Computer Methods in Applied Mechanics and Engineering最新文献

英文中文

A clustering-based multiscale topology optimization framework for efficient design of porous composite structures

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-03-11 DOI: 10.1016/j.cma.2025.117881

Jinlong Liu , Zhiqiang Zou , Zeyang Li , Min Zhang , Jie Yang , Kang Gao , Zhangming Wu

The optimization design of the microstructures and their macro distribution in porous composite structures (PCS) offers significant potential for achieving both lightweight and functional performance. This paper proposes a novel optimization design framework for PCS with varying densities and multiple microstructures. Initially, components topology optimization (TO-Components) using ordered SIMP interpolation is applied to determine the type and density distribution of void, solid and porous materials. Following this, element stress state analysis calculates the stress-to-density ratio (s_e) for each porous material element. A two-level k-means++ clustering method, based on s_e and density, then replaces the widely used manual partitioning, enabling optimal subregion division for the specified number of microstructure types. This approach identifies representative unit cells (RUCs) for the subsequent topology optimization of RUCs (TO-RUCs). The TO-RUCs process designs the microstructures of each RUC using homogenization theory to minimize strain energy. Three benchmark numerical examples take only 1 to 2 min to complete the full-scale design. Additionally, the scalability of the design for both uniform and variable density PCS is explored. The comparison examples demonstrate that the proposed method reduces optimization time by an order of magnitude while maintaining consistent full-scale compliance, using the same material quantity, compared to existing methods. Finally, additive manufacturing and mechanical testing of the optimized structures confirm the performance benefits.

{"title":"A clustering-based multiscale topology optimization framework for efficient design of porous composite structures","authors":"Jinlong Liu , Zhiqiang Zou , Zeyang Li , Min Zhang , Jie Yang , Kang Gao , Zhangming Wu","doi":"10.1016/j.cma.2025.117881","DOIUrl":"10.1016/j.cma.2025.117881","url":null,"abstract":"<div><div>The optimization design of the microstructures and their macro distribution in porous composite structures (PCS) offers significant potential for achieving both lightweight and functional performance. This paper proposes a novel optimization design framework for PCS with varying densities and multiple microstructures. Initially, components topology optimization (TO-Components) using ordered SIMP interpolation is applied to determine the type and density distribution of void, solid and porous materials. Following this, element stress state analysis calculates the stress-to-density ratio (<strong>s<sub>e</sub></strong>) for each porous material element. A two-level k-means++ clustering method, based on <strong>s<sub>e</sub></strong> and density, then replaces the widely used manual partitioning, enabling optimal subregion division for the specified number of microstructure types. This approach identifies representative unit cells (RUCs) for the subsequent topology optimization of RUCs (TO-RUCs). The TO-RUCs process designs the microstructures of each RUC using homogenization theory to minimize strain energy. Three benchmark numerical examples take only 1 to 2 min to complete the full-scale design. Additionally, the scalability of the design for both uniform and variable density PCS is explored. The comparison examples demonstrate that the proposed method reduces optimization time by an order of magnitude while maintaining consistent full-scale compliance, using the same material quantity, compared to existing methods. Finally, additive manufacturing and mechanical testing of the optimized structures confirm the performance benefits.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"439 ","pages":"Article 117881"},"PeriodicalIF":6.9,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143593815","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}

引用次数: 0

Probabilistic learning from real-world observations of systems with unknown inputs for model-form UQ and digital twinning

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-03-11 DOI: 10.1016/j.cma.2025.117863

Zimi J. Zhang , Akmal Bakar , Adrian Humphry , Farhad Javid , Patrick Nadeau , Mehran Ebrahimi , Adrian Butscher , Alexander Tessier , Jesus Rodriguez , Charbel Farhat

In engineering systems, a digital twin serves as a digital replica encompassing both physical assets and their associated processes, such as manufacturing and certification. The implementation of digital twins offers substantial potential for various applications, including improved design, enhanced collaboration, effective energy management, risk mitigation, lifecycle management, and predictive maintenance. However, existing definitions of a “twin” are often ambiguous and lack a structured approach for developing digital twins, particularly for systems with unknown inputs. This paper addresses these shortcomings by proposing a clear definition and a robust methodology for building digital twins. Our methodology integrates projection-based model order reduction, a rapid approach for identifying unknown inputs, and a non-parametric probabilistic method for modeling and quantifying model-form uncertainty. Additionally, it incorporates a probabilistic learning approach for performing stochastic model updating. The effectiveness of this digital twinning methodology is illustrated through a case study involving an elevated truss footbridge located at the Autodesk Research facility at Pier 9 in San Francisco with unknown inputs. This case study underscores the importance of accurately modeling uncertainty to enhance the performance and reliability of digital twins in real-world engineering applications.

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引用次数: 0

Kolmogorov–Arnold PointNet: Deep learning for prediction of fluid fields on irregular geometries

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-03-11 DOI: 10.1016/j.cma.2025.117888

Ali Kashefi

Kolmogorov–Arnold Networks (KANs) have emerged as a promising alternative to traditional Multilayer Perceptrons (MLPs) in deep learning. KANs have already been integrated into various architectures, such as convolutional neural networks, graph neural networks, and transformers, and their potential has been assessed for predicting physical quantities. However, the combination of KANs with point-cloud-based neural networks (e.g., PointNet) for computational physics has not yet been explored. To address this, we present Kolmogorov–Arnold PointNet (KA-PointNet) as a novel supervised deep learning framework for the prediction of incompressible steady-state fluid flow fields in irregular domains, where the predicted fields are a function of the geometry of the domains. In KA-PointNet, we implement shared KANs in the segmentation branch of the PointNet architecture. We utilize Jacobi polynomials to construct shared KANs. As a benchmark test case, we consider incompressible laminar steady-state flow over a cylinder, where the geometry of its cross-section varies over the data set. We investigate the performance of Jacobi polynomials with different degrees as well as special cases of Jacobi polynomials such as Legendre polynomials, Chebyshev polynomials of the first and second kinds, and Gegenbauer polynomials, in terms of the computational cost of training and accuracy of prediction of the test set. Furthermore, we examine the robustness of KA-PointNet in the presence of noisy training data and missing points in the point clouds of the test set. Additionally, we compare the performance of PointNet with shared KANs (i.e., KA-PointNet) and PointNet with shared MLPs. It is observed that when the number of trainable parameters is approximately equal, PointNet with shared KANs (i.e., KA-PointNet) outperforms PointNet with shared MLPs. Moreover, KA-PointNet predicts the pressure and velocity distributions along the surface of cylinders more accurately, resulting in more precise computations of lift and drag.

{"title":"Kolmogorov–Arnold PointNet: Deep learning for prediction of fluid fields on irregular geometries","authors":"Ali Kashefi","doi":"10.1016/j.cma.2025.117888","DOIUrl":"10.1016/j.cma.2025.117888","url":null,"abstract":"<div><div>Kolmogorov–Arnold Networks (KANs) have emerged as a promising alternative to traditional Multilayer Perceptrons (MLPs) in deep learning. KANs have already been integrated into various architectures, such as convolutional neural networks, graph neural networks, and transformers, and their potential has been assessed for predicting physical quantities. However, the combination of KANs with point-cloud-based neural networks (e.g., PointNet) for computational physics has not yet been explored. To address this, we present Kolmogorov–Arnold PointNet (KA-PointNet) as a novel supervised deep learning framework for the prediction of incompressible steady-state fluid flow fields in irregular domains, where the predicted fields are a function of the geometry of the domains. In KA-PointNet, we implement shared KANs in the segmentation branch of the PointNet architecture. We utilize Jacobi polynomials to construct shared KANs. As a benchmark test case, we consider incompressible laminar steady-state flow over a cylinder, where the geometry of its cross-section varies over the data set. We investigate the performance of Jacobi polynomials with different degrees as well as special cases of Jacobi polynomials such as Legendre polynomials, Chebyshev polynomials of the first and second kinds, and Gegenbauer polynomials, in terms of the computational cost of training and accuracy of prediction of the test set. Furthermore, we examine the robustness of KA-PointNet in the presence of noisy training data and missing points in the point clouds of the test set. Additionally, we compare the performance of PointNet with shared KANs (i.e., KA-PointNet) and PointNet with shared MLPs. It is observed that when the number of trainable parameters is approximately equal, PointNet with shared KANs (i.e., KA-PointNet) outperforms PointNet with shared MLPs. Moreover, KA-PointNet predicts the pressure and velocity distributions along the surface of cylinders more accurately, resulting in more precise computations of lift and drag.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"439 ","pages":"Article 117888"},"PeriodicalIF":6.9,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143593814","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}

引用次数: 0

Path-following strategy with consistent Jacobian for periodic solutions in multi-DOF nonlinear dynamic systems

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-03-11 DOI: 10.1016/j.cma.2025.117896

Domenico Magisano , Giovanni Formica

We propose an enhanced pseudo-arclength path-following technique for recovering periodic solutions in high-dimensional nonlinear dynamic systems using the Poincaré map method. The key innovation is the direct computation of the Jacobian matrix within the time-marching algorithm used to obtain periodic orbits, including both the monodromy matrix and derivatives with respect to the continuation parameter. For smooth problems, the resulting Jacobian matrix is algorithmically exact: while the equations of motion are approximated using a user-selected time-integration scheme, the differentiation of the computed solution is performed exactly. This approach eliminates the need for numerical differentiation, significantly improving both the efficiency and robustness of the path-following process. Although the theoretical framework assumes differentiability, the method effectively handles piecewise smooth problems as well. Numerical tests demonstrate the superior performance of the proposed approach compared to traditional techniques that rely on numerical differentiation. To further validate its effectiveness and versatility, we present numerical examples involving the Finite Element discretization of three-dimensional problems, including shell structures.

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引用次数: 0

Self-stabilized virtual element modeling of 2D mixed-mode cohesive crack propagation in isotropic elastic solids

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-03-10 DOI: 10.1016/j.cma.2025.117880

Y. Chen , D. Sun , Q. Li , U. Perego

A comprehensive strategy for the simulation of mixed-mode cohesive crack propagation in a mesh of originally self-stabilized Virtual Elements (VEs) is proposed. Exploiting the VEs substantial insensitivity to mesh distortion, the propagating cohesive crack is accommodated within existing self-stabilized first-order quadrilateral VEs by simply adding new edges separated by a cohesive interface. The added edges make however the VE unstable and a new procedure for the stabilization of initially stable VE is developed. The method is formulated within a recently proposed Hu–Washizu variational framework, allowing for a higher order, independent modeling of stresses. In this way, a more accurate estimate of the stress at the tip of the cohesive process zone can be achieved allowing for a more accurate assessment of crack propagation conditions and direction. The proposed method is validated by application to several benchmark problems.

引用次数: 0

Similarity equivariant graph neural networks for homogenization of metamaterials

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-03-10 DOI: 10.1016/j.cma.2025.117867

Fleur Hendriks , Vlado Menkovski , Martin Doškář , Marc G.D. Geers , Ondřej Rokoš

Soft, porous mechanical metamaterials exhibit pattern transformations that may have important applications in soft robotics, sound reduction and biomedicine. To design these innovative materials, it is important to be able to simulate them accurately and quickly, in order to tune their mechanical properties. Since conventional simulations using the finite element method entail a high computational cost, in this article we aim to develop a machine learning-based approach that scales favorably to serve as a surrogate model. To ensure that the model is also able to handle various microstructures, including those not encountered during training, we include the microstructure as part of the network input. Therefore, we introduce a graph neural network that predicts global quantities (energy, stress, stiffness) as well as the pattern transformations that occur (the kinematics) in hyperelastic, two-dimensional, microporous materials. Predicting these pattern transformations means predicting the displacement field. To make our model as accurate and data-efficient as possible, various symmetries are incorporated into the model. The starting point is an

E (n)

-equivariant graph neural network (which respects translation, rotation and reflection) that has periodic boundary conditions (i.e., it is in-/equivariant with respect to the choice of RVE), is scale in-/equivariant, can simulate large deformations, and can predict scalars, vectors as well as second and fourth order tensors (specifically energy, stress and stiffness). The incorporation of scale equivariance makes the model equivariant with respect to the similarities group, of which the Euclidean group

E (n)

is a subgroup. We show that this network is more accurate and data-efficient than graph neural networks with fewer symmetries. To create an efficient graph representation of the finite element discretization, we use only the internal geometrical hole boundaries from the finite element mesh to achieve a better speed-up and scaling with the mesh size.

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引用次数: 0

Adaptive multi-patch isogeometric analysis for heat transfer in three-dimensional solid

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-03-09 DOI: 10.1016/j.cma.2025.117895

Lin Wang , Tiantang Yu , Sundararajan Natarajan , Weihua Fang , Zhiwei Zhou

This paper presents an adaptive multi-patch isogeometric framework for modeling heat conduction in isotropic/orthotropic media. The proposed adaptive scheme is a novel combination of local mesh refinement and adaptive time-stepping to improve the calculation efficiency and reduce meshing burden. The local adaptive refinement is driven by a recovery-based error estimator. Truncated hierarchical NURBS (TH-NURBS) are utilized for local adaptive mesh refinement due to their excellent properties, such as linear independence, partition-of-unity, and exact description of complex geometry. Multi-patch technique is applied to model complex structures, with Nitsche’s method as the coupling strategy. The computational accuracy of the proposed model is verified through several 3D numerical examples. The high efficiency of the adaptive scheme is demonstrated by comparing with uniform refinement method and fixed time-stepping method separately.

引用次数: 0

FCA method for predicting effective viscosity of particle reinforced thermoplastic melt and a metric for measuring clusters

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-03-09 DOI: 10.1016/j.cma.2025.117899

Zheng Li, Yinghao Nie, Gengdong Cheng

The effective viscosity of particle reinforced thermoplastic melt shows strongly anisotropic behavior and is also shear rate-dependent. The traditional homogenization method may face challenge due to extremely expensive computational cost, when the non-linear effective viscosities on all the directions of Particle Reinforced Thermoplastics (PRT) are demanded. This paper approaches this challenge with the FEM-Cluster based reduced order Analysis (FCA) method [1]. The governing equations are solved by minimizing a cluster-based dual formulation of the dissipating energy, where the cluster-wise Admissible Shear Stress (ASS) set is obtained by FCA together with a Spectrum Analysis Algorithm (SAA). In addition, considering the fact that there is a lack of effective method for determining the proper number of clusters, a cluster metric is developed, which relates the given number of clusters and the prediction accuracy of FCA method. This metric can be easily used in the offline stage to pre-estimate the applicability of the obtained clusters on the given loading conditions with a small amount of additional computation.

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引用次数: 0

Nonlinear dynamic substructuring in the frequency domain

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-03-09 DOI: 10.1016/j.cma.2025.117882

Hossein Soleimani, Niels Aage

In this paper, we introduce a nonlinear dynamic substructuring technique to efficiently evaluate nonlinear systems with localized nonlinearities in the frequency domain. A closed-form equation is derived from coupling the dynamics of substructures and nonlinear connections. The method requires the linear frequency response functions of the substructures, which can be calculated independently using reduced-order methods. Increasing the number of linear bases in the reduction method for substructures does not affect the number of nonlinear equations, unlike in component mode synthesis techniques. The performance of the method is evaluated through three case studies: a lumped parameter system with cubic nonlinearity, bars with a small gap (normal contact), and a plate with a couple of nonlinear energy sinks. The results demonstrate promising accuracy with significantly reduced computational cost.

引用次数: 0

On efficient simulation of self-assembling diblock copolymers using a peridynamic-enhanced Fourier spectral method

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-03-08 DOI: 10.1016/j.cma.2025.117878

Farshid Mossaiby , Gregor Häfner , Arman Shojaei , Alexander Hermann , Christian Cyron , Marcus Müller , Stewart Silling

This study introduces a computational framework for simulating the self-assembly of diblock copolymers using a novel peridynamic (PD)-enhanced Fourier spectral method (FSM). Diblock copolymers, composed of two distinct polymer blocks, are capable of forming nanostructured domains with applications in nanoelectronics, photonics, and advanced membranes. Current simulation techniques face challenges in capturing the multiscale dynamics of polymer systems and are often limited by computational inefficiencies. Our approach combines a phase-field model with FSM for spatial discretization and leverages a PD-based diffusion operator to overcome the stability restrictions of explicit time-stepping schemes. This integration allows for larger time steps, ensuring both stability and computational efficiency. The method’s scalability is enhanced through parallel implementation using C++ and OpenMP, optimized for multi-core CPUs. Validation through phase diagrams of copolymer melts and simulations of evaporation-induced self-assembly (EISA) processes demonstrates the capability of the proposed method to accurately capture large-scale, dynamic morphologies. Our approach provides a versatile framework and was found in certain examples to improve computational efficiency by more than a factor of 6 compared to forward-Euler FSM approach.

{"title":"On efficient simulation of self-assembling diblock copolymers using a peridynamic-enhanced Fourier spectral method","authors":"Farshid Mossaiby , Gregor Häfner , Arman Shojaei , Alexander Hermann , Christian Cyron , Marcus Müller , Stewart Silling","doi":"10.1016/j.cma.2025.117878","DOIUrl":"10.1016/j.cma.2025.117878","url":null,"abstract":"<div><div>This study introduces a computational framework for simulating the self-assembly of diblock copolymers using a novel peridynamic (PD)-enhanced Fourier spectral method (FSM). Diblock copolymers, composed of two distinct polymer blocks, are capable of forming nanostructured domains with applications in nanoelectronics, photonics, and advanced membranes. Current simulation techniques face challenges in capturing the multiscale dynamics of polymer systems and are often limited by computational inefficiencies. Our approach combines a phase-field model with FSM for spatial discretization and leverages a PD-based diffusion operator to overcome the stability restrictions of explicit time-stepping schemes. This integration allows for larger time steps, ensuring both stability and computational efficiency. The method’s scalability is enhanced through parallel implementation using C++ and OpenMP, optimized for multi-core CPUs. Validation through phase diagrams of copolymer melts and simulations of evaporation-induced self-assembly (EISA) processes demonstrates the capability of the proposed method to accurately capture large-scale, dynamic morphologies. Our approach provides a versatile framework and was found in certain examples to improve computational efficiency by more than a factor of 6 compared to forward-Euler FSM approach.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"439 ","pages":"Article 117878"},"PeriodicalIF":6.9,"publicationDate":"2025-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143580587","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}

引用次数: 0

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Computer Methods in Applied Mechanics and Engineering

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