Computer Methods in Applied Mechanics and Engineering最新文献

{"title":"A multiscale design method using interpretable machine learning for phononic materials with closely interacting scales","authors":"Mary V. Bastawrous ,&nbsp;Zhi Chen ,&nbsp;Alexander C. Ogren ,&nbsp;Chiara Daraio ,&nbsp;Cynthia Rudin ,&nbsp;L. Catherine Brinson","doi":"10.1016/j.cma.2025.117833","DOIUrl":"10.1016/j.cma.2025.117833","url":null,"abstract":"<div><div>Manipulating the dispersive characteristics of vibrational waves is beneficial for many applications, e.g., high-precision instruments. architected hierarchical phononic materials have sparked promise tunability of elastodynamic waves and vibrations over multiple frequency ranges. In this article, hierarchical unit-cells are obtained, where features at each length scale result in a band gap within a targeted frequency range. Our novel approach, the “hierarchical unit-cell template method,” is an interpretable machine-learning approach that uncovers global unit-cell shape/topology patterns corresponding to predefined band-gap objectives. A scale-separation effect is observed where the coarse-scale band-gap objective is mostly unaffected by the fine-scale features despite the closeness of their length scales, thus enabling an efficient hierarchical algorithm. Moreover, the hierarchical patterns revealed are not predefined or self-similar hierarchies as common in current hierarchical phononic materials. Thus, our approach offers a flexible and efficient method for the exploration of new regions in the hierarchical design space, extracting minimal effective patterns for inverse design in applications targeting multiple frequency ranges.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"440 ","pages":"Article 117833"},"PeriodicalIF":6.9,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143672841","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Self-propelling, soft, and slender structures in fluids: Cosserat rods immersed in the velocity–vorticity formulation of the incompressible Navier–Stokes equations","authors":"Arman Tekinalp ,&nbsp;Yashraj Bhosale ,&nbsp;Songyuan Cui ,&nbsp;Fan Kiat Chan ,&nbsp;Mattia Gazzola","doi":"10.1016/j.cma.2025.117910","DOIUrl":"10.1016/j.cma.2025.117910","url":null,"abstract":"<div><div>We present a hybrid Eulerian–Lagrangian method for the direct simulation of three-dimensional, heterogeneous, active, and self-propelling structures made of soft fibers and operating in incompressible viscous flows. Fiber-based organization of matter is pervasive in nature and engineering, from biological architectures made of cilia, hair, muscles or bones to polymers, composite materials or soft robots. In nature, many such structures are adapted to manipulate flows for feeding, swimming or energy harvesting, through mechanisms that are often not fully understood. While simulations can support the analysis (and subsequent translational engineering) of these systems, extreme fibers’ aspect-ratios, large elastic deformations, two-way coupling with three-dimensional flows, and self-propulsion all render the problem numerically challenging. To address this, we couple Cosserat rod theory, where fibers’ dynamics is accurately captured in one-dimensional fashion, with the velocity–vorticity formulation of the Navier–Stokes equations, through a virtual boundary technique. The favorable properties of the resultant hydroelastic solver are demonstrated against a battery of benchmarks, and further showcased in a range of multi-physics scenarios, involving magnetic actuation, viscous streaming, biomechanics, multi-body interaction, and untethered swimming.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"440 ","pages":"Article 117910"},"PeriodicalIF":6.9,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143644321","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Harnessing dynamic turbulent dynamics in parrot optimization algorithm for complex high-dimensional engineering problems","authors":"Mahmoud Abdel-Salam ,&nbsp;Saleh Ali Alomari ,&nbsp;Jing Yang ,&nbsp;Sangkeum Lee ,&nbsp;Kashif Saleem ,&nbsp;Aseel Smerat ,&nbsp;Vaclav Snasel ,&nbsp;Laith Abualigah","doi":"10.1016/j.cma.2025.117908","DOIUrl":"10.1016/j.cma.2025.117908","url":null,"abstract":"<div><div>The Parrot Optimization Algorithm (PO) is a nature-inspired metaheuristic algorithm developed based on the social and adaptive behaviors of Pyrrhura molinae parrots. PO demonstrates robust optimization performance by balancing exploration and exploitation, mimicking foraging and cooperative activities. However, as the algorithm progresses through iterations, it faces critical challenges in maintaining search diversity and movement efficiency diminishes, leading to premature convergence and a reduced ability to find optimal solutions in complex search space. To address these limitations, this work introduces the Dynamic Turbulent-based Parrot Optimization Algorithm (DTPO), which represents a significant advancement over the original PO by incorporating three novel strategies: a novel Differential Mutation (DM), Dynamic Opposite Learning (DOL), and Turbulent Operator (TO). The DM Strategy enhances exploration by introducing controlled variations in the population, allowing DTPO to escape local optima. Also, the DOL Strategy dynamically generates opposite solutions to refresh stagnated populations, expanding the search space and maintaining adaptability. Finally, the TO strategy simulates chaotic movements inspired by turbulence, ensuring a thorough local search while preserving population diversity. Together, these strategies improve the algorithm's ability to explore, exploit, and converge efficiently. Furthermore, the DTPO's performance was rigorously evaluated on benchmark functions from CEC2017 and CEC2022, comparing it against 23 state-of-the-art algorithms. The results demonstrate DTPO's superior convergence speed, search efficiency, and optimization accuracy. Additionally, DTPO was tested on seven engineering design problems, achieving significant improvements over the original PO algorithm, with superior performance gains compared to other algorithms in real-world scenarios. Particularly, DTPO outperformed competing algorithms in 37 out of 41 benchmark functions, achieving an overall success rate of 90.24%. Moreover, DTPO obtained the best Friedman ranks across all comparisons, with values ranging from 3.03 to 1.18, demonstrating its superiority over classical, advanced, and recent algorithms. These results validate the proposed enhancements and highlight DTPO's robustness and effectiveness in solving complex optimization problems.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"440 ","pages":"Article 117908"},"PeriodicalIF":6.9,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143644323","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Spatiotemporal modeling based on manifold learning for collision dynamic prediction of thin-walled structures under oblique load","authors":"Jian Xie ,&nbsp;Junyuan Zhang ,&nbsp;Hao Zhou ,&nbsp;Zihang Li ,&nbsp;Zhongyu Li","doi":"10.1016/j.cma.2025.117926","DOIUrl":"10.1016/j.cma.2025.117926","url":null,"abstract":"<div><div>Numerical simulation of the collision dynamics in thin-walled structures under oblique load involves complex spatiotemporal processes, including material, geometric, and contact nonlinearities, which often require significant computational resources and time. Moreover, predicting high-dimensional spatiotemporal responses remains a challenge for most surrogate-based models. This paper proposes a deep learning framework based on manifold learning for spatiotemporal modeling of collision dynamics in thin-walled structures under oblique load. The framework leverages multiple deep learning models, including Variational Autoencoders (VAE), Radial Basis Function Interpolation (RBFI), and regression Residual Network (ResNet18), to capture the complex nonlinearities inherent in structural deformation, stress distribution, and crush force, enabling continuous prediction of multimodal spatiotemporal responses. Using a rectangular thin-walled tube under oblique load as an example, the models are validated with simulation data, yielding average prediction errors of 5.80 % for structural deformation, 6.01 % for Energy Absorption (EA), 10.66 % for Peak Crush Force (PCF), and 16.66 % for crush force. Compared to traditional finite element (FE) simulations, prediction time is reduced by 98.6 % for structural deformation and stress distribution, and 97.4 % for crush force. Additionally, the method demonstrates stability and broad applicability across different design parameters and structural configurations, including rectangular and double-cell tubes. This work underscores the potential of deep learning techniques to enhance computational efficiency and predictive accuracy in the crashworthiness design of thin-walled structures.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"440 ","pages":"Article 117926"},"PeriodicalIF":6.9,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143644320","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mutual-information-based dimensional learning: Objective algorithms for identification of relevant dimensionless quantities","authors":"Lei Zhang,&nbsp;Guowei He","doi":"10.1016/j.cma.2025.117922","DOIUrl":"10.1016/j.cma.2025.117922","url":null,"abstract":"<div><div>The classical dimensional analysis provides powerful insights into underlying physical mechanisms, but has limitations in determining the uniqueness and measuring the relative importance of dimensionless quantities. To address these limitations, we propose a data-driven approach, called mutual-information-based dimensional learning, to identify unique and relevant dimensionless quantities from available data. The proposed method employs a novel information-theoretic criterion to measure the relative importance of dimensionless quantities, whereas the existing methodologies rely on sensitivity/derivative-based measures. This entropy-based measure provides two significant advantages: (1) invariance (objectivity) with respect to reparametrizations of variables, and (2) robustness against outliers. Numerical results show that our method outperforms the current state-of-the-art method in these aspects, and enables identifying dominant dimensionless quantities. Examples include the study of the friction factor in benchmark pipe flows, the eddy viscosity coefficients in turbulent channel flows and the vapor depression dynamics in laser–metal interaction.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"440 ","pages":"Article 117922"},"PeriodicalIF":6.9,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143644319","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A novel energy-fitted hexagonal quadrature scheme enables low-cost and high-fidelity peridynamic computations","authors":"Emely Schaller ,&nbsp;Ali Javili ,&nbsp;Paul Steinmann","doi":"10.1016/j.cma.2025.117918","DOIUrl":"10.1016/j.cma.2025.117918","url":null,"abstract":"<div><div>In this contribution, we propose a novel hexagonal quadrature scheme for one-neighbor interactions in continuum-kinematics-inspired peridynamics equivalent to bond-based peridynamics. The hexagonal quadrature scheme is fitted to correctly integrate the stored energy density within the nonlocal finite-sized neighborhood of a continuum point subject to affine expansion. Our proposed hexagonal quadrature scheme is grid-independent by relying on appropriate interpolation of pertinent quantities from collocation to quadrature points. In this contribution, we discuss linear and quadratic interpolations and compare our novel hexagonal quadrature scheme to common grid-dependent quadrature schemes. For this, we consider both, tetragonal and hexagonal discretizations of the domain. The accuracy of the presented quadrature schemes is first evaluated and compared by computing the stored energy density of various prescribed affine deformations within the nonlocal neighborhood. Furthermore, we perform three different boundary value problems, where we measure the effective Poisson’s ratio resulting from each quadrature scheme and evaluate the deformation of a unit square under extension and beam bending. Key findings of our studies are: The Poisson’s test is a good indicator for the convergence behavior of quadrature schemes with respect to the grid density. The accuracy of quadrature schemes depends, as expected, on their ability to appropriately capture the deformation within the nonlocal neighborhood. Our novel hexagonal quadrature scheme, rendering the correct effective Poisson’s ratio of <span><math><mrow><mn>1</mn><mo>/</mo><mn>3</mn></mrow></math></span> for small deformations, together with quadratic interpolation consequently yields the most accurate results for the studies presented in this contribution, thereby effectively reducing the computational cost.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"440 ","pages":"Article 117918"},"PeriodicalIF":6.9,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143644324","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the mesh insensitivity of the edge-based smoothed finite element method for moving-domain problems","authors":"Tao He","doi":"10.1016/j.cma.2025.117917","DOIUrl":"10.1016/j.cma.2025.117917","url":null,"abstract":"<div><div>Although much less sensitive to mesh distortion, the edge-based smoothed finite element method (ESFEM) can become ineffective on severely distorted elements whose Jacobians are less than or equal to zero, especially in transient cases. In this work, we first prove that the ESFEM may be unable to get over severe mesh distortion occurring even in a very simple mesh of four four-node quadrilateral (Q4) elements. We then propose a slight modification that makes the ESFEM inherently applicable to negative-Jacobian Q4 elements without requiring any <em>ad hoc</em> stabilization. For the ESFEM, a smoothing cell (SC) attached to negative-Jacobian Q4 element is rebuilt on the midpoint of the shorter diagonal of the damaged element. Thus, the SC has a positive area that accounts correctly for inertial effects of transient problems. Such a treatment is compatible with the regular procedure for constructing an edge-based SC in normal Q4 elements. The mesh insensitivity of the ESFEM is highlighted by solving fluid–structure interaction on negative-Jacobian Q4 elements. Importantly, the present scheme can be generalized to other linear <span><math><mi>n</mi></math></span>-sided elements which are more likely to be badly distorted in complex moving-domain problems.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"440 ","pages":"Article 117917"},"PeriodicalIF":6.9,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143644322","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Deep learning-based surrogate capacity models and multi-objective fragility estimates for reinforced concrete frames","authors":"Lili Xing ,&nbsp;Paolo Gardoni ,&nbsp;Ge Song ,&nbsp;Ying Zhou","doi":"10.1016/j.cma.2025.117928","DOIUrl":"10.1016/j.cma.2025.117928","url":null,"abstract":"<div><div>This paper proposes surrogate capacity models for reinforced concrete frames (RCFs) using deep neural networks (DNNs) and Transformers to address the strong nonlinearity in structural deformation. After validating the finite element modeling method, an extensive stochastic finite element analysis is conducted to construct a comprehensive capacity database. The hyperparameters for the DNN architecture are initially determined, balancing accuracy with model complexity to finalize the surrogate capacity models. However, due to the strong nonlinearity in deformation-related surrogate models, lower accuracies are observed, which are further improved by applying a logarithmic transformation and the more advanced Transformer model. Despite these enhancements, the accuracy achieved by standard DNNs remains the most optimal, indicating their suitability for this task. Considering uncertainties in input features and neural network hyperparameters, fragility estimates for example RCFs are rapidly predicted using the surrogate capacity models. The fragility assessment indicates that the peak deformation is strongly influenced by structural nonlinearity among all output responses.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"440 ","pages":"Article 117928"},"PeriodicalIF":6.9,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143644325","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multi-Objective Loss Balancing for Physics-Informed Deep Learning","authors":"Rafael Bischof ,&nbsp;Michael A. Kraus","doi":"10.1016/j.cma.2025.117914","DOIUrl":"10.1016/j.cma.2025.117914","url":null,"abstract":"<div><div>Physics-Informed Neural Networks (PINN) are deep learning algorithms that leverage physical laws by including partial differential equations together with a respective set of boundary and initial conditions as penalty terms in their loss function. In this work, we observe the significant role of correctly weighting the combination of multiple competitive loss functions for training PINNs effectively. To this end, we implement and evaluate different methods aiming at balancing the contributions of multiple terms of the PINN’s loss function and their gradients. After reviewing three existing loss scaling approaches (Learning Rate Annealing, GradNorm and SoftAdapt), we propose a novel self-adaptive loss balancing scheme for PINNs named <em>ReLoBRaLo</em> (Relative Loss Balancing with Random Lookback). We extensively evaluate the performance of the aforementioned balancing schemes by solving both forward as well as inverse problems on three benchmark PDEs for PINNs: Burgers’ equation, Kirchhoff’s plate bending equation, Helmholtz’s equation and over 20 PDEs from the ”PINNacle” collection. The results show that ReLoBRaLo is able to consistently outperform the baseline of existing scaling methods in terms of accuracy while also inducing significantly less computational overhead for a variety of PDE classes.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"439 ","pages":"Article 117914"},"PeriodicalIF":6.9,"publicationDate":"2025-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143629206","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Projection-based model order reduction of embedded boundary models for CFD and nonlinear FSI","authors":"Noah B. Youkilis ,&nbsp;Charbel Farhat","doi":"10.1016/j.cma.2025.117920","DOIUrl":"10.1016/j.cma.2025.117920","url":null,"abstract":"<div><div>Embedded boundary methods (EBMs) for Computational Fluid Dynamics (CFD) and nonlinear fluid–structure interaction (FSI) – also known as immersed boundary methods, Cartesian methods, or fictitious domain methods – are the most robust methods for the solution of flow problems past obstacles that undergo large relative motions, significant deformations, large shape modifications, and/or surface topology changes. They can also introduce a high degree of automation in the task of grid generation and significant flexibility in the gridding of complex geometries. However, just like in the case of their counterpart body-fitted methods, their application to parametric flow computations at high Reynolds numbers remains today impractical in most engineering environments. For body-fitted CFD, the state of the art of projection-based model order reduction (PMOR) has significantly advanced during the last decade and demonstrated a remarkable success at reducing the dimensionality and wall-clock time of high Reynolds number models, while maintaining a desirable level of accuracy. For non-body-fitted CFD however, PMOR is still in its infancy, primarily because EBMs dynamically partition the computational fluid domain into real and ghost subdomains, which complicates the collection of solution snapshots and their compression into a reduced-order basis. In an attempt to fill this gap, this paper presents a robust computational framework for PMOR in the context of high Reynolds number flows and in the EBM setting of CFD/FSI (PMOR-EBM). The framework incorporates a hyperreduction approach based on the energy-conserving sampling and weighting (ECSW) method to accelerate the evaluation of the repeated projections arising in nonlinear implicit computations; and a piecewise-affine approach for constructing a nonlinear low-dimensional approximation of the solution to mitigate the Kolmogorov <span><math><mi>n</mi></math></span>-width barrier to the reducibility of transport models. The paper also assesses the performance of the proposed computational framework PMOR-EBM for two unsteady turbulent flow problems whose predictions necessitate or benefit from the application of an EBM; and two shape-parametric steady-state studies of the academic type but of relevance to design analysis and optimization.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"439 ","pages":"Article 117920"},"PeriodicalIF":6.9,"publicationDate":"2025-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143637432","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}