International Journal for Numerical Methods in Engineering最新文献

Interval-based multi-objective robust optimization aims to achieve high-performance solutions insensitive to uncertainty, has garnered significant attention. However, efficiently analyzing the maximum fluctuations of solutions in both objective and constraint functions to assess their robustness remains challenging. To address this issue, this article proposes an adaptive coevolution method, which can evaluate the maximum fluctuations of multiple candidate solutions with respect to a function in a single run. This method is integrated with the multi-objective evolutionary algorithm (MOEA) to develop a framework termed adaptive coevolution-based multi-objective robust optimization (AC-MORO) for solving multi-objective robust optimization problems. To evaluate the performance of AC-MORO, it is compared with MODE-RO on a set of benchmark problems; meanwhile, a performance metric is proposed to test the accuracy of the adaptive coevolution method in analyzing the robustness of solutions. The impact of various parameter settings on the efficiency of the proposed method is also investigated. Subsequently, a variant of the adaptive coevolution method is explored to further enhance the performance of AC-MORO. Finally, AC-MORO is applied to address robust optimization problems in practical engineering.

The study of debris-fluid-structure interaction (DFSI) poses challenges for engineers and animators alike due to its complex nature involving multiple materials, multiple phases, constitutive nonlinearity, and large deformations across varying scales. Current numerical methods frequently overlook critical aspects of DFSI, can be overly complicated to implement, and require excessive computational resources for practical applications. To alleviate this problem, this paper introduces a flexible and explicit Material Point Method (MPM) that achieves a 100-fold improvement over traditional MPM formulations in terms of CPU-based computation. The key improvement results from the implementation of computer graphics techniques (MLS-MPM, APIC, ASFLIP, Simple F-Bar) and hardware (Multiple Graphics Processing Units). However, while computer graphics prioritizes qualitative realism, engineering needs quantitative accuracy. Therefore, this paper concentrates on a series of DFSI validation benchmarks using an enhanced graphics tool for engineering applications. Carefully chosen examples highlight critical aspects of DFSI. To show stability and favorability for next-generation scales, we simulate 100,000 to 1,000,000,000 particles within hours for all benchmarks. Accuracy relative to experiments, analytical equations, and alternative numerical models is demonstrated.

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.