α, β) distance transformation. Different sizes of time steps, positions of source point, and shapes of integration elements are considered in numerical examples. Comparative studies of the numerical results for the domain integrals using various methods demonstrate that higher accuracy and efficiency are achieved by the proposed method. [ABSTRACT FROM AUTHOR]

This study focused on optimizing the power generation of a heaving point-absorber wave energy converter (HPA-WEC) by integrating submerged breakwaters. An optimization analysis was conducted based on a framework developed in the authors' previous work, aiming to maximize the capture width ratio (CWR) by inducing Bragg resonance. Numerical simulations were conducted using a two-dimensional frequency domain boundary element method (FD-BEM) under irregular wave conditions. Advanced particle swarm optimization (PSO) was used for the optimization, with design variables that included the power take-off (PTO) damping coefficient, spring constant, and position and shape of the submerged breakwaters. The results showed that the CWR almost doubled when two breakwaters were used compared with the case without breakwaters. The CWR significantly increased, even with only one breakwater installed behind the WEC. A coastal stability analysis showed that installing two breakwaters provided the best performance, reducing the transmitted wave energy by approximately 25%. Furthermore, the CWR reached its maximum when the distance between the breakwater endpoints equaled the wavelength of the peak wave frequency, indicating the occurrence of Bragg resonance. This study underscores the potential of submerged breakwaters in enhancing power generation and coastal stability in the design of HPA-WECs. [ABSTRACT FROM AUTHOR]

Considering the lack of studies on the transient vibro-acoustic properties of conical shell structures, a Jacobi–Ritz boundary element method for forced vibro-acoustic behaviors of structure is proposed based on the Newmark-β integral method and the Kirchhoff time domain boundary integral equation. Based on the idea of the differential element method and the first-order shear deformation theory (FSDT), the vibro-acoustic model of conical shells is established. The axial and circumferential displacement tolerance functions are expressed using Jacobi polynomials and the Fourier series. The time domain response of the forced vibration of conical shells is calculated based on the Rayleigh–Ritz method and Newmark-β integral method. On this basis, the time domain response of radiated noise is solved based on the Kirchhoff integral equation, and the acoustic radiation characteristics of conical shells from forced vibration are analyzed. Compared with the coupled FEM/BEM method, the numerical results demonstrate the high accuracy and great reliability of this method. Furthermore, the semi-vertex angle, load characteristics, and boundary conditions related to the vibro-acoustic response of conical shells are examined. [ABSTRACT FROM AUTHOR]

A high-speed advancing ship will cause significant squats in shallow water, which could increase the risk of grounding. To this end, a program based on the Rankine higher-order boundary element method (HOBEM) is developed to investigate a high-speed displacement ship with a transom stern moving in shallow water. The nonlinear free surface condition is satisfied by adopting an iterative algorithm on the real free surface. The transom condition is considered by implementing a modified transom condition. Computations of wave-making resistance, sinkage and trim in deep water are first performed, and satisfactory agreement is achieved by comparing with the experimental results; the simulations are then extended to the shallow water case. It indicates that the present method can provide a suitable balance of practicability and robustness, which can be considered as an efficient tool for the guidance in ship design stage. [ABSTRACT FROM AUTHOR]

This paper provides a new fractional boundary element method (BEM) solution for nonlinear nonlocal thermoelastic problems with anisotropic fibrous polymer nanoparticles. This comprehensive BEM solution comprises two solutions: the anisotropic fibrous polymer nanoparticles problem solution and the nonlinear nonlocal thermoelasticity problem. The nonlinear nonlocal thermoelasticity problem solution separates the displacement field into complimentary and specific components. The overall displacement is obtained using the boundary element methodology, which solves a Navier-type problem, and the specific displacement is derived using the local radial point interpolation method (LRPIM). The new modified shift-splitting (NMSS) technique, which minimizes memory and processing time requirements, was utilized to solve BEM-created linear systems. The performance of NMSS was evaluated. The numerical results show how fractional and graded parameters influence the thermal stresses of nonlinear nonlocal thermoelastic issues involving anisotropic fibrous polymer nanoparticles. The numerical findings further reveal that the BEM results correlate very well with the finite element method (FEM) and analytical results, demonstrating the validity and correctness of the proposed methodology. [ABSTRACT FROM AUTHOR]

In this paper, a multi-patch weakly singular isogeometric boundary element method (WSIGABEM) for two-dimensional elastostatics is proposed. Since the method is based on the weakly singular boundary integral equation, quadrature techniques, dedicated to the weakly singular and regular integrals, are applied in the method. A new formula for the generation of collocation points is suggested to take full advantage of the multi-patch technique. The generated collocation points are essentially inside the patches without any correction. If the boundary conditions are assumed to be continuous in every patch, no collocation point lies on the discontinuous boundaries, thus simplifying the implementation. The multi-patch WSIGABEM is verified by simple examples with analytical solutions. The features of the present multi-patch WSIGABEM are investigated by comparison with the traditional IGABEM. Furthermore, the combination of the present multi-patch WSIGABEM and the particle swarm optimization algorithm results in a shape optimization method in two-dimensional elastostatics. By changing some specific control points and their weights, the shape optimizations of the fillet corner, the spanner, and the arch bridge are verified to be effective. [ABSTRACT FROM AUTHOR]

Interactions between wave energy converters (WECs) can significantly affect the overall energy-harnessing performance of a wave park. Although large-size wave parks with many WEC units are commonly considered in practical applications, it is challenging to simulate such parks due to huge computational costs. This paper presents a numerical model that uses the boundary element method (BEM) to simulate wave parks. Each wave energy converter (WEC) was modelled as a comprehensive system, including WEC buoys, power take-off, and mooring systems, with hydrodynamic interactions included. Two classical layouts for arranging 16 units were simulated using this numerical model. The energy-harnessing performance of these array layouts was analyzed for both regular waves and a selection of irregular sea state conditions with different wave directions, wave heights, wave periods and water depths. For each layout, three WEC separation distances were studied. An increase of up to 16% in the power performance of the WEC under regular waves was observed, which highlights the importance of interaction effects. [ABSTRACT FROM AUTHOR]

During the hydraulic-fracturing process, stress interference occurs among multiple wells and fractures, potentially affecting the trajectory of hydraulic fracture propagation. Previous studies have largely overlooked the influence of proppant support stresses on the trajectories of fracture propagation. This paper establishes a mathematical model, grounded in the boundary element method, designed to compute the propagation of multiple fractures, considering both proppant support on the fracture surface and dynamic perturbations within the local stress field. The findings of this research reveal that the stress field induced by hydraulic fracturing exhibits dynamic evolution characteristics, necessitating a comprehensive study of the fracture initiation and extension across the entire fracturing time domain. The effect of the residual fracture width under proppant action on the in situ stress field cannot be ignored. During simultaneous fracturing, hydraulic fractures are inclined to propagate in the direction of the maximum horizontal principal stress, particularly as the in situ differential stress escalates. Staggered fracturing between wells has been proven to be more effective than head-to-head fracturing. Simply increasing the well spacing cannot solve the problem of inter-well fracture interference. In zipper fracturing, adjusting the fracturing sequence can inhibit the fracture intersections between wells, thereby controlling the trajectory of fracture propagation. The aforementioned research has considerable significance in guiding the control of fracture morphology during hydraulic-fracturing processes. [ABSTRACT FROM AUTHOR]

This paper proposes an improved method to calculate the mutual capacitance between interdigital transducer (IDT) electrodes to enhance the accuracy of the traditional coupling-of-modes (COM) model, which is commonly used to simulate surface acoustic wave (SAW) filters and duplexers. In this method, the boundary element method (BEM) is adopted to obtain the capacitance per unit length in a layered medium, while the partial capacitance (PC) method is used to derive the effective relative permittivity of the multi-layered IDT. Numerical results from commercially available software are provided for comparison with the results calculated using the proposed method. The consistent results verify the validity and accuracy of this method, which also demonstrates significantly faster calculation speed compared to commercially available software. Precise electrical response prediction of a dual-mode SAW (DMS) filter can be achieved by applying this method to the COM model, and this ultra-fast calculation method can also be included in filter design optimization. [ABSTRACT FROM AUTHOR]

This paper introduces an innovative approach to numerically model Structure–Soil-Structure Interaction (SSSI) by integrating the Boundary Element Method (BEM) and the Finite Element Method (FEM) in a coupled manner. To assess the accuracy of the proposed method, a comparative study is undertaken, comparing its outcomes with those generated by the conventional FEM technique. Alongside accuracy, the computational efficiency aspect is crucial for the analysis of large-scale SSSI problems. Hence, the computational performance of the coupled BEM–FEM method undergoes a thorough examination and is compared with that of the standalone FEM method. The results from these comparisons illustrate the superior capabilities of the proposed method in comparison to the FEM method. The novel approach provides more reliable results compared to traditional FEM methods, serving as a valuable tool for engineers and researchers involved in structural analysis and design. [ABSTRACT FROM AUTHOR]

This study determines the equivalent stress intensity factor (SIF) model that best fits the experimental behavior of low-carbon steel under mixed modes ( I and I I ). The study assessed Tanaka, Richard, and Pook's equivalent SIF models. The theoretical values used for comparison correspond to the experimental results in a modified C(T) geometry by machining a hole ahead of the crack tip subjected to fatigue loads with a load ratio of R = 0.1. The comparison involved the SIF for six experimental points and the values computed through the numerical simulation. The Paris, Klesnil, and Modified Forman–Newman crack growth models were used with each equivalent SIF to analyze the prediction in the estimated number of cycles. The Klesnil model showed the closest prediction since the error between the calculated and experimentally recorded number of cycles is the lowest. However, the material behavior reflects a reduced crack propagation rate attributed to plasticity in the crack tip. The results suggest that Asaro equivalent SIF conservatively estimates the element lifespan with increasing errors from 2.3% at the start of growth to 27% at the end of the calculation. This study sheds light on the accuracy and limitations of different equivalent SIF models, providing valuable insights for structural integrity assessments in engineering applications. [ABSTRACT FROM AUTHOR]

Acoustic emissions play a major role in the usability of many product categories. Therefore, mitigating the emitted sound directly at the source is paramount to improve usability and customer satisfaction. To reliably predict acoustic emissions, numerical methods such as the boundary element method (BEM) are employed, which allow for predicting, e.g., the acoustic emission into the free field. BEM algorithms need appropriate boundary conditions to couple the sound field with the structural motion of the vibrating body. In this contribution, firstly, an interpolation scheme is presented, which allows for appropriate interpolation of arbitrary velocity data to the computational grid of the BEM. Secondly, the free-field Helmholtz problem is solved with the open-source BEM software framework NiHu. The forward coupling between the device of interest and BEM is based on the surface normal velocities (i.e., a Neumann boundary condition). The BEM simulation results are validated using a previously established aeroacoustic benchmark problem. Furthermore, an application to a medical device (knee prosthesis frame) is presented. Furthermore, the radiated sound power is evaluated and contextualized with other low-cost approximations. Regarding the validation example, very good agreements are achieved between the measurements and BEM results, with a mean effective pressure level error of 0.63 dB averaged across three microphone positions. Applying the workflow to a knee prosthesis frame, the simulation is capable of predicting the acoustic radiation to four microphone positions with a mean effective pressure level error of 1.52 dB. [ABSTRACT FROM AUTHOR]

A digital twin is a virtual model of a real-world structure (such as a device or equipment) which supports various problems or operations that occur throughout the life cycle of the structure through linkage with the actual structure. Digital twins have limitations as a general simulation method because the characteristic changes (motion, stress, vibration, etc.) that occur in the actual structure must be acquired through installed sensors. Additionally, it takes a huge computing cost to output changes in the structure's characteristics in real time. In particular, in the case of ships and offshore structures, simulation requires a lot of time and resources due to the size of the analysis model and environmental conditions where the wave load acts irregularly, so the application of a different simulation methodology from existing ones is required. The order reduction method, which accurately represents the system's characteristics and expresses them in a smaller model, can significantly reduce analysis time and is an effective option. In this study, to analyze the applicability of the order reduction method to the development of digital twins for offshore structures, the structural responses of a multi-connected floating offshore structure were estimated by applying the order reduction method based on distortion base mode. The order reduction method based on the distortion base mode predicts the responses by constructing an order-reduced conversion matrix consisting of the selected distortion base mode, based on the mode vector's orthogonality and autocorrelation coefficients. The predicted structural responses with the reduced order model (ROM) were compared with numerical analysis results derived using the higher order boundary element method and finite element method with in-house code owned by the Korea Research Institute of Ship & Ocean Engineering and measured responses with a model test. When compared with the numerical analysis results, the structural responses were predicted with high accuracy in the wave direction and wave frequency band of the selected distortion base mode, but there are differences due to changed characteristics of the structure when compared with the results of the model test. In addition, differences were also seen in reduced order model evaluation with different sensor locations, and it was confirmed that the more similar the extracted distortion base modes of input sensor location set is to the distortion base modes of predicted location set, the higher accuracy is in predicting the structural responses. As a result, the performance of the reduced order model is determined by the distortion base mode selection method, the locations of the sensor, and the prediction for the structural response. [ABSTRACT FROM AUTHOR]

This study contributes to the understanding of the adhesive properties in normal contacts, providing valuable information on the influence of various factors on adhesive strength and energy dissipation. The adhesive normal contact between a steel spherical indenter and a soft sheet of elastomer is studied experimentally. The dependencies of contact strength and mechanical energy dissipation in the complete indentation–detachment cycle on the indentation depth, the velocity of the indenter, its radius, thickness, and elastic modulus of the elastomer, the specific work of adhesion, as well as the roughness of the indenter surface, were analyzed. Experimental results are compared with simulations using the boundary element method (BEM), and the reasons leading to discrepancies between experiments and simulations are analyzed. It is shown that over a wide range of experimental parameters, the rate of mechanical energy dissipation can be estimated with sufficient accuracy using a simple empirical relation. [ABSTRACT FROM AUTHOR]

The interaction of water waves with floating bodies can be modeled with linear potential flow theory and numerically solved with the boundary element method (BEM). This method requires the construction of dense matrices and the resolution of the corresponding linear systems. The cost of this method in terms of time and memory grows at least quadratically with the size of the mesh, and the resolution of large problems (such as large farms of wave energy converters) can, thus, be very costly. Approximating some blocks of the matrix with data-sparse matrices can limit this cost. While matrix compression with low-rank blocks has become a standard tool in the larger BEM community, the present paper provides its first application (to our knowledge) to linear potential flows. In this paper, we assess how efficiently low-rank blocks can approximate interaction matrices between distant meshes when using the Green function of linear potential flow. Due to the complexity of this Green function, a theoretical study is difficult, and numerical experiments are used to test the approximation method. Typical results on large arrays of floating bodies show that 99% of the accuracy can be reached with 10% of the coefficients of the matrix. [ABSTRACT FROM AUTHOR]

The quasi-static regime of friction between a rigid steel indenter and a soft elastomer with high adhesion is studied experimentally. An analysis of the formally calculated dependencies of a friction coefficient on an external load (normal force) shows that the friction coefficient monotonically decreases with an increase in the load, following a power law relationship. Over the entire range of contact loads, a friction mode is realized in which constant shear stresses are maintained in the tangential contact, which corresponds to the "adhesive" friction mode. In this mode, Amonton's law is inapplicable, and the friction coefficient loses its original meaning. Some classical works, which show the existence of a transition between "adhesive" and "normal" friction, were analyzed. It is shown that, in fact, there is no such transition. A computer simulation of the indentation process was carried out within the framework of the boundary element method, which confirmed the experimental results. [ABSTRACT FROM AUTHOR]

This research deals with precision calculations of stationary magnetic fields of volumetric bodies. The electrostatics analogy allows for the use of a scalar magnetic potential, which reformulates the original task as a boundary value problem for the Laplace equation. We approach this with the boundary element method, specifically in distance ranges close to the magnetized surface, where existing standard numerical methods are known to struggle. This work presents an approach based on the improved quadrature formulas for the simple layer potential and its normal derivative. Numerical tests confirm significant improvements in calculating the field at any distance from the surface of the magnet. [ABSTRACT FROM AUTHOR]

The streamlines of the energy flux (Poynting vectors) and chirality flux as well as the intensity of the electric field around various plasmonic nanostructures (nanocube, nanocuboid, nanotriangle, hexagonal nanoplate and bowtie nanoantenna) induced by a circularly polarized (CP) or linearly polarized (LP) light were studied theoretically. The boundary element method combined with the method of moment was used to solve a set of surface integral equations, based on the Stratton–Chu formulation, for analyzing the highly distorted electromagnetic (EM) field in the proximity of these nanostructures. We discovered that the winding behavior of these streamlines exhibits versatility for various modes of the surface plasmon resonance of different nanostructures. Recently, using plasmonic nanostructures to facilitate a photochemical reaction has gained significant attention, where the hot carriers (electrons) play important roles. Our findings reveal a connection between the flow pattern of energy flux and the morphology of the photochemical deposition around various plasmonic nanostructures irradiated by a CP light. For example, numerical results exhibit vertically helical streamlines of the Poynting vector around an Au nanocube and transversely twisted-roll streamlines around a nanocuboid. Additionally, the behaviors of the winding energy and chirality fluxes at the gap and corners of a plasmonic bowtie nanoantenna, implying a highly twisted EM field, depend on the polarization of the incident LP light. Our analysis of the streamlines of the Poynting vector and chirality flux offers an insight into the formation of plasmon-enhanced photocatalysis. [ABSTRACT FROM AUTHOR]

For the direct differentiation technique-based modeling of acoustic fluid–structure interaction and structural-acoustic sensitivity analysis, a coupling algorithm based on the finite element method (FEM) and the fast multipole boundary element method (FMBEM) is suggested. By bypassing the challenging volume parameterization process in isogeometric finite element techniques and the laborious meshing process in traditional FEM/BEM, non-uniform rational B-splines (NURBS) isogeometric analysis (IGA) is utilized to immediately perform numerical analysis on CAD models. The matrix-vector products in the boundary element analysis are accelerated using the fast multipole method (FMM). To hasten the solution of the linear system of equations, the iterative solver GMRES is used. The numerical prediction of the effects of arbitrarily shaped vibrating structures on the sound field is made feasible by the FEM/FMBEM technique. A number of numerical examples are provided to show the applicability and effectiveness of the suggested approach. [ABSTRACT FROM AUTHOR]

Aiming at the deficiencies of the traction helical gear transmission system when the EMU is running at high speed, this paper proposes and designs a kind of arc toothed cylindrical gear adapted to the traction of higher speed EMU. A parametric arc toothed cylindrical gear model was constructed using CREO, and its dynamic contact characteristics and acoustic response characteristics were analyzed under sustained operating conditions using the finite element boundary element method. The design of a tooth profile combined with the radius of the arc toothed line of the comprehensive trimming program put forward a virtual trimming prototype method through MATLAB and CREO reconstruction gear, and trimming before and after the gear transmission simulation experiments occurred for comparison and analysis. This study shows that the traction arc toothed cylindrical gear comprehensive modification method proposed in this study achieves better dynamic performance optimization, effectively reduces the contact stress and radiation noise of the gear transmission, and provides a theoretical basis for the development of a new generation of high-speed EMU stock traction drive systems. [ABSTRACT FROM AUTHOR]

The flight of a migratory bird-like flapping-wing aircraft is characterized by a low Reynolds number and unsteadiness. The selection of airfoil profiles is critical to designing an efficient flapping-wing aircraft. To choose the suitable airfoil for various wing sections, it is necessary to calculate the aerodynamic forces of the unsteady two-dimensional airfoil with a Reynolds number in the range of 105. While accurate, calculating this by solving the Navier–Stokes equations is impractical for early design stages due to its high consumption of computing resources and time. The computational demands for extending it to 3D aerodynamic calculations are even more prohibitive. In this paper, a relatively simple method is proposed. The two-dimensional unsteady panel method is utilized to derive the inviscid flow field, the unsteady integral boundary layer method is utilized to solve the boundary layer viscous flow, and the eN transition model is adopted to predict the position of the transition. These models are coupled with the semi-inverse interaction method to solve the aerodynamics of the unsteady low-Reynolds-number two-dimensional airfoil. The unsteady aerodynamics of the symmetric and cambered airfoils at different wing sections are calculated respectively by the proposed method. Mechanism analysis of the calculation results is conducted, and a symmetrical airfoil or a slightly cambered airfoil is recommended for the wing tip, a moderately cambered airfoil is suggested for the outer-wing section, and a highly cambered airfoil is suggested for the inner-wing section. [ABSTRACT FROM AUTHOR]

This paper describes, for the first time, the application of an Elastodynamic Boundary Element Method (BEM) in Laplace Domain for the Structural Health Monitoring (SHM) of poly-crystalline materials. The study focuses on Ultrasonic Guided Wave (UGW) propagation and investigates the wave–material interactions at micro-scale. The study aims to investigate the interaction of UGWs with assessing micro-structural features such as grain size, morphology, degradation, and flaws. Numerical simulations of the most common micro-structural features demonstrate the accuracy and validity of the proposed method. Particular attention is paid to the study of porosity and its influence on material macro-properties. Different crystal morphologies such as cubic, rhombic, and truncated octahedral are considered. The detection of voids based on the changes in the amplitude and Time of Arrival (ToA) of the backscattered signal is investigated. The study also considers inter-granular cracks, which cause laceration, and examines flaw position/orientation, length, and distance from a specific reference. Furthermore, a framework is proposed for generating Probability of Detection (PoD) curves using numerical simulations. Experimental tests in pristine conditions are shown to be in good agreement with the numerical simulations in terms of ToA, signal amplitude, and wave velocity. The numerical simulations provide insights into wave propagation and wave–material interactions, including different types of defects at the micro-scale. Overall, the BEM and UGW methods are shown to be effective tools for better understanding micro-structural features and their influence on the macro-structural properties of poly-crystalline materials. [ABSTRACT FROM AUTHOR]

Numerical investigation facilitates the development and exploitation phase of a coal mine, incorporating geological settings by forecasting the overall stability. This study proposes a generalized numerical simulation calibration approach to predict potential geotechnical hazards in an explored coal mine, focusing on the Khalashpir coal basin in Bangladesh. This research investigates the feasibility of initiating mining at the central block, which is associated with major faults by the finite element method (FEM), which is a valuable tool for understanding the variations of stress distribution in the rock mass. The study verifies the findings of the FEM by further assessing the seam convergence, vertical stress, and strain safety factor using the boundary element method (BEM), which involves numerical discretization in a reduced spatial dimension. The results illustrate that there will be significant displacements in the formation, which infer subsidence and increase vastly along the fault lines. This numerical investigation approach provides essential insights for future research concerning newly explored coal mines, particularly ones in the Gondwana basin. [ABSTRACT FROM AUTHOR]

Numerical modelling is an important instrument for rock engineering; it can assist in the design and prediction of failure in rock masses. Dependable results can be obtained from the models if, and only if, the underlying assumptions, strengths, and weaknesses of the model are known. A set of guidelines to implement a numerical modelling program can also be used to obtain high-quality and reliable results. The importance of a well-structured numerical modelling program to attain practically reasonable results cannot be overstated. This paper presents an analysis of the results of modelling a rock engineering problem involving deep mining excavations prone to high-stress challenges. The study used Lamodel and Examine 2D. The results obtained show that the two software programs can be used together to complement each other in attaining a deeper understanding of the influence of high stresses on mining excavations at depth. Lamodel and Examine 2D are both boundary element code-based software and are quick and easy to use. More advanced numerical modelling tools could be used, but these two were found to be suitable for the problem at hand. Many diagrams and results can be obtained from the numerical modelling of any rock engineering challenge; in this paper, only those diagrams and results deemed to be most relevant and appropriate to demonstrate the capabilities, limitations, and validity of the numerical modelling of the problem have been presented. [ABSTRACT FROM AUTHOR]

The attractiveness of the boundary element method—the reduction in the problem dimension by one—is lost when solving nonlinear solid mechanics problems. The point collocation method applied to strong-form differential equations is appealing because it is easy to implement. The method becomes inaccurate in the presence of traction boundary conditions, which are inevitable in solid mechanics. A judicious combination of the point collocation and the boundary integral formulation of Navier's equation allows a pure boundary element method to be obtained for the solution of nonlinear elasticity problems. The potential of the approach is investigated in some simple examples considering isotropic and anisotropic material models in the total Lagrangian framework. [ABSTRACT FROM AUTHOR]

Computing backscattering of harmonic acoustic waves from underwater elastic targets of arbitrary shape is a problem of considerable practical significance. The finite element method is commonly applied to the discretization of the target; on the other hand, the boundary element method naturally incorporates the radiation boundary condition at infinity. The coupled model tends to be expensive, primarily due to the need to manipulate large, dense, and complex matrices and to repeatedly solve systems of complex linear algebraic equations of significant size for each frequency of interest. In this article, we develop a model reduction transformation based on the notion of coherence applied to the surface pressures, which considerably reduces the size of the systems to be solved. We found that the proposed model reduction approach delivers acceptably accurate results at a fraction of the cost of the full model. A typical speedup of an order of magnitude was realized in our numerical experiments. Our approach enables backscattering computations with considerably larger models than have been feasible to date. [ABSTRACT FROM AUTHOR]

Pile raft foundation (PRF) is a common foundation type for buildings and bridge piers which has been commonly subjected to eccentric vertical load in engineering applications. Dissimilar PRF is often adopted to reduce the excessive settlement and differential settlement of superstructures. The behavior of dissimilar PRF under eccentric vertical load is a significant issue and investigated with the boundary element method in this paper. In this method, the dissimilar pile–soil system is decomposed into extended soil elements and fictitious pile elements. The second kind of Fredholm integral governing equation of the axial force of fictitious piles is established based on the compatibility condition of axial strain between the extended soil and fictitious piles. An iterative procedure is adopted to analyze the average settlement w and rotation slope θ of raft stemming from the settlement compatibility condition of the top of each element and the equilibrium condition of the raft. Furthermore, the axial force and settlement of each element along its depth can be predicted. The corresponding results agree well with a reported case and the finite element method. The characteristics of 3 × 1 and 3 × 3 dissimilar PRFs under eccentric vertical load, including non-dimensional vertical stiffness N0/wEsd, differential settlement wd and the load sharing ratio of typical elements Ni/N0, are systematically investigated by considering different eccentricity e, length/diameter ratios of pile l/d and pile–soil stiffness ratio Ep/Es conditions. The N0/wEsd increases with l/d, while the load sharing ratios of the raft Nraft/N0 and wd decreases with l/d. The eccentricity e has a significant effect on wd and Ni/N0 and a neglect effect on N0/wEsd and Nraft/N0. The N0/wEsd, wd and Ni/N0 are significantly increased with Ep/Es. This research is expected to provide insights to the practitioners into the dissimilar PRF design under eccentric vertical load. [ABSTRACT FROM AUTHOR]

Subwavelength gratings have received considerable attention in the fields of photonics, optoelectronics, and image sensing. This paper presents simple analytical expressions for the near-field intensity distribution of radiation scattered by these gratings. Our proposed methodology employs a 2D point dipole model and a specialized version of perturbation theory. By validating our models via numerical techniques including boundary and finite element methods, we demonstrate their effectiveness, even for narrow slits. [ABSTRACT FROM AUTHOR]

The study of ship waves is important for ship detection, coastal erosion and wave drag. This paper proposed a highly paralleled numerical computation method for efficiently simulating three-dimensional nonlinear kelvin waves. First, a numerical model for nonlinear ship waves is established based on potential flow theory, the Jacobian-free Newton–Krylov (JFNK) method and the boundary integral method. To reduce the amount of data stored in the JFNK method and improve the computational efficiency, a banded preconditioner method is then developed by formulating the optimal bandwidth selection rule. After that, a Graphics Process Unit (GPU)-based parallel computing framework is designed, and we used the Compute Unified Device Architecture (CUDA) language to develop a GPU solution. Finally, numerical simulations of 3D nonlinear ship waves under multiple scales are performed by using the GPU and CPU solvers. Simulation results show that the proposed GPU solver is more efficient than the CPU solver with the same accuracy. More than 66% GPU memory can be saved, and the computational speed can be accelerated up to 20 times. Hence, the computation time for Kelvin ship waves simulation can be significantly reduced by applying the GPU parallel numerical scheme, which lays a solid foundation for practical ocean engineering. [ABSTRACT FROM AUTHOR]

Crack problems in multilayered elastic media have attracted extensive attention for years due to their wide applications in both a theoretical analysis and practical industry. The boundary element method (BEM) is widely chosen among various numerical methods to solve the crack problems. Compared to other numerical methods, such as the phase field method (PFM) or the finite element method (FEM), the BEM ensures satisfying accuracy, broad applicability, and satisfactory efficiency. Therefore, this paper reviews the state-of-the-art progress in a boundary-element analysis of the crack problems in multilayered elastic media by concentrating on implementations of the two branches of the BEM: the displacement discontinuity method (DDM) and the direct method (DM). The review shows limitation of the DDM in applicability at first and subsequently reveals the inapplicability of the conventional DM for the crack problems. After that, the review outlines a pre-treatment that makes the DM applicable for the crack problems and presents a DM-based method that solves the crack problems more efficiently than the conventional DM but still more slowly than the DDM. Then, the review highlights a method that combines the DDM and the DM so that it shares both the efficiency of the DDM and broad applicability of the DM after the pre-treatment, making it a promising candidate for an analysis of the crack problems. In addition, the paper presents numerical examples to demonstrate an even faster approximation with the combined method for a thin layer, which is one of the challenges for hydraulic-fracturing simulation. Finally, the review concludes with a comprehensive summary and an outlook for future study. [ABSTRACT FROM AUTHOR]

We present a general approximate analytical solution for the normal contact of layered and functionally graded elastic materials for almost axisymmetric contact profiles. The solution only requires knowledge of the corresponding contact solution for indentation using a rigid cylindrical flat punch. It is based on the generalizations of Barber's maximum normal force principle and Fabrikant's approximation for the pressure distribution under an arbitrary flat punch in an inhomogeneous case. Executing an asymptotic procedure suggested recently for almost axisymmetric contacts of homogeneous elastic media results in a simple approximate solution to the inhomogeneous problem. The contact of elliptical paraboloids and indentation using a rigid pyramid with a square planform are considered in detail. For these problems, we compare our results to rigorous numerical solutions for a general (bonded or unbonded) single elastic layer based on the boundary element method. All comparisons show the quality and applicability of the suggested approximate solution. Based on our results, any compact axisymmetric or almost axisymmetric contact problem of layered or functionally graded elastic materials can be reduced asymptotically to the problem of indenting the material using a rigid cylindrical flat punch. The procedure can be used for different problems in tribology, e.g., within the framework of indentation testing or as a tool for the analysis of local features on a rough surface. [ABSTRACT FROM AUTHOR]

In railway systems, layered structures could be induced in wheel–rail contact interfaces due to several causes, such as head hardening, work hardening, plastic deformation, and mechanical or thermal excursion-induced phase transformation. This study proposes an explicit finite element (FE) method for investigating elastic layer effects in wheel–rail rolling contact. The proposed method is first validated by comparing its solution with that of Kalker's boundary element method (BEM) when the layer is not present, with a focus on the tractive rolling contact. To investigate general layer effects, the rail is assumed to consist of two layers, i.e., the top layer and the matrix material. The top layer is assumed to have different elastic moduli from the matrix material and then the top elastic layer effects on contact characteristics such as contact stress, contact patch, and subsurface stress are investigated. Different layer thicknesses are also considered. It is observed that a harder layer tends to introduce larger contact pressure and surface shear stress, but a smaller contact patch. A harder layer also produces larger subsurface stresses. A thicker layer may intensify these effects. The results suggest that in engineering applications, the analysis of wheel–rail rolling contact consequences such as wear and rolling contact fatigue (RCF) may need to consider the layered structures using appropriate methods. [ABSTRACT FROM AUTHOR]

This study aimed to examine the acoustic field radiated by propellers and underwater vehicles. For the verification of sound radiation in underwater vehicles, numerical methods are widely used in addition to experiments and propeller blade frequencies for calculation and validation. Numerical convergence and accuracy are more important for near-field and far-field problems. This paper uses the boundary element method (BEM) to assess the convergence of the finite volume method (FVM). In this study, the FVM, including the Reynolds-averaged Navier–Stokes method and the Ffowcs Williams–Hawkings (FW-H) acoustic model, is used to investigate the influence of various geometric inflows on the hydrodynamic and noise performance of the propeller. Then, the sound radiation of the FVM is compared with the BEM at the far field to determine the number of meshed elements. Furthermore, spectral analysis is being conducted to examine the noise generated by the underwater vehicle and propeller. The objective is to investigate the influence of the free surface on propeller efficiency. After verifying the numerical simulation, the results indicate that a relationship can be established between water pressure and propeller thrust under specific conditions. This relationship can be used to estimate the magnitude of propeller thrust at different water depths. The simulated results of propeller thrust, torque coefficient, propulsion efficiency, and sound radiation in this study are consistent with experimental values. This demonstrates the accuracy and practicality of the findings of numerical procedures in engineering applications. [ABSTRACT FROM AUTHOR]