Computer Methods in Applied Mechanics and Engineering最新文献_第6页

An ensemble score filter for tracking high-dimensional nonlinear dynamical systems 用于跟踪高维非线性动力系统的集合得分过滤器

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-10-22 DOI: 10.1016/j.cma.2024.117447

We propose an ensemble score filter (EnSF) for solving high-dimensional nonlinear filtering problems with superior accuracy. A major drawback of existing filtering methods, e.g., particle filters or ensemble Kalman filters, is the low accuracy in handling high-dimensional and highly nonlinear problems. EnSF addresses this challenge by exploiting the score-based diffusion model, defined in a pseudo-temporal domain, to characterize the evolution of the filtering density. EnSF stores the information of the recursively updated filtering density function in the score function, instead of storing the information in a set of finite Monte Carlo samples (used in particle filters and ensemble Kalman filters). Unlike existing diffusion models that train neural networks to approximate the score function, we develop a training-free score estimation method that uses a mini-batch-based Monte Carlo estimator to directly approximate the score function at any pseudo-spatial–temporal location, which provides sufficient accuracy in solving high-dimensional nonlinear problems while also saving a tremendous amount of time spent on training neural networks. High-dimensional Lorenz-96 systems are used to demonstrate the performance of our method. EnSF provides superior performance, compared with the state-of-the-art Local Ensemble Transform Kalman Filter, in reliably and efficiently tracking extremely high-dimensional Lorenz systems (up to 1,000,000 dimensions) with highly nonlinear observation processes.

我们提出了一种集合得分滤波器（EnSF），用于解决高维非线性滤波问题，且精度极高。现有滤波方法（如粒子滤波器或集合卡尔曼滤波器）的一个主要缺点是处理高维和高度非线性问题的精度较低。EnSF 利用在伪时域中定义的基于分数的扩散模型来描述滤波密度的演变，从而解决了这一难题。EnSF 将递归更新滤波密度函数的信息存储在分数函数中，而不是存储在一组有限蒙特卡罗样本中（粒子滤波器和集合卡尔曼滤波器中使用）。与现有的通过训练神经网络来逼近得分函数的扩散模型不同，我们开发了一种无需训练的得分估计方法，该方法使用基于迷你批处理的蒙特卡罗估计器直接逼近任意伪空间-时间位置的得分函数，在解决高维非线性问题时提供了足够的精度，同时还节省了大量训练神经网络的时间。我们使用高维 Lorenz-96 系统来证明我们方法的性能。与最先进的局部集合变换卡尔曼滤波器相比，EnSF 在可靠、高效地跟踪具有高度非线性观测过程的极高维 Lorenz 系统（多达 1,000,000 维）方面表现出色。

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引用次数: 0

Mesh-driven resampling and regularization for robust point cloud-based flow analysis directly on scanned objects 网格驱动的重采样和正则化，可直接对扫描物体进行基于点云的稳健流动分析

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-10-21 DOI: 10.1016/j.cma.2024.117426

Point cloud representations of three-dimensional objects have remained indispensable across a diverse array of applications, given their ability to represent complex real-world geometry with just a set of points. The high fidelity and versatility of point clouds have been utilized in directly performing numerical analysis for engineering applications, bypassing the labor-intensive and time-consuming tasks of creating analysis-suitable CAD models. However, point clouds exhibit various levels of quality, often containing defects such as holes, noise, and sparse regions, leading to sub-optimal geometry representation that can impact the stability and accuracy of any analysis study. This paper aims to overcome such challenges by proposing a novel method that expands upon our recently developed direct point cloud-to-CFD approach based on immersogeometric analysis. The proposed method features a mesh-driven resampling technique to fill any unintended gaps and regularize the point cloud, making it suitable for CFD analysis. Additionally, ghost penalty stabilization is employed for incompressible flow to improve the conditioning and stability compromised by the small cut elements in immersed methods. The developed method is validated against standard benchmark geometries and real-world point clouds obtained in-house with photogrammetry. Results demonstrate the proposed framework’s robustness in facilitating CFD simulations directly on point clouds of varying quality, underscoring its potential for practical applications in analyzing real-world structures.

三维物体的点云表示法能够用一组点来表示复杂的真实世界几何图形，因此在各种应用中仍然不可或缺。点云的高保真性和多功能性被直接用于工程应用中的数值分析，从而避免了创建适合分析的 CAD 模型这一耗费大量人力和时间的任务。然而，点云的质量水平参差不齐，通常包含孔洞、噪声和稀疏区域等缺陷，导致几何表示效果不理想，从而影响分析研究的稳定性和准确性。本文旨在通过提出一种新方法来克服这些挑战，该方法扩展了我们最近开发的基于沉浸几何分析的直接点云到计算机有限元方法。该方法采用网格驱动的重采样技术来填补任何意外间隙，并对点云进行正则化处理，使其适用于 CFD 分析。此外，对不可压缩流采用了鬼影惩罚稳定技术，以改善沉浸式方法中因小切口元素而受到影响的调节和稳定性。所开发的方法通过标准基准几何图形和内部摄影测量获得的真实世界点云进行了验证。结果表明，所提出的框架在直接对不同质量的点云进行 CFD 模拟时非常稳健，突出了其在实际应用中分析现实世界结构的潜力。

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引用次数: 0

Transient anisotropic kernel for probabilistic learning on manifolds 流形上概率学习的瞬态各向异性内核

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-10-21 DOI: 10.1016/j.cma.2024.117453

PLoM (Probabilistic Learning on Manifolds) is a method introduced in 2016 for handling small training datasets by projecting an Itô equation from a stochastic dissipative Hamiltonian dynamical system, acting as the MCMC generator, for which the KDE-estimated probability measure with the training dataset is the invariant measure. PLoM performs a projection on a reduced-order vector basis related to the training dataset, using the diffusion maps (DMAPS) basis constructed with a time-independent isotropic kernel. In this paper, we propose a new ISDE projection vector basis built from a transient anisotropic kernel, providing an alternative to the DMAPS basis to improve statistical surrogates for stochastic manifolds with heterogeneous data. The construction ensures that for times near the initial time, the DMAPS basis coincides with the transient basis. For larger times, the differences between the two bases are characterized by the angle of their spanned vector subspaces. The optimal instant yielding the optimal transient basis is determined using an estimation of mutual information from Information Theory, which is normalized by the entropy estimation to account for the effects of the number of realizations used in the estimations. Consequently, this new vector basis better represents statistical dependencies in the learned probability measure for any dimension. Three applications with varying levels of statistical complexity and data heterogeneity validate the proposed theory, showing that the transient anisotropic kernel improves the learned probability measure.

PLoM （Probabilistic Learning on Manifolds）是 2016 年推出的一种方法，通过投影随机耗散哈密顿动力系统的伊托方程来处理小型训练数据集，作为 MCMC 生成器，训练数据集的 KDE 估计概率度量是其不变度量。PLoM 使用与时间无关的各向同性核构建的扩散图 (DMAPS) 基础，在与训练数据集相关的降阶矢量基础上执行投影。在本文中，我们提出了一种由瞬态各向异性核构建的新 ISDE 投影矢量基础，提供了 DMAPS 基础的替代方案，以改进具有异质数据的随机流形的统计代用。这种构造确保了在初始时间附近，DMAPS 基础与瞬态基础相吻合。对于更长的时间，两个基础之间的差异是由它们所跨向量子空间的角度决定的。产生最佳瞬态基础的最佳瞬间是通过信息论中的互信息估计来确定的，该估计由熵估计归一化，以考虑估计中使用的实现次数的影响。因此，这种新的矢量基础能更好地代表任何维度的已学概率度量中的统计依赖性。三个具有不同统计复杂性和数据异质性的应用验证了所提出的理论，表明瞬态各向异性内核改善了所学概率度量。

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引用次数: 0

High-efficient sample point transform algorithm for large-scale complex optimization 大规模复杂优化的高效采样点变换算法

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-10-19 DOI: 10.1016/j.cma.2024.117451

Decomposition algorithms and surrogate model methods are frequently employed to address large-scale, intricate optimization challenges. However, the iterative resolution phase inherent to decomposition algorithms can potentially alter the background vector, leading to the repetitive evaluation of samples across disparate iteration cycles. This phenomenon significantly diminishes the computational efficiency of optimization. Accordingly, a novel approach, designated the Sample Point Transformation Algorithm (SPTA), is put forth in this paper as a means of enhancing efficiency through a process of mathematical deduction. The mathematical deduction reveals that the difference between sample points in each iteration loop is a simple function related to the inter-group dependent variables. Consequently, the SPTA method achieves the comprehensive transformation of the sample set by establishing a surrogate model of the difference between the sample sets of two cycles with a limited number of sample points, as opposed to conducting a substantial number of repeated samplings. This SPTA is employed to substitute the most time-consuming step of direct calculation in the classical optimization process. To validate the calculation efficiency, a series of numerical examples were conducted, demonstrating an improvement of approximately 75 % while maintaining optimal accuracy. This illustrates the advantage of the SPTA in addressing large-scale and complex optimization problems.

分解算法和代用模型方法经常被用来解决大规模、复杂的优化难题。然而，分解算法固有的迭代解析阶段可能会改变背景向量，导致在不同的迭代周期中重复评估样本。这种现象大大降低了优化的计算效率。因此，本文提出了一种名为 "采样点变换算法"（SPTA）的新方法，通过数学推导过程来提高效率。数学推导表明，每个迭代循环中样本点之间的差值是一个与组间因变量相关的简单函数。因此，相对于进行大量重复采样，SPTA 方法通过建立有限数量样本点的两个循环样本集之差的代用模型，实现了样本集的综合转换。这种 SPTA 被用来替代经典优化过程中最耗时的直接计算步骤。为了验证计算效率，我们进行了一系列数值示例，结果表明在保持最佳精度的同时，计算效率提高了约 75%。这说明了 SPTA 在解决大规模复杂优化问题方面的优势。

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引用次数: 0

Tackling the curse of dimensionality in fractional and tempered fractional PDEs with physics-informed neural networks 利用物理信息神经网络解决分数和节制分数 PDE 中的维度诅咒问题

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-10-18 DOI: 10.1016/j.cma.2024.117448

Fractional and tempered fractional partial differential equations (PDEs) are effective models of long-range interactions, anomalous diffusion, and non-local effects. Traditional numerical methods for these problems are mesh-based, thus struggling with the curse of dimensionality (CoD). Physics-informed neural networks (PINNs) offer a promising solution due to their universal approximation, generalization ability, and mesh-free training. In principle, Monte Carlo fractional PINN (MC-fPINN) estimates fractional derivatives using Monte Carlo methods and thus could lift CoD. However, this may cause significant variance and errors, hence affecting convergence; in addition, MC-fPINN is sensitive to hyperparameters. In general, numerical methods and specifically PINNs for tempered fractional PDEs are under-developed. Herein, we extend MC-fPINN to tempered fractional PDEs to address these issues, resulting in the Monte Carlo tempered fractional PINN (MC-tfPINN). To reduce possible high variance and errors from Monte Carlo sampling, we replace the one-dimensional (1D) Monte Carlo with 1D Gaussian quadrature, applicable to both MC-fPINN and MC-tfPINN. We validate our methods on various forward and inverse problems of fractional and tempered fractional PDEs, scaling up to 100,000 dimensions. Our improved MC-fPINN/MC-tfPINN using quadrature consistently outperforms the original versions in accuracy and convergence speed in very high dimensions. Code is available at https://github.com/zheyuanhu01/Tempered_Fractional_PINN.

分式和节制分式偏微分方程（PDE）是长程相互作用、反常扩散和非局部效应的有效模型。解决这些问题的传统数值方法以网格为基础，因此在维度诅咒（CoD）问题上举步维艰。物理信息神经网络（PINNs）因其普遍近似性、泛化能力和无网格训练而提供了一种有前途的解决方案。原则上，蒙特卡洛分数 PINN（MC-fPINN）使用蒙特卡洛方法估计分数导数，因此可以消除 CoD。然而，这可能会导致显著的方差和误差，从而影响收敛性；此外，MC-fPINN 对超参数很敏感。总体而言，针对有节制分式 PDE 的数值方法，特别是 PINN 还不够成熟。在此，我们将 MC-fPINN 扩展到回火分式 PDE，以解决这些问题，从而产生蒙特卡罗回火分式 PINN（MC-tfPINN）。为了减少蒙特卡洛采样可能产生的高方差和误差，我们用一维高斯正交代替了一维蒙特卡洛，适用于 MC-fPINN 和 MC-tfPINN。我们在分式和节制分式 PDEs 的各种正演和反演问题上验证了我们的方法，最多可扩展到 100,000 维。我们使用正交方法改进的 MC-fPINN/MC-tfPINN 在精度和收敛速度上始终优于超高维度的原始版本。代码见 https://github.com/zheyuanhu01/Tempered_Fractional_PINN。

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引用次数: 0

Approach for multi-valued integer programming in multi-material topology optimization: Random discrete steepest descent (RDSD) algorithm 多材料拓扑优化中的多值整数编程方法：随机离散最陡降法（RDSD）算法

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-10-17 DOI: 10.1016/j.cma.2024.117449

The present study models the multi-material topology optimization problems as the multi-valued integer programming (MVIP) or named as combinatorial optimization. By extending classical convex analysis and convex programming to discrete point-set functions, the discrete convex analysis and discrete steepest descent (DSD) algorithm are introduced. To overcome combinatorial complexity of the DSD algorithm, we employ the sequential approximate integer programming (SAIP) to explicitly and linearly approximate the implicit objective and constraint functions. Considering the multiple potential changed directions for multi-valued design variables, the random discrete steepest descent (RDSD) algorithm is proposed, where a random strategy is implemented to select a definitive direction of change. To analytically calculate multi-material discrete variable sensitivities, topological derivatives with material contrast is applied. In all, the MVIP is finally transferred as the linear 0–1 programming that can be efficiently solved by the canonical relaxation algorithm (CRA). Explicit nonlinear examples demonstrate that the RDSD algorithm owns nearly three orders of magnitude improvement compared with the commercial software (GUROBI). The proposed approach, without using any continuous variable relaxation and interpolation penalization schemes, successfully solves the minimum compliance problem, strength-related problem, and frequency-related optimization problems. Given the algorithm efficiency, mathematical generality and merits over other algorithms, the proposed RDSD algorithm is meaningful for other structural and topology optimization problems involving multi-valued discrete design variables.

本研究将多材料拓扑优化问题建模为多值整数编程（MVIP），或称为组合优化。通过将经典的凸分析和凸编程扩展到离散点集函数，引入了离散凸分析和离散最陡降法（DSD）算法。为了克服 DSD 算法的组合复杂性，我们采用了顺序近似整数编程（SAIP）来显式线性近似隐式目标函数和约束函数。考虑到多值设计变量的多个潜在变化方向，我们提出了随机离散最陡降法（RDSD）算法，通过随机策略来选择确定的变化方向。为了分析计算多材料离散变量的敏感性，应用了具有材料对比度的拓扑导数。总之，MVIP 最终被转换为线性 0-1 程序，可通过典型松弛算法 (CRA) 高效求解。显式非线性实例表明，与商业软件（GUROBI）相比，RDSD 算法拥有近三个数量级的改进。在不使用任何连续变量松弛和插值惩罚方案的情况下，所提出的方法成功地解决了最小顺应性问题、强度相关问题和频率相关优化问题。考虑到算法的效率、数学通用性以及与其他算法相比的优点，所提出的 RDSD 算法对其他涉及多值离散设计变量的结构和拓扑优化问题很有意义。

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引用次数: 0

Deep learning-driven domain decomposition (DLD3): A generalizable AI-driven framework for structural analysis 深度学习驱动的领域分解（DLD3）：结构分析的通用人工智能驱动框架

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-10-17 DOI: 10.1016/j.cma.2024.117446

A novel, generalizable Artificial Intelligence (AI)-driven technique, termed Deep Learning-Driven Domain Decomposition (DLD

^{3}

), is introduced for simulating two-dimensional linear elasticity problems with arbitrary geometries and boundary conditions (BCs). The DLD

^{3}

framework leverages trained AI models to predict the displacement field within small subdomains, each characterized by varying geometries and BCs. To enforce continuity across the entire domain, the overlapping Schwarz domain decomposition method (DDM) iteratively updates the BCs of each subdomain, thus approximating the overall solution. After evaluating multiple model architectures, the Fourier Neural Operator (FNO) was selected as the AI engine for the DLD

^{3}

method, owing to its data efficiency and high accuracy. We also present a framework that utilizes geometry reconstruction and automated meshing algorithms to generate millions of training data points from high-fidelity finite element (FE) simulations. Several case studies are provided to demonstrate the DLD

^{3}

algorithm’s ability to accurately predict displacement fields in problems involving complex geometries, diverse BCs, and material properties.

本文介绍了一种新颖的、可推广的人工智能（AI）驱动技术，称为深度学习驱动的领域分解（DLD3），用于模拟具有任意几何形状和边界条件（BC）的二维线性弹性问题。DLD3 框架利用训练有素的人工智能模型来预测小型子域内的位移场，每个子域的几何形状和边界条件各不相同。为了确保整个域的连续性，重叠施瓦茨域分解法（DDM）会迭代更新每个子域的边界条件，从而逼近整体解决方案。在对多种模型架构进行评估后，我们选择了傅立叶神经运算器（FNO）作为 DLD3 方法的人工智能引擎，因为它具有数据效率高、精度高的特点。我们还介绍了一个框架，该框架利用几何重构和自动网格划分算法，从高保真有限元（FE）模拟中生成数百万个训练数据点。我们提供了几个案例研究，以证明 DLD3 算法在涉及复杂几何形状、不同 BC 和材料属性的问题中准确预测位移场的能力。

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引用次数: 0

DiffMat: Data-driven inverse design of energy-absorbing metamaterials using diffusion model DiffMat：利用扩散模型进行数据驱动的吸能超材料反设计

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-10-17 DOI: 10.1016/j.cma.2024.117440

Energy-absorbing materials and structures are widely applied in industrial areas. Presently, design methods of energy-absorbing metamaterials mainly rely on empirical or bio-inspired configurations. Inspired by AI-generated content, this paper proposes a novel inverse design framework for energy-absorbing metamaterial using diffusion model called DiffMat, which can be customized to generate microstructures given desired stress–strain curves. DiffMat learns the conditional distribution of microstructure given mechanical properties and can realize the one-to-many mapping from properties to geometries. Numerical simulations and experimental validations demonstrate the capability of DiffMat to generate a diverse array of microstructures based on given mechanical properties. This indicates the validity and high accuracy of DiffMat in generating metamaterials that meet the desired mechanical properties. The successful demonstration of the proposed inverse design framework highlights its potential to revolutionize the development of energy-absorbing metamaterials and underscores the broader impact of integrating AI-inspired methodologies into metamaterial design and engineering.

吸能材料和结构被广泛应用于工业领域。目前，吸能超材料的设计方法主要依靠经验或生物启发配置。受人工智能生成内容的启发，本文提出了一种新颖的吸能超材料反向设计框架，该框架采用名为 DiffMat 的扩散模型，可根据所需的应力应变曲线定制生成微结构。DiffMat 可根据机械特性学习微结构的条件分布，并实现从特性到几何形状的一对多映射。数值模拟和实验验证证明，DiffMat 能够根据给定的机械性能生成各种微观结构。这表明 DiffMat 在生成符合所需机械特性的超材料方面具有很高的有效性和准确性。所提出的反向设计框架的成功演示突出了其彻底改变吸能超材料开发的潜力，并强调了将人工智能启发方法整合到超材料设计和工程中的广泛影响。

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引用次数: 0

A new exploration of mesoscopic structure in the nonlocal macro-meso-scale consistent damage model for quasi-brittle materials 准脆性材料非局部宏观-介观尺度一致损伤模型的介观结构新探索

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-10-16 DOI: 10.1016/j.cma.2024.117456

In the present study, a new exploration of the mesoscopic structure is proposed for the nonlocal macro‑meso-scale consistent damage (NMMD) model, and the definition from mesoscopic damage to macroscopic damage in the original NMMD model is expanded. In the proposed model, material points are divided into two types: macroscopic and mesoscopic. For each macroscopic material point, there are mesoscopic material points within its influence domain, and every two different mesoscopic material points form a material point pair. The macroscopic damage at a macroscopic material point is also evaluated as the weighted average of mesoscale damage over material point pairs in the influence domain. However, compared with the original NMMD model, the mesoscale damage of material point pairs is determined by the motion of mesoscopic material points, rather than macroscopic material points. The macroscopic material points in the proposed model only represent the nonlocal effect and the macroscopic damage. Moreover, the shape of the influence domain and the arrangement of material point pairs are arbitrary and not fixed, i.e., the unified mesoscopic structure is abstract. To verify the proposed model, a specific mesoscopic structure is generated for quasi-brittle materials without considering the randomness of material properties. In this mesoscopic structure, the shape of the influence domain is a circle, and the mesoscopic material points are generated by the tangent sphere method. The numerical results indicate that the proposed model can accurately capture the crack patterns of quasi-brittle materials and exhibits excellent numerical robustness. Meanwhile, through a mode-I failure example, it is demonstrated that the computational efficiency of the proposed model is not lower than the original NMMD model. More importantly, the framework of mesoscopic structure modeling provides a new feasible approach for the extension of other models, e.g., virtual internal bond model and peridynamics. The urgent work within the NMMD model framework is to extend the proposed model to anisotropic, composite materials and dynamic crack simulation of large structures in the future.

本研究对非局部宏观-介观尺度一致损伤（NMMD）模型的介观结构提出了新的探索，并扩展了原 NMMD 模型中从介观损伤到宏观损伤的定义。在所提出的模型中，材料点分为两种类型：宏观和中观。每个宏观材料点的影响域内都有介观材料点，每两个不同的介观材料点组成一个材料点对。宏观材料点的宏观损伤也是以影响域内材料点对的中观损伤的加权平均值来评估的。不过，与最初的 NMMD 模型相比，材料点对的中尺度损伤是由中观材料点的运动而不是宏观材料点的运动决定的。拟议模型中的宏观材料点仅代表非局部效应和宏观损伤。此外，影响域的形状和材料点对的排列是任意的，并不固定，即统一的介观结构是抽象的。为了验证所提出的模型，在不考虑材料属性随机性的情况下，为准脆性材料生成了一个特定的介观结构。在该介观结构中，影响域的形状为圆，介观材料点由切球法生成。数值结果表明，所提出的模型能准确捕捉准脆性材料的裂纹模式，并表现出优异的数值鲁棒性。同时，通过一个 I 型失效实例，证明了所提出模型的计算效率并不比原始 NMMD 模型低。更重要的是，介观结构建模框架为其他模型（如虚拟内结合模型和周动力学模型）的扩展提供了一种新的可行方法。在 NMMD 模型框架内亟待开展的工作是将提出的模型扩展到各向异性材料、复合材料以及未来大型结构的动态裂缝模拟。

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引用次数: 0

Topology optimization of structures guarding against brittle fracture via peridynamics-based SIMP approach 通过基于周动力学的 SIMP 方法优化防止脆性断裂结构的拓扑结构

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-10-16 DOI: 10.1016/j.cma.2024.117438

Fracture resistance of structures consisting of brittle materials is significantly important in engineering practice. In this work, we explore the application of peridynamics (PD) in the optimization of structures against brittle fracture. A fracture resistance topology optimization scheme under the PD-based analysis framework is proposed, where two fracture-based strategies are adopted to improve the structural fracture behavior. The first one sets the conventional fracture energy as a constraint. While the second constraint is the bond stretch established on the unique concept “bond” of the PD framework, which smoothly transfers the energy-based fracture resistance control to an intuitive and mathematically tractable geometric expression. The topology optimization is carried out under the SIMP framework, where densities are assigned to the bonds via material points to represent the topology changes and crack generation. Numerical examples and experiments demonstrate that the proposed strategies can guarantee the safety of the optimized structure against the occurrence of fracture failure.

在工程实践中，由脆性材料组成的结构的抗断裂性能非常重要。在这项工作中，我们探索了周动力学（PD）在结构抗脆断优化中的应用。在基于 PD 的分析框架下，提出了一种抗断裂拓扑优化方案，其中采用了两种基于断裂的策略来改善结构的断裂行为。第一种策略将常规断裂能作为约束条件。第二个约束条件是建立在基于 PD 框架的独特概念 "键 "上的键拉伸，它将基于能量的断裂抗力控制平滑地转换为直观且数学上可操作的几何表达。拓扑优化是在 SIMP 框架下进行的，通过材料点给键分配密度，以表示拓扑变化和裂缝产生。数值示例和实验证明，所提出的策略可以保证优化结构的安全性，防止断裂失效的发生。

引用次数: 0