Search Results (128)

This paper presents a novel implementation of the Polynomial Point Interpolation Collocation Method (PPCM) for analyzing the coupled electrothermal and thermomechanical behavior of V-shaped microactuators. Within the PPCM framework, the governing equations for heat transfer and structural mechanics are discretized over the computational domain. The resulting discrete electrothermal system is solved in a fully coupled manner via an incremental load method to determine the temperature field. Subsequently, the displacement field is computed by solving the discrete mechanical equation, which incorporates terms from the natural boundary conditions. The MQ radial basis function behaves well in convergence when its parameters p_a and p_q are 1 and 1.8. Under a 6 V voltage, the difference between the PPCM and FEM temperature values is less than 1 °C. Meanwhile, the discrepancy between the PPCM and experimental temperature values is approximately 20 °C, corresponding to an approximate error of 10%. Furthermore, the displacement error between the PPCM and FEM is as low as approximately 2 μm under an applied voltage of 12 V. These results validate the PPCM for predicting the driving characteristics of V-shaped microactuators. Full article

Dam-break flows involve strong non-linearity and complex fluid–solid interactions, often causing severe flooding and structural damage. Particle-based CFD methods, such as the Moving Particle Semi-implicit (MPS) method, are effective in modeling such flows due to their mesh-free, Lagrangian nature. This study presents an improved MPS method with a novel friction model and enhanced fluid–solid interaction scheme to simulate dam-break-induced flows over fixed and mobile beds. The model is validated using experimental and analytical benchmarks, demonstrating improved accuracy and stability. Simulation results show that mobile beds significantly influence wave attenuation, energy dissipation, and sediment transport. In particular, step-down bed conditions promote sediment motion and modify wave behavior. These findings emphasize the importance of accounting for mobile seabed dynamics in numerical modeling of coastal and dam-break scenarios. The proposed MPS model offers a reliable and efficient tool for capturing key phenomena associated with fluid–solid interactions in naval and ocean engineering applications. Full article

We use deep Physics-Informed Neural Networks (PINNs) to simulate stratified forced convection in plane Couette flow. This process is critical for atmospheric boundary layers (ABLs) and oceanic thermoclines under global warming. The buoyancy-augmented energy equation is solved under two boundary conditions: Isolated-Flux (single-wall heating) and Flux–Flux (symmetric dual-wall heating). Stratification is parameterized by the Richardson number $(R_i\in [-1,1\left]\right),$ representing $\pm 2 °\mathrm{C}$ thermal perturbations. We employ a decoupled model (linear velocity profile) valid for low-Re, shear-dominated flow. Consequently, this approach does not capture the full coupled dynamics where buoyancy modifies the velocity field, limiting the results to the laminar regime. Novel contribution: This is the first deep PINN to robustly converge in stiff, buoyancy-coupled flows ($\mid R_i\mid \le 1$) using residual connections, adaptive collocation, and curriculum learning—overcoming standard PINN divergence (errors $>28\%$). The model is validated against analytical ($R_i=0$) and RK4 numerical ($R_i\ne 0$) solutions, achieving $L_2$ errors $\le 0.009\%$ and $L_{\mathrm{\infty }}$ errors $\le 0.023\%$. Results show that stable stratification $(R_i>0)$ suppresses convective transport, significantly reduces local Nusselt number ($Nu$) by up to $100\%$ (driving $Nu$ towards zero at both boundaries), and induces sign reversals and gradient inversions in thermally developing regions. Conversely, destabilizing buoyancy $(R_i<0)$ enhances vertical mixing, resulting in an asymmetric response: $Nu$ increases markedly (by up to $140\%$) at the lower wall but decreases at the upper wall compared to neutral forced convection. At $5–10\times$ lower computational cost than DNS or RK4, this mesh-free PINN framework offers a scalable and energy-efficient tool for subgrid-scale parameterization in general circulation models (GCMs), supporting SDG 13 (Climate Action). Full article

Electromagnetic wave propagation in complex environments demands accurate yet efficient modeling techniques. This study introduces a physics-informed neural network (PINN) framework for two-dimensional transient electromagnetic analysis, where Helmholtz equations are directly incorporated into the loss function. The model learns spatiotemporal field evolution without relying on spatial discretization or labeled data. Various excitation and material conditions are examined, including single and dual Gaussian sources in both free space and inhomogeneous regions with dielectric and conducting inclusions. Through this formulation, the network captures key wave phenomena such as propagation, reflection, and scattering with high precision. Validations against finite-difference time-domain (FDTD) simulations confirm strong agreement in both temporal and spatial field distributions. The results demonstrate that the proposed PINN provides an effective, mesh-free alternative for modeling electromagnetic wave dynamics, offering scalability for complex and data-sparse scenarios. Full article

Although physics-informed neural networks (PINNs) offer a novel, mesh-free paradigm for computational fluid dynamics (CFD), existing models often suffer from poor stability and insufficient accuracy, particularly when dealing with complex flows at high Reynolds numbers. To address this limitation, we propose, for the first time, a novel hybrid architecture, PINN-MRT, which integrates the multi-relaxation-time lattice Boltzmann method (MRT-LBM) with PINNs. The model embeds the MRT-LBM evolution equation as a physical constraint within the loss function and employs a unique dual-network architecture to separately predict macroscopic conserved variables and non-equilibrium distribution functions, enabling both forward and inverse problem-solving through a composite loss function. Benchmark tests on the lid-driven cavity flow demonstrate the superior performance of PINN-MRT. In inverse problems, it remains stable at Reynolds numbers up to 5000 with parameter inversion errors below 15%, whereas standard PINN and single-relaxation-time PINN-LBM models fail at a Reynolds number of 1000 with errors exceeding 80%. In purely physics-driven forward problems, PINN-MRT also provides stable solutions at a Reynolds number of 400, while the other models completely collapse. This study confirms that incorporating mesoscopic kinetic theory into PINNs effectively overcomes the stability bottlenecks of conventional approaches, providing a more robust and accurate architecture for CFD and paving the way for solving more challenging fluid dynamics problems. Full article

Nanostructures, such as carbon nanotubes (CNTs), graphene, nanoplates, etc., show behaviors that classical continuum theories cannot capture. At the nanoscale, size effects, surface stresses, and nonlocal interactions become important, so new models are needed to study nanostructures. The main nanomechanics theories that are used in recently published papers include nonlocal elasticity theory (NET), couple stress theory (CST), and nonlocal strain gradient theories (NSGTs). To solve these models, methods such as finite elements, isogeometric analysis, mesh-free approaches, molecular dynamics (MD), etc., are used. Also, this review categorizes and summarizes the major theories and numerical methods used in nanomechanics for the analysis of nanostructures in recently published papers. Recently, machine learning methods have enabled faster and more accurate prediction of nanoscale behaviors, offering efficient alternatives to traditional methods. Studying these theories, numerical models and data driven approaches provide an important foundation for future research and the design of next generation nanomaterials and devices. Full article

The piezoelectric coating structure constitutes the main configuration of contemporary energy harvesting systems, and its development requires accurate modeling of electromechanical coupling behavior under mechanical loads. The present work prepares a framework to analyze orthotropic piezoelectric coating–substrate systems; based on the fundamental solution theory, it derives two-dimensional Green functions from closed-form elementary functions. The formulation can establish the mesh-free solution paradigm through addressing tangential line force loading onto a coated surface. This method helps reconstruct full-field electromechanical responses upon arbitrary mechanical loading by integrating superposition principles and Gaussian quadrature technologies. An important application is in optimizing coating thickness, where parametric research suggests that piezoelectric layer geometry is non-linearly correlated with energy conversion efficiency. Notably, analytical sensitivity coefficients of this framework contribute to gradient-based optimization algorithms, which enhances efficiency compared with traditional empirical frameworks. Full article

Computation modeling for large thermoplastic deformation of plastic solids is critical for industrial applications like non-invasive assessment of engineering components. While deep learning-based methods have emerged as promising alternatives to traditional numerical simulations, they often suffer from systematic errors caused by geometric mismatches between predicted and ground truth meshes. To overcome this limitation, we propose a novel boundary geometry-constrained neural framework that establishes direct point-wise mappings between spatial coordinates and full-field physical quantities within the deformed domain. The key contributions of this work are as follows: (1) a two-stage strategy that separates geometric prediction from physics-field resolution by constructing direct, point-wise mappings between coordinates and physical quantities, inherently avoiding errors from mesh misalignment; (2) a boundary-condition-aware encoding mechanism that ensures physical consistency under complex loading conditions; and (3) a fully mesh-free approach that operates on point clouds without structured discretization. Experimental results demonstrate that our method achieves a 36–98% improvement in prediction accuracy over deep learning baselines, offering a efficient alternative for high-fidelity simulation of large thermoplastic deformations. Full article

This paper presents a computational framework for resolving a nonlinear extension of the Black–Scholes partial differential equation that accounts for transaction costs through a volatility function dependent on the Gamma of the option price. A meshfree radial basis function-generated finite difference procedure is developed using a modified multiquadric kernel. Analytical weight formulas for first- and second-order differentiations are discussed on 3-node stencils for both uniform and non-uniform point distributions. The proposed method offers an efficient scheme suitable for accurately pricing European scenarios when nonlinear transaction cost effects. Full article

This paper presents a semi-analytical, mesh-free space–time Collocation Trefftz Method (SCTM) for solving two-dimensional (2D) wave equations. Given prescribed initial and boundary data, collocation points are placed on the space–time (ST) boundary, reformulating the initial value problem as an equivalent boundary value problem and enabling accurate reconstruction of wave propagation in complex domains. The main contributions of this work are twofold: (i) a unified ST Trefftz basis that treats time as an analytic variable and enforces the wave equation in the full ST domain, thereby eliminating time marching and its associated truncation-error accumulation; and (ii) a Multiple-Scale Characteristic-Length (MSCL) grading strategy that systematically regularizes the collocation linear system. Several numerical examples, including benchmark tests, validate the method’s feasibility, effectiveness, and accuracy. For both forward and inverse problems, the solutions produced by the method closely match exact results, confirming its accuracy. Overall, the results reveal the method’s feasibility, accuracy, and stability across both forward and inverse problems and for varied geometries. Full article

A physics-informed neural network (PINN) framework is developed to model the large deformation and coupled electromechanical response of dielectric elastomer tubes for energy harvesting. The system integrates incompressible neo-Hookean elasticity with radial electric loading and compressible gas inflation, leading to nonlinear equilibrium equations with deformation-dependent boundary conditions. By embedding the governing equations and boundary conditions directly into its loss function, the PINN enables accurate, mesh-free solutions without requiring labeled data. It captures realistic pressure–volume interactions that are difficult to address analytically or through conventional numerical methods. The results show that internal volume increases by over 290% during inflation at higher reference pressures, with residual stretch after deflation reaching 9.6 times the undeformed volume. The axial force, initially tensile, becomes compressive at high voltages and pressures due to electromechanical loading and geometric constraints. Harvested energy increases strongly with pressure, while voltage contributes meaningfully only beyond a critical threshold. To ensure stable training across coupled stages, the network is optimized using the Optuna algorithm. Overall, the proposed framework offers a robust and flexible tool for predictive modeling and design of soft energy harvesters. Full article

We are especially interested in the general framework and ability of a semi-analytic method (SAM) to use the trigonometric basis function (TBF) in different domains. Moreover, the stabilizing effect of increasing boundary nodes on the convergence of the method when a level of noise is added to the boundary data of the inverse boundary value problem for the nonlinear Rayleigh–Stokes (R-S) equation is investigated. The solution of the ill-conditioned Rayleigh–Stokes equation which the equation is reduced to the linear system $\Im \left[\mathcal{C}\right]=♭$ with corrupted boundary data by quasilinearization technical on nonlinear source terms relies on TBFs and radial basis functions (RBFs). Finally, the implementation of the scheme is supported by the numerical experiments. Full article

Understanding the rheological properties of fresh cement slurries is essential to maintain optimal pumpability, achieve dependable zonal isolation, and preserve long-term well integrity in oil and gas cementing operations and the 3D printing cement and concrete industry. However, accurately and efficiently modeling the rheological behavior of cement slurries remains challenging due to the complex fluid properties of fresh cement slurries, which exhibit non-Newtonian and thixotropic behavior. Traditional numerical solvers typically require mesh generation and intensive computation, making them less practical for data-scarce, high-dimensional problems. In this study, a physics-informed neural network (PINN)-based framework is developed to solve the governing equations of steady-state cement slurry flow in a tilted channel. The slurry is modeled as a non-Newtonian fluid with viscosity dependent on both the shear rate and particle volume fraction. The PINN-based approach incorporates physical laws into the loss function, offering mesh-free solutions with strong generalization ability. The results show that PINNs accurately capture the trend of velocity and volume fraction profiles under varying material and flow parameters. Compared to conventional solvers, the PINN solution offers a more efficient and flexible alternative for modeling complex rheological behavior in data-limited scenarios. These findings demonstrate the potential of PINNs as a robust tool for cement slurry rheological modeling, particularly in scenarios where traditional solvers are impractical. Future work will focus on enhancing model precision through hybrid learning strategies that incorporate labeled data, potentially enabling real-time predictive modeling for field applications. Full article

A meshless, quasi-convex reproducing kernel particle framework for three-dimensional steady-state thermomechanical coupling problems is presented in this paper. A meshfree, second-order, quasi-convex reproducing kernel scheme is employed to approximate field variables for solving the linear Poisson equation and the elastic thermal stress equation in sequence. The quasi-convex reproducing kernel approximation proposed by Wang et al. to construct almost positive reproducing kernel shape functions with relaxed monomial reproducing conditions is applied to improve the positivity of the thermal matrixes in the final discreated equations. Two numerical examples are given to verify the effectiveness of the developed method. The numerical results show that the solutions obtained by the quasi-convex reproducing kernel particle method agree well with the analytical ones, with a slightly better-improved numerical accuracy than the element-free Galerkin method and the reproducing kernel particle method. The effects of different parameters, i.e., the scaling parameter, the penalty factor, and node distribution on computational accuracy and efficiency, are also investigated. Full article

Noise levels of anthropogenic origin in urban environments have reached thresholds that pose serious public health and quality of life problems. This paper/work aims to examine these noise levels, the underlying causes of their increase and possible solutions through the implementation of predictive models. To address this problem, as a first step, a simplified mathematical model capable of accurately predicting anthropogenic noise levels in a given area is developed. As variables, this model considers the crowd density, estimated using an Artificial Neural Network (ANN) capable of detecting people in images, as well as the geometric and architectural characteristics of the environment. To verify the model, several protocols have been developed for collecting experimental data. In a first phase, these experimental measurements were carried out in controlled environments, using loudspeakers as noise sources. In a second phase, these measurements were carried out in real environments, accounting for the specific noise sources present in each setting. The difference in sound levels between the model and reality is proven to be less than 3 dB in 75% and less than 3.5 dB in 100% of the cases examined in a controlled environment. In the real problem, in general terms and taking into account that the study is carried out on pedestrian streets, it seems that the model is able to reproduce most of the noise of anthropogenic origin. Full article