Search Results (170)

Time-fractional interface problems arise in systems where interacting materials exhibit memory effects or anomalous diffusion. These models provide a more realistic description of physical processes than classical formulations and appear in heat conduction, fluid flow, porous media diffusion, and electromagnetic wave propagation. However, the presence of complex interfaces and the nonlocal nature of fractional derivatives makes their numerical treatment challenging. This article presents a numerical scheme that combines radial basis functions (RBFs) with the finite difference method (FDM) to solve time-fractional partial differential equations involving interfaces. The proposed approach applies to both linear and nonlinear models with constant or variable coefficients. Spatial derivatives are approximated using RBFs, while the Caputo definition is employed for the time-fractional term. First-order time derivatives are discretized using the FDM. Linear systems are solved via Gaussian elimination, and for nonlinear problems, two linearization strategies, a quasi-Newton method and a splitting technique, are implemented to improve efficiency and accuracy. The method’s performance is assessed using maximum absolute and root mean square errors across various grid resolutions. Numerical experiments demonstrate that the scheme effectively resolves sharp gradients and discontinuities while maintaining stability. Overall, the results confirm the robustness, accuracy, and broad applicability of the proposed technique. Full article

Traditional electrical resistivity tomography (ERT) technology confronts bottlenecks such as the volume effect in the detection of termite nests in levees, while the ERT based on deep learning has insufficient interpretation accuracy due to small sample data. This study proposes an intelligent ERT diagnosis framework that integrates generative adversarial networks (GANs) with semantic segmentation models. The GAN-enhanced networks (GFU-Net and GFL-Net) are developed, incorporating a Squeeze-and-Excitation (SE) attention mechanism to suppress false anomalies. Additionally, a comprehensive loss function combining binary cross-entropy (BCE) and the Focal loss function is used to address the issue of sample imbalance. Using forward modeling based on the finite difference method (FDM), a termite nest hidden danger ERT dataset, which includes seven types of high-resistance anomaly configurations, is generated. Numerical simulations demonstrate that GFL-Net achieves a mean intersection-over-union (mIoU) of 97.68% and a spatial positioning error of less than 0.04 m. In field validation on a red clay embankment in Jiangxi Province, this method significantly improves the positioning accuracy of hidden termite nests compared to traditional least squares (LS) inversion. Excavation verification results show that the maximum error in the horizontal center and top burial depth of the termite nest identified by GFL-Net is less than 7% and 16%, respectively. The research findings provide reliable technical support for the accurate identification of termite nest hidden dangers in embankments. Full article

Bellows compensators are critical components in pipeline systems, designed to absorb thermal expansions, vibrations, and pressure reflections. Ensuring their operational reliability requires accurate prediction of the stress–strain state (SSS) and stability under internal pressure. This study presents a comprehensive mathematical model for analyzing corrugated bellows compensators, formulated as a boundary value problem for a system of partial differential equations (PDEs) within the Kirchhoff–Love shell theory framework. Two numerical approaches are developed and compared: a finite difference method (FDM) applied to a reduced axisymmetric formulation to ordinary differential equations (ODEs) and a finite element method (FEM) for the full variational formulation. The FDM scheme utilizes a second-order implicit symmetric approximation, ensuring stability and efficiency for axisymmetric geometries. The FEM model, implemented in Ansys 2020 R2, provides high fidelity for complex geometries and boundary conditions. Convergence analysis confirms second-order spatial accuracy for both methods. Numerical experiments determine critical pressures based on the von Mises yield criterion and linearized buckling analysis, revealing the influence of geometric parameters (wall thickness, number of convolutions) on failure mechanisms. The results demonstrate that local buckling can occur at lower pressures than that of global buckling for thin-walled bellows with multiple convolutions, which is critical for structural reliability assessment. The proposed combined approach (FDM for rapid preliminary design and FEM for final verification) offers a robust and efficient methodology for bellows design, enhancing reliability and reducing development time. The work highlights the importance of integrating rigorous PDE-based modeling with modern numerical techniques for solving complex engineering problems with a focus on structural integrity and long-term performance. Full article

The instability of bank slopes with uneven and soft geological layers under a heaped load will influence the safe and normal operation of ports. Therefore, this paper takes the bank slope in Xiaqinglong Port for slope stability evaluation and treatment measure effectiveness analysis. Firstly, the geological conditions, material composition and potential failure modes of the bank slope were determined through a field investigation and engineering geological analysis. Moreover, the slope stability was evaluated and calculated using the finite difference method (FDM) and the limit equilibrium method (LEM) with Bishop and Morgenstern–Price and a method considering pile resistance. Moreover, passing flow analysis (PFA) was applied to optimize the treatment measure design, and the treatment measures’ effectiveness was analyzed with simulation results. The results indicated that (1) the upper soft and lower hard strata are the main cause of the bank slope’s instability and deformation under heaped loads; (2) PFA can effectively calculate the maximum resistance of the pile and optimize the pile arrangement, with three rows with spacing of 2.3 m and a length of 22 m; (3) with piles, the stability of the bank slope improves from unstable to stable, along with an increase in the stability coefficient and a reduction in displacement, as well as a maximum shear strain increment and plastic zones. The study provides certain contributions to stability evaluation and treatment design optimization to prevent the potential instability and failure of similar bank slopes under the action of heaped loads. Full article

Using traditional methods to fabricate geometrically complicated items was challenging, but Additive Manufacturing (AM) has made it possible. Although AM (3D printing) was first developed to produce prototypes, in recent years it has also been utilized for the fabrication of end-use products. As a result, the mechanical strength of AMed parts has gained considerable significance. Three-dimensional printing has proved its capabilities in the fabrication of customizable parts with complex geometries. In the current study, the effects of manufacturing parameters on the mechanical strength and the fracture behavior of 3D-printed components have been investigated. To this aim, we fabricated specimens using Polyethylene Terephthalate Glycol (PETG) and the Fused Deposition Modeling (FDM) process. Particularly, the dumbbell-shaped and Single Edge Notched Bend (SENB) specimens were fabricated and examined to determine their tensile and fracture behaviors. Particularly, the notches in SENB specimens were introduced by two different techniques to investigate the influence of the manufacturing process on the mechanical performance of 3D-printed PETG parts. Moreover, finite element simulations were conducted to investigate the fracture behavior of the parts. The results indicate that the fracture loads of 3D-printed and milled parts are 599.1 N and 417.2 N, respectively. In addition, experiments confirm brittle fracture with no plastic deformation in all specimens with 3D-printed and milled notches. The outcomes of this study can be used for the future designs of FDM 3D-printed parts with a better structural performance. Full article

The fast and accurate calculation of the internal temperature rise in the oil-immersed transformer is the premise to realize the thermal health management and load energy evaluation of the in-service transformer. In view of the influence of nanofluids on the heat transfer process of transformer, a numerical simulation algorithm based on lattice Boltzmann method (LBM) and finite difference method (FDM) is proposed to study the heat and mass transfer process inside nano-modified oil-immersed transformer. Firstly, the D2Q9 lattice model is used to solve the fluid and thermal lattice Boltzmann equations inside the oil-immersed transformer at the mesoscopic scale, and the temperature field and velocity field are obtained by macroscopic transformation. Secondly, the electric field distribution inside the oil-immersed transformer is calculated by FDM. The viscous resistance in LBM analysis and the electric field force in FDM analysis, as well as the gravity and buoyancy of particles, are used to explore the motion characteristics of nanoparticles and metal particles. Finally, compared with the thermal ring method and the finite volume method (FVM), the relative error is less than 5%, which verifies the effectiveness of the numerical model and provides a method for studying the internal electrothermal convection of nano-modified oil-immersed transformers. Full article

Natural convection of liquid metals under magnetic fields is a phenomenon of interest in various industrial and scientific applications, including fusion reactor blankets and magnetohydrodynamic (MHD) power systems. While the application of a magnetic field generally suppresses convection and reduces the heat transfer rate, recent studies have reported cases where the Nusselt number increases under certain magnetic field conditions. In this study, we conduct numerical simulations of natural convection in an annular container filled with a liquid metal, subject to a circumferential static magnetic field. The governing equations, incorporating both temperature and electromagnetic fields, are solved using a high-order finite difference scheme. The results show that, within a specific range of parameters, the Nusselt number increases at moderate Hartmann numbers, even under low Rayleigh number conditions. Notably, this enhancement in heat transfer occurs alongside a reduction in kinetic energy, indicating that convective strength is not necessarily the dominant factor. Further analysis confirms that this phenomenon weakens and eventually vanishes as the Rayleigh number approaches 10⁶. These findings provide evidence that magnetic field-induced heat transfer enhancement can occur without a corresponding increase in convective motion, thereby challenging conventional assumptions in magnetoconvection theory. Full article

In this paper, we develop the explicit finite difference method (FDM) to solve an ill-posed Cauchy problem for the 3D acoustic wave equation in a time domain with the data on a part of the boundary given (continuation problem) in a cube. FDM is one of the numerical methods used to compute the solutions of hyperbolic partial differential equations (PDEs) by discretizing the given domain into a finite number of regions and a consequent reduction in given PDEs into a system of linear algebraic equations (SLAE). We present a theory, and through Matlab Version: 9.14.0.2286388 (R2023a), we find an efficient solution of a dense system of equations by implementing the numerical solution of this approach using several iterative techniques. We extend the formulation of the Jacobi, Gauss–Seidel, and successive over-relaxation (SOR) iterative methods in solving the linear system for computational efficiency and for the properties of the convergence of the proposed method. Numerical experiments are conducted, and we compare the analytical solution and numerical solution for different time phenomena. Full article

Hydrogen fuel cells are gaining attention as an eco-friendly propulsion system for ships, but the structural safety of storage tanks, which store hydrogen at high pressure and supply it to the fuel cell, is a critical concern. Marine liquid hydrogen storage tanks, typically designed as rotationally symmetric structures, face challenges when subjected to asymmetric wave-induced sloshing loads that break geometric symmetry and induce localized stress concentrations. This study conducted a fluid–structure interaction (FSI) analysis of a rotationally symmetric liquid hydrogen storage tank for marine applications to evaluate the impact of asymmetric liquid sloshing induced by wave loads on the tank structure and propose symmetry-guided structural improvement measures to ensure fatigue life. Sensitivity analysis using the finite difference method (FDM) revealed the asymmetric influences of design variables on stress distribution: increasing the thickness of triangular mounts (T1) reduced stress 3.57 times more effectively than circular ring thickness (T2), highlighting a critical symmetry-breaking feature in support geometry. This approach enables rapid and effective design modifications without complex optimization simulations. The study demonstrates that restoring structural symmetry through targeted reinforcement is essential to mitigate fatigue failure caused by asymmetric loading. Full article

Annealing of steel coils in bell-type furnaces is a critical process in steel production, requiring precise temperature control to ensure desired mechanical properties and microstructure. However, direct measurement of inner coil temperatures is impractical in industrial conditions, necessitating model-based estimation. This study presents a comparative analysis of physics-based and machine learning (ML) approaches for predicting internal temperatures during annealing. A finite difference method (FDM) was developed as a physics-based model and validated against experimental data from both laboratory and industrial annealing cycles. Furthermore, several ML models, including support vector regression (SVR), neural networks (NN), multivariate adaptive regression splines (MARS), k-nearest neighbors (k-NN), and random forests (RFs), were trained on surface temperature measurements to predict inner temperatures. The results demonstrate that the MARS, k-NN, and RF models achieved high prediction accuracy with performance index (PI) values below 1.0 on unseen data, demonstrating excellent generalization capabilities. In contrast, SVR with polynomial kernels and NN exhibited poor performance in specific configurations, highlighting their sensitivity to overfitting and data variability. The findings suggest that combining physics-based models with data-driven techniques offers a robust framework for soft-sensing in annealing operations, enabling improved process monitoring and control. Full article

A time-domain semi-empirical simulation model based on the wake oscillator approach is developed to investigate the coupled in-line (IL) and cross-flow (CF) vortex-induced vibration (VIV) of a flexible riser in uniform oscillatory flow. A novel nondimensionalization method is introduced by utilizing the dimensionless parameter $StKC$, which effectively replicates the fundamental lift frequency caused by the complex vortex motion around the riser. The structural responses of the riser are described using the Euler–Bernoulli beam theory, and the van der Pol equations are used to calculate the fluid forces acting on the riser, which can replicate the nonlinear vortex dynamics. The coupled equations are discretized in both time and space with a finite difference method (FDM), enabling iterative computations of the VIV responses of the riser. A total of six cases are examined with four different Keulegan–Carpenter ($KC$) numbers (i.e., $KC=31$, 56, 121, and 178) to investigate the VIV characteristics of small-scale and large-scale risers in uniform oscillatory flow. Key features such as intermittent VIV, amplitude modulation, and hysteresis, as well as the VIV development process, are analyzed in detail. The simulation results show good agreement with the experimental data, indicating that the proposed numerical model is able to reliably reproduce the riser VIV in uniform oscillatory flow. Overall, the VIV characteristics of the large-scale riser resemble those of the small-scale riser but exhibit higher vibration modes, stronger traveling wave features, and more complex energy transfer mechanisms. Full article

Hyperbolic interface problems frequently arise in a wide range of scientific and engineering applications, particularly in scenarios involving wave propagation or transport phenomena across media with discontinuous properties. These problems are characterized by abrupt changes in material coefficients or domain features, which pose significant challenges for numerical approximation. In this study, we propose an efficient and robust computational framework for solving one-dimensional hyperbolic interface problems with both single and double interfaces. The methodology combines the finite difference method (FDM) for time discretization with meshless radial basis functions (RBFs) for spatial approximation, enabling accurate resolution of interface discontinuities. This hybrid approach is adaptable to both linear and nonlinear models and is capable of handling constant as well as variable coefficients. Linear systems are solved using Gaussian elimination, while nonlinear systems are addressed through a quasi-Newton linearization method. To validate the performance of the proposed method, we compute the maximum absolute errors (MAEs) and root mean square errors (RMSEs) over various spatial and temporal discretizations. Numerical experiments demonstrate that the approach exhibits fast convergence, excellent accuracy, and ease of implementation, making it a practical tool for solving complex hyperbolic problems with interface conditions. Overall, the method provides a reliable and scalable solution for a class of problems where traditional numerical techniques often discontinuties. Full article

This study proposes an integrated framework that combines nonlinear stochastic vibration analysis with reliability assessment to address the safety issues of cable systems under damage conditions. First of all, a mathematical model of the damaged cable is established by introducing damage parameters, and its static configuration is determined. Using the Pearl River Huangpu Bridge as a case study, the accuracy of the analytical solution for the cable’s sag displacement is validated through the finite difference method (FDM). Furthermore, a quantitative relationship between the damage parameters and structural response under stochastic excitation is developed, and the nonlinear stochastic dynamic equations governing the in-plane and out-of-plane motions of the damaged cable are derived. Subsequently, a Gaussian Radial Basis Function Neural Network (GRBFNN) method is employed to solve for the steady-state probability density function of the system response, enabling a detailed analysis of how various damage parameters affect structural behavior. Finally, the First-Order and Second-Order Reliability Method (FORM/SORM) are used to compute the reliability index and failure probability, which are further validated using Monte Carlo simulation (MCS). Results show that the severity parameter η shows the highest sensitivity in influencing the failure probability among the damage parameters. For the system of the Pearl River Huangpu bridge, an increase in the damage extent δ from 0.1 to 0.4 can reduce the reliability-based service life of by approximately 40% under fixed values of the damage severity and location, and failure risk is highest when the damage is located at the midspan of the cable. This study provides a theoretical framework from the point of stochastic vibration for evaluating the response and associated reliability of mechanical systems; the results can be applied in practice with guidance for the engineering design and avoid potential damages of suspended cables. Full article

Material Extrusion (MEX) process is increasingly used to fabricate components for structural applications, driven by the availability of advanced materials and greater industrial adoption. In these contexts, understanding the mechanical performance of printed parts is crucial. However, conventional methods for assessing anisotropic elastic behavior often rely on expensive equipment and time-consuming procedures. The aim of this study is to evaluate the applicability of the impulse excitation of vibration (IEV) in characterizing the dynamic mechanical properties of a 3D-printed composite material. Tensile tests were also performed to compare quasi-static properties with the dynamic ones obtained through IEV. The tested material, Nylon 12CF, contains 35% short carbon fibers by weight and is commercially available from Stratasys. It is used in the fused deposition modeling (FDM) process, a Material Extrusion technology, and exhibits anisotropic mechanical properties. This is further reinforced by the filament deposition process, which affects the mechanical response of printed parts. Young’s modulus obtained in the direction perpendicular to the deposition plane (E₃₃), obtained via IEV, was 14.77% higher than the value in the technical datasheet. Comparing methods, the Young’s modulus obtained in the deposition plane, in an inclined direction of 45 degrees in relation to the deposition direction (E₄₅), showed a 22.95% difference between IEV and tensile tests, while Poisson’s ratio in the deposition plane (v₁₂) differed by 6.78%. This data is critical for designing parts subject to demanding service conditions, and the results obtained (orthotropic elastic properties) can be used in finite element simulation software. Ultimately, this work reinforces the potential of the IEV method as an accessible and consistent alternative for characterizing the anisotropic properties of components produced through additive manufacturing (AM). Full article

Building-integrated photovoltaic (BIPV) windows present a viable path towards carbon neutrality in the building sector. However, conventional BIPV windows, such as semi-transparent photovoltaic (STPV) glazings, still suffer from inadequate thermal insulation, which limits their effectiveness across different climate conditions. To address this issue, the cadmium telluride-based vacuum PV glazing has been developed to enhance the thermal performance of BIPV applications. To fully understand the complex thermal behaviour under real-world operational scenarios, this study introduces a one-dimensional transient heat transfer model that can efficiently capture the time-dependent thermal dynamics of this novel glazing system. Based on the numerical solutions using the explicit finite difference method (FDM), the temperature profile of the vacuum PV glazing can be obtained dynamically. Consequently, the heat gain of the semi-transparent vacuum PV glazing can be calculated under time-varying outdoor and indoor conditions. The validated heat transfer model was applied under four different scenarios, viz. summer daytime, summer nighttime, winter daytime, and winter nighttime, to provide a detailed analysis of the dynamic thermal behaviour, including the temperature variation and the energy flow. The dynamic thermal characteristics of the vacuum PV glazing calculated by the transient heat transfer model demonstrate its excellent thermal insulation and solar control capabilities. Moreover, the thermal performance of vacuum PV glazing was compared with a standard double-pane window under various weather conditions of a typical summer day and a typical winter day. The results indicate that the vacuum PV glazing can effectively minimise both heat gain and heat loss. The fluctuation of the inner surface temperature can be controlled within a limited range away from the set point of the indoor room temperature. Therefore, the vacuum PV glazing contributes to stabilising the temperature of the indoor environment despite the fluctuating solar radiation and periodic outdoor temperature. It is suggested that the vacuum PV glazing has the potential to enhance the climate adaptability of BIPV windows under different climate backgrounds. Full article