Computer Methods in Applied Mechanics and Engineering最新文献_第2页

A data-driven modeling framework for nonlinear static aeroelasticity

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-03-14 DOI: 10.1016/j.cma.2025.117911

Trent White , Darren Hartl

Analyzing the multiphysical coupling between a deformable structural body and the forces imposed on that body from a surrounding fluid can be a challenging and computationally expensive task, especially when the structure, fluid, or both exhibit nonlinear behavior. Consequently, there exists a need for novel reduced-order static aeroelasticity analysis techniques that make efficient use of high-fidelity computational models, especially for preliminary design of next-generation aerostructures with high-aspect ratio lifting surfaces exhibiting large deformations or in situ geometric reconfigurations driven by nonlinear mechanisms. This work presents the compositional static aeroelastic analysis method: an embarrassingly parallelizable data-driven modeling technique that seeks to construct a system-level aeroelastic surrogate model representing the function composition of high-fidelity structural and fluid models in terms of shape parameters characterizing a reduced-order geometric description of the deformed fluid–structure interface. By formulating the static aeroelasticity problem as a fixed point problem, the proposed reduced-order modeling framework removes the need for a reduced-order representation of the traction field acting on the structure, unlike previous data-driven methods that independently train separate fluid and structural surrogate models. Additionally, by replacing the iterative exchange of full-order aeroelastic coupling variables with a statistical exploration of a reduced-order shape parameter space, the minimum computational time for approximating a static aeroelastic response is equivalent to one set of high-fidelity fluid and structural model evaluations. The following work presents the theoretical development of the proposed compositional method and demonstrates its use in two case studies, one of which involves a cantilevered baffle comprised of linear and nonlinear material with large deformations exceeding 35%. Numerical results show close agreement with a conventional partitioned analysis scheme, where tip displacement error is less than 1% in both material cases. It is also demonstrated how traction field information can be reused when considering structural modifications to circumvent the need for additional computationally expensive fluid model evaluations.

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引用次数: 0

Gradient flow based phase-field modeling using separable neural networks

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-03-14 DOI: 10.1016/j.cma.2025.117897

Revanth Mattey , Susanta Ghosh

Allen–Cahn equation is a reaction–diffusion equation and is widely used for modeling phase separation. Machine learning methods for solving the Allen–Cahn equation in its strong form suffer from inaccuracies in collocation techniques, errors in computing higher-order spatial derivatives, and the large system size required by the space–time approach. To overcome these challenges, we propose solving the

L^{2}

gradient flow of the Ginzburg–Landau free energy functional, which is equivalent to the Allen–Cahn equation, thereby avoiding the second-order spatial derivatives associated with the Allen–Cahn equation. A minimizing movement scheme is employed to solve the gradient flow problem, eliminating the complexities of a space–time approach. We utilize a separable neural network that efficiently represents the phase field through low-rank tensor decomposition. As we use the minimizing movement scheme to numerically solve the gradient flow problem, we thus, refer to the proposed method as the Separable Deep Minimizing Movement (SDMM) method. The evaluation of the functional in the minimizing movement scheme using the Gauss quadrature technique bypasses the inaccuracies associated with collocation techniques traditionally used to solve partial differential equations. A hyperbolic tangent transformation is introduced on the phase field prior to the evaluation of the functional to ensure that it remains strictly bounded within the values of the two phases. For this transformation, theoretical guarantee for energy stability of the minimizing movement scheme is established. Our results suggest that this transformation helps to improve the accuracy and efficiency significantly. The proposed method resolves the challenges faced by state-of-the-art machine learning techniques, outperforming them in both accuracy and efficiency. It is also the first machine learning method to achieve an order of magnitude speed improvement over the finite element method. In addition to its formulation and computational implementation, several case studies illustrate the applicability of the proposed method.¹

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引用次数: 0

Compatible finite element interpolated neural networks

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-03-13 DOI: 10.1016/j.cma.2025.117889

Santiago Badia , Wei Li , Alberto F. Martín

We extend the finite element interpolated neural network (FEINN) framework from partial differential equations (PDEs) with weak solutions in

H^{1}

to PDEs with weak solutions in

H (curl)

or

H (div)

. To this end, we consider interpolation trial spaces that satisfy the de Rham Hilbert subcomplex, providing stable and structure-preserving neural network discretisations for a wide variety of PDEs. This approach, coined compatible FEINNs, has been used to accurately approximate the

H (curl)

inner product. We numerically observe that the trained network outperforms finite element solutions by several orders of magnitude for smooth analytical solutions. Furthermore, to showcase the versatility of the method, we demonstrate that compatible FEINNs achieve high accuracy in solving surface PDEs such as the Darcy equation on a sphere. Additionally, the framework can integrate adaptive mesh refinements to effectively solve problems with localised features. We use an adaptive training strategy to train the network on a sequence of progressively adapted meshes. Finally, we compare compatible FEINNs with the adjoint neural network method for solving inverse problems. We consider a one-loop algorithm that trains the neural networks for unknowns and missing parameters using a loss function that includes PDE residual and data misfit terms. The algorithm is applied to identify space-varying physical parameters for the

H (curl)

model problem from partial, noisy, or boundary observations. We find that compatible FEINNs achieve accuracy and robustness comparable to, if not exceeding, the adjoint method in these scenarios.

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引用次数: 0

Output probability distribution estimation of stochastic static and dynamic systems using Laplace transform and maximum entropy

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-03-13 DOI: 10.1016/j.cma.2025.117887

Yang Zhang , Chao Dang , Jun Xu , Michael Beer

Effectively estimating output probability distributions in stochastic static and dynamic systems with a limited number of simulations is a significant challenge, especially for complex distributions with multi-modality and heavy tails. To address this challenge, this work explores the potential of the Laplace Transform (LT) and its inversion. First, the statistical information embedded in the derivatives of the LT is analysed, establishing the theoretical foundation for recovering output probability distributions. Subsequently, a novel analytical expression for the response probability density function (PDF) is derived by decomposing its inverse LT (ILT) using Euler’s formula. Building on the numerically estimated LT, a non-parametric numerical solution, termed the Numerical Decomposed ILT (NDILT) algorithm, is developed to flexibly estimate the main body of complex PDFs with limited samples. Second, the Taylor expansion of the real component of LT (RCLT) reveals its rich statistical content. Exploiting this property, another parametric method, the LT-based Maximum Entropy Method (LT-MEM), is proposed, incorporating estimated RCLT as constraints of the maximum entropy principle. By solving an optimization problem, LT-MEM can effectively reconstruct complex PDFs across their entire distribution domain using a small sample size. The proposed methods rediscover and harness the power of the LT and ILT to reconstruct complex-shaped probability distributions, offering a valuable alternative. Parameter selection strategies for NDILT and LT-MEM are provided, and their robust accuracy is validated through analytical and numerical examples across various challenging distributions.

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引用次数: 0

Multi-fidelity physics-informed machine learning framework for fatigue life prediction of additive manufactured materials

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-03-13 DOI: 10.1016/j.cma.2025.117924

Lanyi Wang , Shun-Peng Zhu , Borui Wu , Zijian Xu , Changqi Luo , Qingyuan Wang

The development direction of high reliability and longer serviceable life for major equipment requires accurate fatigue life predictions of additively manufactured (AM) components. However, small samples and high scatter of fatigue performance have become significant challenges in accurately modeling the fatigue failure behavior of AM components. To overcome the limitation of traditional fatigue life prediction models, a multi-fidelity physics-informed machine learning (PIML) framework is proposed. In this framework, the uncertainty quantification of fatigue performance and the fitting low-fidelity fatigue data with physical consistency are achieved through a physics-guided Wasserstein generative adversarial network with gradient penalty (WGAN-GP). The introduced concept of transfer learning allows training a physics-informed neural network (PiNN) using multi-fidelity fatigue data during the training process. Embedding the effect of manufacturing defects on fatigue performance as physical constraints can ensure the physical consistency of the overall multi-fidelity framework. Compared with traditional neural network (NN) and PiNN, the multi-fidelity framework has significant advantages in strong prediction performance, generalization ability and effectiveness. Moreover, the results of deep feature transfer demonstrate that the proposed multi-fidelity framework is expected to be a unified fatigue life prediction framework for AM materials.

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引用次数: 0

A coupled immersed boundary method and isogeometric shell analysis for fluid–structure interaction of flexible and lightweight shells in high-Reynolds number flows

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-03-12 DOI: 10.1016/j.cma.2025.117898

Keye Yan , Yue Wu , Qiming Zhu , Boo Cheong Khoo

This study presents an efficient numerical framework for simulating fluid–structure interactions (FSIs) involving flexible, lightweight shells subjected to high-Reynolds-number flows. By combining the immersed boundary method (IBM) and isogeometric analysis (IGA), the framework incorporates three major innovations: (1) a wall-modeling, direct-forcing, diffused-interface IBM tailored for FSI simulations with high-Reynolds-number turbulent flows, employing non-equilibrium explicit wall functions; (2) integration of the interface quasi-Newton inverse least-squares (IQN-ILS) method into the IBM/IGA framework to enhance the accuracy and efficiency of iterative Gauss–Seidel coupling in strongly coupled FSI scenarios; and (3) high-order solvers for both fluid and structural domains, featuring a sixth-order compact finite difference method (FDM) for fluid dynamics and isogeometric shell formulations for structural analysis. The framework is validated through four numerical test cases, including simulations of a hinged flag, an inverted flag, a membrane airfoil, and an air-supported membrane structure. The results demonstrate good agreement with reference data, showing the framework’s efficiency, accuracy, and applicability for solving large-scale shell-related FSI problems across diverse engineering and scientific domains.

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引用次数: 0

Locking and stabilization free Hybrid Virtual Elements for the coarse mesh analysis of elastic thick plates

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-03-12 DOI: 10.1016/j.cma.2025.117883

F. Liguori , A. Madeo , S. Marfia , G. Garcea , E. Sacco

This work presents a Virtual Element formulation (VE) for shear-deformable elastic plates. In particular, the Hybrid Virtual Element Method (HVEM) is adopted, which assumes a self-equilibrated stress interpolation and an energy-based projection, eliminating the need for stabilization terms. This choice, together with a cubic linked interpolation for displacement and rotations, makes the approach free from locking, even for very thin plates and highly distorted element geometries. These features enable the proposed VE to achieve high accuracy even for coarse meshes, yielding low errors when compared to analytical solutions and providing a smooth reconstruction of all the stress field components. Furthermore, low error in both the displacement and stress fields are obtained in the challenging case of single element polygonal discretization. The same performance are guaranteed in presence of bulk loads, thanks to a consistent treatment within the projection operation that a-priori assumes equilibrium for the stress field interpolation.

A random-based benchmark is proposed for assessing numerically the absence of spurious modes in concave and convex distorted elements. The proposed HVEM for plate is validated in classical benchmark problems, demonstrating the superior accuracy of polygonal meshes compared to the quadrilateral ones, for an equivalent number of degrees of freedom. This result is relevant in all the applications where polygonal element shapes are necessary. In addition, it opens up the way to new modeling scenarios where polygonal meshes are preferred not only for their versatility but also for their enhanced accuracy.

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引用次数: 0

An analytical exact, locking free element formulation for thin-walled composite Timoshenko beams

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-03-12 DOI: 10.1016/j.cma.2025.117886

Michael Jäger, Jacqueline Albertsen, Sandro Wartzack

Spatial truss structures represent a robust, cost-effective, and efficient lightweight design, especially when isotropic materials are substituted with lightweight materials such as composites. During early design phases, truss structures are often subject to optimisations. In order to achieve this in an efficient manner, it is essential to employ a precise yet cost-effective computational model. The most common methodology for the analysis of spatial truss structures employs hinged joints in conjunction with struts that are only subject to tension or compression. However, this approach does not account for the bending and coupling effects inherent to struts manufactured from composite materials. In particular, when employing asymmetric laminates, these effects can no longer be ignored. In order to incorporate these effects, it is common practice to use Finite Element Analysis tools. Particularly for large spatial truss structures comprising struts with slender and thin-walled cross-sections, a large number of solid or shell elements is required, which results in time-consuming simulations. This contribution presents a fully analytical thin-walled composite beam element, applicable to an arbitrarily shaped, closed cross-section. The beam model incorporates two distinct composite material models, namely the Classical Laminate Plate Theory and the First Order Shear Deformation Theory. Moreover, it is capable of simulating asymmetric laminates and modelling the coupling effects within these laminates. Utilising the exact third-order solution of a composite Timoshenko-Ehrenfest beam enables the locking-free representation of an individual strut with a single beam element. In comparison to the conventional shell / solid Finite Element Analysis, this approach results in a substantial reduction in the number of degrees of freedom, by a factor of several orders of magnitude. As a result, the required computational time is significantly reduced. In the case of a single strut, the computational time is reduced by a factor between 160 and 430. For an exemplary truss structure comprising 64 struts, a reduction in computational time of approximately 100 000 times is reached. The numerical comparisons presented in this contribution demonstrate that the model is highly accurate, particularly for tubular and elliptical cross-sections including symmetric and asymmetric laminates.

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引用次数: 0

Explicit Dual-Mesh virtual element method for 2D nonlinear dynamic problems

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.2025.117893

Ruopu Zhou, Zhixin Zeng, Xiong Zhang

A novel explicit Dual-Mesh virtual element method (DM-VEM) for two dimensional nonlinear dynamic problems is proposed. The DM-VEM employs an Eulerian background grid to solve the momentum equation of the virtual element method (VEM), which significantly improves the spatial stability and the temporal stability of the VEM. An explicit critical time step formula is first developed for one dimensional problems and then extended to two dimensional problems, which takes the effect of vertex position and neighboring cell interaction into consideration. An efficient Lagrangian multiplier contact method based on the background grid is also proposed to deal with contact phenomena. Several numerical examples are studied to verify the proposed explicit DM-VEM in nonlinear dynamic problems.

引用次数: 0

Prediction of damage evolution in CMCs considering the real microstructures through a deep-learning scheme

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.2025.117923

Rongqi Zhu, Guohao Niu, Panding Wang, Chunwang He, Zhaoliang Qu, Daining Fang

The real microstructures of ceramic matrix composites (CMCs) play a crucial role in determining their damage behavior. However, considering the real microstructure within the high-fidelity numerical simulation usually leads to expensive computational costs. In this study, an end-to-end deep-learning (DL) framework is proposed to predict the evolution of damage fields for CMCs from their real microstructures, which are characterized through computed tomography (CT). Three sub-networks, including the microstructure processing network (MPN), elastic deformation prediction network (EPN), and damage sequence prediction network (DPN), are used to construct a two-stage DL model. In the first stage, the geometrical characteristics of real microstructure are precisely captured by the MPN with over 92 % precision for the yarns and matrix. In the second stage, the elastic deformation predicted by the EPN is taken as the intermediate variable to motivate the damage prediction of DPN with the MPN-predicted microstructure as input. The damage evolution of real microstructure is finally predicted with a mean relative error of 10.8 % for the primary damage variable fields. The high-damage regions in the microstructure can also be accurately captured with a mean precision of 87.9 %. The proposed model is further validated by the in-situ tensile experiment. The micro-cracks are proven to initiate and propagate in the high-damage regions. Compared with the high-fidelity numerical methods, this DL-based method can predict the damage evolution on the fly, avoiding time-consuming computation and poor convergence during the damage analysis.

{"title":"Prediction of damage evolution in CMCs considering the real microstructures through a deep-learning scheme","authors":"Rongqi Zhu, Guohao Niu, Panding Wang, Chunwang He, Zhaoliang Qu, Daining Fang","doi":"10.1016/j.cma.2025.117923","DOIUrl":"10.1016/j.cma.2025.117923","url":null,"abstract":"<div><div>The real microstructures of ceramic matrix composites (CMCs) play a crucial role in determining their damage behavior. However, considering the real microstructure within the high-fidelity numerical simulation usually leads to expensive computational costs. In this study, an end-to-end deep-learning (DL) framework is proposed to predict the evolution of damage fields for CMCs from their real microstructures, which are characterized through computed tomography (CT). Three sub-networks, including the microstructure processing network (MPN), elastic deformation prediction network (EPN), and damage sequence prediction network (DPN), are used to construct a two-stage DL model. In the first stage, the geometrical characteristics of real microstructure are precisely captured by the MPN with over 92 % precision for the yarns and matrix. In the second stage, the elastic deformation predicted by the EPN is taken as the intermediate variable to motivate the damage prediction of DPN with the MPN-predicted microstructure as input. The damage evolution of real microstructure is finally predicted with a mean relative error of 10.8 % for the primary damage variable fields. The high-damage regions in the microstructure can also be accurately captured with a mean precision of 87.9 %. The proposed model is further validated by the <em>in-situ</em> tensile experiment. The micro-cracks are proven to initiate and propagate in the high-damage regions. Compared with the high-fidelity numerical methods, this DL-based method can predict the damage evolution on the fly, avoiding time-consuming computation and poor convergence during the damage analysis.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"439 ","pages":"Article 117923"},"PeriodicalIF":6.9,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143593810","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