Computer Methods in Applied Mechanics and Engineering最新文献

{"title":"Unsupervised machine learning classification for accelerating FE2 multiscale fracture simulations","authors":"","doi":"10.1016/j.cma.2024.117278","DOIUrl":"10.1016/j.cma.2024.117278","url":null,"abstract":"<div><p>An approach is proposed to accelerate multiscale simulations of heterogeneous quasi-brittle materials exhibiting an anisotropic damage response. The present technique uses unsupervised machine learning classification based on k-means clustering to select integration points in the macro mesh within an FE<span><math><msup><mrow></mrow><mrow><mn>2</mn></mrow></msup></math></span> strategy to track redundant micro nonlinear problems and to avoid unnecessary Representative Volume Element (RVE) calculations. More specifically, a classification vector including strains and internal damage variables is defined for each macro integration point. The macro internal damage variables are constructed using harmonic analysis of damage. At each step of the macro iterations, the integrations points are grouped into clusters and only one nonlinear problem is solved for each cluster. As a result, the computations are accelerated within an FE<span><math><msup><mrow></mrow><mrow><mn>2</mn></mrow></msup></math></span> scheme by reducing the total number of RVE problems to be solved. The developed algorithm includes a macro regularization and an arc-length technique to capture macro snap-back due to the softening. Applications are proposed to simulate the response of different heterogeneous quasi-brittle materials with strong anisotropic responses. speed-up factors of the order of 12 to 15 can be achieved without the need to build a database, and without reduced-order modeling approximations at the micro level. Estimates of structural strength can be obtained with Speed-up factors between 45 and 85.</p></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142099202","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":"Application of proper orthogonal decomposition to flow fields around various geometries and reduced-order modeling","authors":"","doi":"10.1016/j.cma.2024.117340","DOIUrl":"10.1016/j.cma.2024.117340","url":null,"abstract":"<div><p>This study is focused on a reduced-order model (ROM) based on proper orthogonal decomposition (POD) for unsteady flow around a stationary object, which allows prediction with different object geometry as a parameter. The conventional POD method is applicable only to data with the same computational grid for all snapshots. This study proposed a novel POD methodology that performs on flow snapshots, including some time-series data of flow fields around objects of different shapes and numerically computed by different computational grids. The concept of the proposed POD involved mapping the flow fields computed on different grids in computational space. Consequently, the optimal POD basis for minimizing reconstruction errors in physical space was obtained in the computational space. The proposed POD was applied to the flow around ellipses and airfoils generated via conformal mapping to a cylinder. The ROM formulated using the proposed POD bases reconstructed the flow fields around the ellipses with different aspect ratios and airfoils with varying shapes. Using the modes obtained by the proposed POD, the ROM was demonstrated to stably predict the time evolution of the flow around objects, which is not included in the snapshots. In the ROM, the difference between the frequency of the flow field in the POD snapshot and that of the reconstructed flow field resulted in a phase error owing to the time evolution. The mean squared error between the flow fields obtained via the ROM and the directly solved Navier–Stokes equations was under <span><math><mrow><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>7</mn></mrow></msup></mrow></math></span> when the reconstructed flow and the flow included in the snapshot had the same frequency as that of Kármán vorticities behind the objects. Based on these observations, the proposed POD is suitable for constructing an ROM to reconstruct the flow around various geometries.</p></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0045782524005954/pdfft?md5=215bfbc2d1e95400ccfe282c76776c86&pid=1-s2.0-S0045782524005954-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142099204","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":"Free-Form Deformation as a non-invasive, discrete unfitted domain method: Application to the time-harmonic acoustic response of a saxophone","authors":"","doi":"10.1016/j.cma.2024.117345","DOIUrl":"10.1016/j.cma.2024.117345","url":null,"abstract":"<div><p>The Finite Element method, widely used for solving Partial Differential Equations, may result in suboptimal computational costs when computing smooth fields within complex geometries. In such situations, IsoGeometric Analysis often offers improved per degree-of-freedom accuracy but building analysis-suitable representation of complex shapes is generally not obvious. This paper introduces a non-invasive, spline-based fictitious domain method using Free-Form Deformation to efficiently solve the Helmholtz equation in complex domains, such as in musical instruments. By immersing a fine FE mesh into a simple B-spline box, the approximation subspace size is significantly reduced without compromising accuracy. Accompanied by specific conditioning treatment, the method not only proves to be efficient, but also robust and easy to implement in existing FE software. Applied to an alto saxophone, the method reduces the number of degrees of freedom by over two orders of magnitude and the computation time by more than one compared to standard FE methods with comparable accuracy when compared to experimental tests.</p></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0045782524006005/pdfft?md5=228e33820ead6b3264f1123031aedfbb&pid=1-s2.0-S0045782524006005-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142099206","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":"Three-dimensional continuum point cloud method for large deformation and its verification","authors":"","doi":"10.1016/j.cma.2024.117307","DOIUrl":"10.1016/j.cma.2024.117307","url":null,"abstract":"<div><p>This study presents a strong form based meshfree collocation method, which is named Continuum Point Cloud Method, to solve nonlinear field equations derived from classical mechanics for deformed bodies in three-dimensional Euclidean space. The method and its implementation are benchmarked against a nonlinear vector field using manufactured solutions. The analysis of mechanical fields firstly focuses on the study of St. Venant Kirchhoff and compressible neo-Hookean materials. Results for various initial boundary value problems are presented, including benchmark cases involving unidirectional tension and simple shear. Subsequently, the study concludes with an analysis of a displacement-controlled simulation of a compressible neo-Hookean material, specifically a bar that is pulled to 50% of its original length and rotated 90°. The pure tension case yields a 1.5% error in displacement between computed and expected values and a combined tension and torsion loading case provides further insight into material behavior under complex loading conditions. The resulting normal axial and transverse stress-strain curves are also presented. Finally, the consistency and robustness of the proposed nonlinear numerical schemes are successfully demonstrated through various numerical experiments.</p></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142098675","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":"Dynamical system prediction from sparse observations using deep neural networks with Voronoi tessellation and physics constraint","authors":"","doi":"10.1016/j.cma.2024.117339","DOIUrl":"10.1016/j.cma.2024.117339","url":null,"abstract":"<div><p>Despite the success of various methods in addressing the issue of spatial reconstruction of dynamical systems with sparse observations, spatio-temporal prediction for sparse fields remains a challenge. Existing Kriging-based frameworks for spatio-temporal sparse field prediction fail to meet the accuracy and inference time required for nonlinear dynamic prediction problems. In this paper, we introduce the Dynamical System Prediction from Sparse Observations using Voronoi Tessellation (DSOVT) framework, an innovative methodology based on Voronoi tessellation which combines convolutional encoder–decoder (CED) and long short-term memory (LSTM) and utilizing Convolutional Long Short-Term Memory (ConvLSTM). By integrating Voronoi tessellations with spatio-temporal deep learning models, DSOVT is adept at predicting dynamical systems with unstructured, sparse, and time-varying observations. CED-LSTM maps Voronoi tessellations into a low-dimensional representation for time series prediction, while ConvLSTM directly uses these tessellations in an end-to-end predictive model. Furthermore, we incorporate physics constraints during the training process for dynamical systems with explicit formulas. Compared to purely data-driven models, our physics-based approach enables the model to learn physical laws within explicitly formulated dynamics, thereby enhancing the robustness and accuracy of rolling forecasts. Numerical experiments on real sea surface data and shallow water systems clearly demonstrate our framework’s accuracy and computational efficiency with sparse and time-varying observations.</p></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0045782524005942/pdfft?md5=9cdf601048a4c05d5d278b964e9dcb98&pid=1-s2.0-S0045782524005942-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142099203","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":"A mixed-dimensional formulation for the simulation of slender structures immersed in an incompressible flow","authors":"","doi":"10.1016/j.cma.2024.117316","DOIUrl":"10.1016/j.cma.2024.117316","url":null,"abstract":"<div><p>We consider the simulation of slender structures immersed in a three-dimensional (3D) flow. By exploiting the special geometric configuration of the slender structures, this particular problem can be modeled by mixed-dimensional coupled equations. Taking advantage of the slenderness of the structure and thus considering 3D/1D coupled problems raise several challenges and difficulties. From a mathematical point of view, these include defining well-posed trace operators of co-dimension two. On the computational standpoint, the non-standard mathematical formulation makes it difficult to ensure the accuracy of the solutions obtained with the mixed-dimensional discrete formulation as compared to a fully resolved one. Here we proposed to circumvent theses issues by imposing the fluid–structure coupling conditions on the 2D fluid–structure interface but in a reduced way still taking advantage of the 1D dynamic of the slender structure. We consider the Navier–Stokes equations for the fluid and a Timoshenko beam model for the structure. We complement these models with a mixed-dimensional version of the fluid–structure interface conditions, based on the projection of kinematic coupling conditions on a finite-dimensional Fourier space on each beam cross section. Furthermore, we develop a discrete fictitious domain formulation within the framework of the finite element method, establish the energy stability of the scheme, provide extensive numerical evidence of the accuracy of the discrete formulation, notably with respect to a fully resolved (ALE based) model and a standard reduced modeling approach.</p></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142099205","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":"Damage identification method based on interval regularization theory","authors":"","doi":"10.1016/j.cma.2024.117288","DOIUrl":"10.1016/j.cma.2024.117288","url":null,"abstract":"<div><p>In the field of damage identification, traditional regularization methods neglect the impact of uncertainty factors on the selection of regularization parameters, leading to a decrease in the accuracy of damage identification. Therefore, this study proposes a damage identification based on interval truncated singular value decomposition (DI-ITSVD) method that considers the uncertainty in the selection of regularization parameter. This method treats model errors and measurement noise as interval uncertainties, and introduces the quantified uncertainties into the damage identification solutions through uncertainty propagation methods to determine the interval boundary. Uncertainty regularization parameters are selected to balance residuals and solutions using interval and generalized cross-validation methods. The key aspect of the proposed method in this paper is the integration of interval uncertainty propagation with the truncated singular value decomposition method to ensure the accuracy and stability of the damage identification equation solution. A numerical example of a 29-bar planar truss has been performed to test the effectiveness of the proposed method. The superiority of this method is verified by comparing the identification results with other improved truncated singular value decomposition methods. Finally, the practical application effect of the proposed method was also verified through an experimental work.</p></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142097992","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":"Peridynamics-fueled convolutional neural network for predicting mechanical constitutive behaviors of fiber reinforced composites","authors":"","doi":"10.1016/j.cma.2024.117309","DOIUrl":"10.1016/j.cma.2024.117309","url":null,"abstract":"<div><p>Despite advancements in predicting the constitutive relationships of composite materials, characterizing the effects of microstructural randomness on their mechanical behaviors remains challenging. In this study, we propose a data-driven convolutional neural network (CNN) to efficiently predict the stress-strain curves containing three key material features (Tensile strength, modulus, and toughness) of fiber reinforced composites. Firstly, stress-strain curves for composites with arbitrary fiber distributions were generated using experimentally validated peridynamics (PD) model. Principal component analysis (PCA) was then employed to learn these curves in a lower-dimensional space, reducing computational costs. Subsequently, these reduced data, along with randomly distributed microstructural features, were used to train, validate, and evaluate the CNN models. The combined CNN and PCA model accurately predicted stress-strain curves with maximum errors of 2.5 % for tensile strength, 10% for modulus, and 20 % for toughness. Furthermore, data augmentation and Mean Squared Error (MSE) as a loss function significantly enhanced the model's prediction accuracy. Our findings indicated that DenseNet121 outperformed other CNN models in predicting the properties of fiber-reinforced materials, further demonstrating the effectiveness of the proposed model. This work successfully demonstrates the applicability of a data-driven CNN approach to predict stress-strain relations for engineering materials with intricate heterogeneous microstructures, paving the way for data-driven computational mechanics applied in composites.</p></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142097993","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 weight index-based uniform partition technique of multi-dimensional probability space for structural uncertainty quantification","authors":"","doi":"10.1016/j.cma.2024.117297","DOIUrl":"10.1016/j.cma.2024.117297","url":null,"abstract":"<div><p>Accurately and efficiently achieving the uncertainty quantification of engineering structures is a challenging issue. The direct probability integral method (DPIM) provides an effective pathway to address this issue. However, the key partition technique via Voronoi cell of DPIM requires a prohibitive computational burden for multi-dimensional probability space. Moreover, due to the distributed nonuniformity of representative points, the accuracy of DPIM with the partition technique via Voronoi cell (DPIM-Voronoi) for obtaining the response probability density function (PDF) of structures with multi-dimensional probability space still needs to be improved. To this end, a novel weight index-based uniform partition technique is proposed in this study. This technique can generate uniformly distributed representative points and calculate their assigned probabilities using the weight indexes of representative regions. This feature ensures that the representative points can fill the probability space in a highly uniform manner, and avoid the resource-consuming calculation process of assigned probability by Monte Carlo simulation in the original partition technique via Voronoi cell. Based on the proposed technique, DPIM with a Weight index-based Uniform partition technique (DPIM-WU) is developed. Compared to DPIM-Voronoi, the advantages of DPIM-WU include: (1) improving the computational accuracy of response PDF for structures with multi-dimensional probability space, especially in the tail region, leading to improved accuracy of the dynamic reliability; (2) remarkably reducing the computational cost, with minimal computer memory required for the partition process of multi-dimensional probability space; (3) enhancing the robustness to the number of representative points. These advantages are verified through the stochastic response and dynamic reliability analyses of four typical examples, including the 5-story buildings, dry friction system, cylinder structure, and adjacent buildings with pounding motion. Notably, in the stochastic pounding response analysis of adjacent buildings, a stochastic P-bifurcation occurs as the coefficient of variation of the structural parameters decreases.</p></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142089178","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":"Greedy identification of latent dynamics from parametric flow data","authors":"","doi":"10.1016/j.cma.2024.117332","DOIUrl":"10.1016/j.cma.2024.117332","url":null,"abstract":"<div><p>Projection-based reduced-order models (ROMs) play a crucial role in simplifying the complex dynamics of fluid systems. Such models are achieved by projecting the Navier-Stokes equations onto a lower-dimensional subspace while preserving essential dynamics. However, this approach requires prior knowledge of the underlying high-fidelity model, limiting its effectiveness when applied to black-box data. This article introduces a novel, non-intrusive, data-driven method–Greedy Identification of Latent Dynamics (GILD)–for constructing parametric fluid ROMs. Unlike traditional methods, GILD constructs models directly from data, without relying on specific high-fidelity model information. It also employs interpolation within the manifold <span><math><mrow><msubsup><mrow><mi>R</mi></mrow><mrow><mo>∗</mo></mrow><mrow><mi>N</mi><mo>×</mo><mi>q</mi></mrow></msubsup><mo>/</mo><msub><mrow><mi>O</mi></mrow><mrow><mi>q</mi></mrow></msub></mrow></math></span> to accommodate parameter variability. Numerical experiments on various fluid dynamics scenarios, including lid-driven cavity flow, flow past a cylinder with varying Reynolds number, and Ahmed body flow with variable geometry, demonstrate GILD’s robust performance across both training and unseen parameter values. GILD’s ability to accurately capture system dynamics and its adaptability to diverse data sources highlight its potential as a powerful tool for constructing parametric reduced-order models in an easy and general way for complex fluid dynamics and beyond.</p></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142083147","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}