International Journal for Numerical Methods in Engineering最新文献

Based on Matching Boundary Conditions (MBCs) for the linear wave equation and Helmholtz decomposition, we design MBCs to treat elastic wave propagation in a two-dimensional unbounded domain. MBCs are designed to effectively absorb waves traveling in specific directions. High-order MBCs are derived from the product of MBC operators. Reflection coefficients are calculated, rigorously proving that P- and S-waves have the same form of reflection coefficients as those for the wave equation, and no wave conversion occurs. The MBCs are implemented using a staggered grid, under finite difference semi-discretization and the velocity Verlet scheme for time integration. Numerical experiments are conducted to demonstrate the performance of the scheme.

Smoothed Particle Hydrodynamics (SPH) has emerged as a promising meshless computational method with applications in diverse fields. However, SPH faces significant challenges in computational efficiency and resolution adaptability. To address these limitations, this study introduces a novel SPH framework with anisotropic adaptive spatial resolution (AASR), which combines the strengths of anisotropic SPH (ASPH) and adaptive spatial resolution (ASR). The proposed method enables directionally anisotropic particle spacing for any single particle, along with gradual resolution transitions between neighboring particles, achieving grid-like refinement flexibility while preserving the Lagrangian nature of SPH. Several auxiliary SPH techniques, including free surface detection, particle shifting technique and the renormalized density gradient, are improved to match the AASR framework. The framework is further enhanced by coupling with the Finite Particle Method (FPM), which improves numerical stability and accuracy in non-uniform particle distributions. Numerical validations are conducted in five benchmark cases, including lid-driven shear cavity flow, Taylor–Green vortex, solitary wave propagation, standing wave dissipation, and wave–floating–breakwater interaction. Results demonstrate that the AASR technique can maintain resolution in any critical regions while coarsening elsewhere. While notably improving computational efficiency, the new method preserves satisfactory numerical accuracy, with about a first-order convergence rate in the benchmark. In addition, existing SPH enhancements or auxiliary techniques are compatible with the AASR framework after necessary modification. This work advances SPH applicability to large-scale and multi-resolution problems, establishing a meshless alternative with comparable resolution control to grid-based methods.

A numerical model has been developed to simulate shear horizontal (SH) waves and their interaction with various structural interfaces in concrete-like media. The model employs an arbitrary quadrilateral-element mesh, allowing flexibility in modelling internal heterogeneities. It also effectively accommodates intricate internal features, like defects, arbitrary thin cracks, reinforcement bars and drains in concrete structure. The spectral element method is utilized, offering significantly faster convergence rate and reduced computational time compared to the conventional finite element method. The model is compared with the conventional FEM method, commercially available software and validated through comparisons with experimentally obtained scattered field on a multiple concrete specimen. The results show strong agreement in terms of waveform shapes in both time and frequency domain, and arrival time. Therefore, the developed shear horizontal model has the potential to simulate large and complex domains, such as concrete members and joints, and may contribute to the evolving field of non-destructive evaluation of concrete.

In this work, we focus on the early design phase of cruise ship hulls, where the designers are tasked with ensuring the structural resilience of the ship against extreme waves while reducing steel usage and respecting safety and manufacturing constraints. At this stage, the geometry of the ship is already finalized, and the designer can choose the thickness of the primary structural elements, such as decks, bulkheads, and the shell. Reduced order modeling and black-box optimization techniques reduce the use of expensive finite element analysis (FEA) to only validate the most promising configurations, thanks to the efficient exploration of the domain of decision variables. However, the quality of the final results heavily relies on the problem formulation and on how the structural elements are assigned to the decision variables. A parameterization that does not capture well the stress configuration of the model prevents the optimization procedure from achieving the most efficient allocation of the steel. With the increased request for alternative fuels and engine technologies, the designers are often faced with unfamiliar structural behaviors and risk producing ill-suited parameterizations. To address this issue, we enhanced a structural optimization pipeline for cruise ships developed in collaboration with Fincantieri S.p.A. with a novel data-driven hierarchical reparameterization procedure, based on the optimization of a series of subproblems. Moreover, we implemented a multi-objective optimization module to provide the designers with insights into the efficient trade-offs between competing quantities of interest and enhanced the single-objective Bayesian optimization (BO) module. The new pipeline is tested on a simplified midship section and a full ship hull, comparing the automated reparameterization to a baseline model provided by the designers. The tests show that the iterative refinement outperforms the baseline on the more complex hull, proving that the pipeline streamlines the initial design phase and helps the designers tackle more innovative projects. The reparameterization procedure only relies on the evaluation of surrogate models and can be applied with minimal changes to other large-scale structural problems where yielding and buckling constitute the limiting factor to the design.

Material Point Method (MPM) demonstrates excellent capability in simulating large deformations by circumventing the mesh distortion issues inherent in the Finite Element Method (FEM). However, MPM suffers from cell-crossing error and volumetric locking when modeling large deformations of near-incompressible materials, such as rubbers and biological tissues. A unified exact quadrature based on the particle domain is introduced into the B-spline Material Point Method (uqBSMPM) to mitigate non-physical pressure oscillations caused by cell-crossing errors and volumetric locking in traditional MPM. The high-order continuity of B-spline basis functions enables the implementation of the proposed exact quadrature over the material particle's domain in a unified analytical form, free from singularities at the background grid nodes. Numerical results demonstrate that the computational accuracy of the proposed method is comparable to that of the explicit dynamic finite element method for the linear elastic small deformation problem. With the elimination of pressure oscillations, the large deformation of near-incompressible materials under shear and torsion has been accurately modeled, suggesting the uqBSMPM's ability to model practical soft material applications.

From characterizing the speed of a thermal system's response to computing natural modes of vibration, eigenvalue analysis is ubiquitous in engineering. In spite of this, eigenvalue problems have received relatively little treatment compared to standard forward and inverse problems in the physics-informed machine learning (PIML) literature. In particular, neural network discretizations of solutions to eigenvalue problems have seen only a handful of studies. Owing to their nonlinearity, neural network discretizations prevent the conversion of the continuous eigenvalue differential equation into a standard discrete eigenvalue problem. In this setting, eigenvalue analysis requires more specialized techniques. Using a neural network discretization of the eigenfunction, we show that a variational form of the eigenvalue problem called the “Rayleigh quotient,” in tandem with a Gram–Schmidt orthogonalization procedure, is a particularly simple and robust approach to find the eigenvalues and their corresponding eigenfunctions. This method is shown to be useful for finding sets of Laplacian eigenfunctions on irregular domains, parametric and nonlinear eigenproblems, and high-dimensional eigenanalysis. We also discuss the utility of eigenfunctions as a spectral basis for approximating solutions to partial differential equations. Through various examples from engineering mechanics, the combination of the Rayleigh quotient objective, Gram–Schmidt procedure, and the neural network discretization of the eigenfunction is shown to offer unique advantages for handling continuous eigenvalue problems.

This study formulates a differential integral quadrature method (DIQM) to analyze the free vibration characteristics of multi-directional functionally graded material (MFGM) viscoelastic porous plates. The kinematic relations are derived using a unified shear deformation plate theory, while material behavior is governed by the integer-order Kelvin-Voigt viscoelastic constitutive model. Power-law functions define the spatial gradation of material constituents along the length, width, and thickness directions. Two distinct porosity distributions are incorporated to characterize void and cavity variations through the plate's thickness. Hamilton's variational principle yields five coupled governing equations expressed as partial differential equations with variable coefficients. The differential quadrature method (DQM) discretizes these governing equations, with integral quadrature method (IQM) efficiently resolving the variable coefficients. This discretization results in an algebraic system constituting a quadratic eigenvalue problem. The eigenvalues' real and imaginary components provide the damping coefficients and natural frequencies, respectively. The proposed model and solution methodology are validated against established unified shear formulations, MFGM porous plates, and viscoelastic plate solutions available in literature. Comprehensive parametric studies systematically investigate the influence of material gradation indices, porosity parameters, boundary conditions, and viscoelastic coefficients on the natural vibration response of thick MFGM viscoelastic porous plates. The results demonstrate that an increase in either of the material gradation indices leads to a decrease in both of the real and imaginary parts of the fundamental frequencies.

In this study, the dominant process parameters in the air-jet continuous galvanizing line on coating thickness were estimated by computational fluid dynamics and machine learning approaches. First, 128 different cases consisting of different levels of process parameters were created with the Taguchi method. Then, numerical analyses were performed for each case, calculating the maximum pressure gradient and maximum shear stress values on the strip, which were then used in the analytical model developed based on one-dimensional lubrication theory to obtain coating thickness values. Lastly, artificial intelligence techniques based on different machine learning algorithms such as K-Nearest Neighbors, linear regression, random forest and Adaboost, the relative effects of the process parameters influencing the coating thickness were compared through the feature importance values. It was observed that the dominant process parameters differ in low and high jet pressure cases. Accordingly, in the case of low jet pressure, air jet pressure, nozzle slot opening and velocity of the steel strip stand out as the dominant parameters, while in the case of high jet pressure, the most effective parameters influencing the coating thickness are air jet pressure and nozzle slot opening. In addition to this, the effect of the distance between the nozzle and the zinc pot influencing the coating thickness can also be neglected in both low and high pressure cases. Moreover, it was also noticed that the effects of nozzle angle and the distance between the nozzle and the steel strip influencing the coating thickness increase with increasing jet pressure.