Computer Methods in Applied Mechanics and Engineering最新文献_第10页

Constructing boundary-identical microstructures via guided diffusion for fast multiscale topology optimization 基于引导扩散构建边界相同微结构的快速多尺度拓扑优化

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-01-14 DOI: 10.1016/j.cma.2025.117735

Jingxuan Feng , Lili Wang , Xiaoya Zhai , Kai Chen , Wenming Wu , Ligang Liu , Xiao-Ming Fu

Hierarchical structures exhibit critical features across multiple scales. However, designing multiscale structures demands significant computational resources, and ensuring connectivity between microstructures remains a key challenge. To address these issues, large-range, boundary-identical microstructure datasets are successfully constructed, where the microstructures share the same boundaries and exhibit a wide range of elastic moduli. This approach enables highly efficient multiscale topology optimization. Central to our technique adopts a deep generative model, guided diffusion, to generate microstructures under the two conditions, including the specified boundary and homogenized elastic tensor. We generate the desired datasets using active learning approaches, where microstructures with diverse elastic moduli are iteratively added to the dataset, which is then retrained. After that, sixteen boundary-identical microstructure datasets with wide ranges of elastic modulus are constructed. We demonstrate the effectiveness and practicability of the obtained datasets over various multiscale design examples. Specifically, in the design of a mechanical cloak, we utilize macrostructures with 30 × 30 elements and microstructures filled with 256 × 256 elements. The entire reverse design process is completed within one minute, significantly enhancing the efficiency of the multiscale topology optimization.

等级结构在多个尺度上表现出关键特征。然而，设计多尺度结构需要大量的计算资源，并且确保微观结构之间的连接仍然是一个关键挑战。为了解决这些问题，成功构建了大范围，边界相同的微观结构数据集，其中微观结构共享相同的边界并表现出大范围的弹性模量。该方法实现了高效的多尺度拓扑优化。我们技术的核心是采用一种深度生成模型，即引导扩散，在两种条件下生成微观结构，包括指定边界和均质弹性张量。我们使用主动学习方法生成所需的数据集，其中迭代地将具有不同弹性模量的微结构添加到数据集中，然后重新训练数据集。在此基础上，构建了16个弹性模量范围大、边界相同的微观结构数据集。我们通过各种多尺度设计实例证明了所获得的数据集的有效性和实用性。具体来说，在机械斗篷的设计中，我们使用了30 × 30单元的宏观结构和256 × 256单元的微观结构。整个反设计过程在1分钟内完成，大大提高了多尺度拓扑优化的效率。

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引用次数: 0

SUPG-stabilized time-DG finite and virtual elements for the time-dependent advection–diffusion equation 用于时变平流扩散方程的 SUPG 稳定时间-DG 有限元和虚拟元

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-01-14 DOI: 10.1016/j.cma.2024.117722

L. Beirão da Veiga , F. Dassi , S. Gómez

We carry out a stability and convergence analysis for the fully discrete scheme obtained by combining a finite or virtual element spatial discretization with the upwind-discontinuous Galerkin time-stepping applied to the time-dependent advection–diffusion equation. A space–time streamline-upwind Petrov–Galerkin term is used to stabilize the method. More precisely, we show that the method is inf–sup stable with constant independent of the diffusion coefficient, which ensures the robustness of the method in the convection- and diffusion-dominated regimes. Moreover, we prove optimal convergence rates in both regimes for the error in the energy norm. An important feature of the presented analysis is the control in the full

L^{2} (0, T; L^{2} (Ω))

norm without the need of introducing an artificial reaction term in the model. We finally present some numerical experiments in

(3 + 1)

-dimensions that validate our theoretical results.

将有限元或虚元空间离散化与逆风不连续Galerkin时间步进相结合，对时变平流扩散方程的完全离散格式进行了稳定性和收敛性分析。利用时空流线逆风彼得罗夫-伽辽金项稳定该方法。更准确地说，我们证明了该方法是稳定的，常数与扩散系数无关，这保证了该方法在对流和扩散占主导地位的情况下的鲁棒性。此外，对于能量范数误差，我们证明了两种情况下的最优收敛速率。所提出的分析的一个重要特征是控制在完整的L2（0，T;L2（Ω））范数中，而不需要在模型中引入人工反应项。最后给出了（3+1）维的数值实验，验证了我们的理论结果。

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引用次数: 0

DeepOKAN: Deep operator network based on Kolmogorov Arnold networks for mechanics problems DeepOKAN：基于力学问题Kolmogorov Arnold网络的深度算子网络

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-01-14 DOI: 10.1016/j.cma.2024.117699

Diab W. Abueidda , Panos Pantidis , Mostafa E. Mobasher

The modern digital engineering design often requires costly repeated simulations for different scenarios. The prediction capability of neural networks (NNs) makes them suitable surrogates for providing design insights. However, only a few NNs can efficiently handle complex engineering scenario predictions. We introduce a new version of the neural operators called DeepOKAN, which utilizes Kolmogorov Arnold networks (KANs) rather than the conventional neural network architectures. Our DeepOKAN uses Gaussian radial basis functions (RBFs) rather than the B-splines. RBFs offer good approximation properties and are typically computationally fast. The KAN architecture, combined with RBFs, allows DeepOKANs to represent better intricate relationships between input parameters and output fields, resulting in more accurate predictions across various mechanics problems. Specifically, we evaluate DeepOKAN’s performance on several mechanics problems, including 1D sinusoidal waves, 2D orthotropic elasticity, and transient Poisson’s problem, consistently achieving lower training losses and more accurate predictions compared to traditional DeepONets. This approach should pave the way for further improving the performance of neural operators.

现代数字工程设计往往需要对不同场景进行昂贵的重复模拟。神经网络（NNs）的预测能力使其成为提供设计见解的合适替代品。然而，只有少数神经网络可以有效地处理复杂的工程场景预测。我们引入了一种名为DeepOKAN的新版本的神经算子，它利用Kolmogorov Arnold网络（KANs）而不是传统的神经网络架构。我们的DeepOKAN使用高斯径向基函数（rbf）而不是b样条。rbf提供了良好的近似特性，并且通常计算速度很快。KAN架构与rbf相结合，使DeepOKANs能够表示输入参数和输出字段之间更复杂的关系，从而对各种力学问题进行更准确的预测。具体来说，我们评估了DeepOKAN在几个力学问题上的性能，包括1D正弦波、2D正交异性弹性和瞬态泊松问题，与传统deeponet相比，始终实现更低的训练损失和更准确的预测。这种方法将为进一步提高神经算子的性能铺平道路。

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引用次数: 0

Constraints adjusted material with penalization method for topology optimization with minimum and maximum length controls 用最小和最大长度控制拓扑优化的惩罚法调整约束材料

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-01-14 DOI: 10.1016/j.cma.2025.117731

Chuan Luo

This paper presents the Constraints Adjusted Material with Penalization (CAMP) method, a novel approach to computational design for manufacturing, e.g. minimum and maximum length controls in topology optimization, without the need for additional explicit constraints. The proposed method is demonstrated on benchmark problems of minimum compliance and heat transfer, demonstrating its ability to yield crisp optimized designs while adhering to length scale requirements. Numerical results show that CAMP outperforms traditional constraint-aggregation methods, offering superior design performance and improved computational efficiency. CAMP’s simplicity, robustness, and versatility make it a promising solution for a broad range of constrained optimization challenges.

本文提出了约束调整材料惩罚（CAMP）方法，这是一种新的制造计算设计方法，例如拓扑优化中的最小和最大长度控制，而不需要额外的显式约束。该方法在最小顺应性和传热的基准问题上进行了验证，证明了其在满足长度尺度要求的同时产生清晰优化设计的能力。数值结果表明，该方法优于传统的约束聚合方法，具有更好的设计性能和计算效率。CAMP的简单性、健壮性和多功能性使其成为解决广泛约束优化挑战的有希望的解决方案。

引用次数: 0

Shear-flexible geometrically exact beam element based on finite differences 基于有限差分的剪切柔性几何精确梁单元

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-01-13 DOI: 10.1016/j.cma.2024.117671

Milan Jirásek , Martin Horák , Emma La Malfa Ribolla , Chiara Bonvissuto

The proposed two-dimensional geometrically exact beam element extends our previous work by including the effects of shear distortion, and also of distributed forces and moments acting along the beam. The general flexibility-based formulation exploits the kinematic equations combined with the inverted sectional equations and the integrated form of equilibrium equations. The resulting set of three first-order differential equations is discretized by finite differences and the boundary value problem is converted into an initial value problem using the shooting method. Due to the special structure of the governing equations, the scheme remains explicit even though the first derivatives are approximated by central differences, leading to high accuracy. The main advantage of the adopted approach is that the error can be efficiently reduced by refining the computational grid used for finite differences at the element level while keeping the number of global degrees of freedom low. The efficiency is also increased by dealing directly with the global centerline coordinates and sectional inclination with respect to global axes as the primary unknowns at the element level, thereby avoiding transformations between local and global coordinates. Two formulations of the sectional equations, namely the widely used Reissner model and a less common version referred to as the Ziegler model, are presented and compared. In particular, stability of an axially loaded beam/column is investigated and the connections to the Haringx and Engesser stability theories are discussed. Both approaches are tested in a series of numerical examples, which illustrate (i) high accuracy with quadratic convergence when the spatial discretization is refined, (ii) easy modeling of variable stiffness along the element (such as rigid joint offsets), (iii) efficient and accurate characterization of the buckling and post-buckling behavior.

提出的二维几何精确梁单元扩展了我们以前的工作，包括剪切变形的影响，以及沿梁作用的分布力和力矩。基于柔性的一般公式利用运动学方程与逆截面方程和平衡方程的积分形式相结合。将三个一阶微分方程的结果集用有限差分离散化，用射击法将边值问题转化为初值问题。由于控制方程的特殊结构，即使一阶导数由中心差分近似，该方案仍然显式，从而导致高精度。所采用的方法的主要优点是，在保持较低的全局自由度的同时，通过在单元级别上细化用于有限差分的计算网格，可以有效地减少误差。通过直接处理全局中心线坐标和相对于全局轴的截面倾角作为元素级的主要未知数，从而避免了局部坐标和全局坐标之间的转换，也提高了效率。提出并比较了截面方程的两种形式，即广泛使用的Reissner模型和不太常用的Ziegler模型。特别地，研究了轴向加载梁/柱的稳定性，并讨论了其与哈林克斯和恩格尔稳定性理论的联系。这两种方法都在一系列数值实例中进行了测试，结果表明：(1)当空间离散化得到改进时，具有二次收敛的高精度；(2)沿单元（如刚性关节偏移量）的可变刚度易于建模；(3)有效和准确地表征屈曲和后屈曲行为。

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引用次数: 0

Hybrid-PFC: Coupling the phase-field crystal model and its amplitude-equation formulation 混合相场晶体模型：耦合相场晶体模型及其振幅方程公式

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-01-13 DOI: 10.1016/j.cma.2024.117719

Maik Punke , Marco Salvalaglio

The phase-field crystal (PFC) model describes crystal structures on diffusive timescales through a periodic, microscopic density field. It has been proposed to model elasticity in crystal growth and encodes most of the phenomenology related to the mechanical properties of crystals like dislocation nucleation and motion, grain boundaries, and elastic or interface-energy anisotropies. To overcome limitations to small systems, previous studies introduced a coarse-grained formulation focusing on slowly varying complex amplitudes of the microscopic density field. This amplitude-PFC (APFC) model describes well elasticity and dislocations while approximating microscopic features and being limited in describing large-angle grain boundaries. We present here the foundational concepts for a hybrid multiscale PFC-APFC framework that combines the coarse-grained description of the APFC model in bulk-like crystallites while exploiting PFC resolution at dislocations, grain boundaries, and interfaces or surfaces. This is achieved by coupling the two models via an advanced discretization based on the Fourier spectral method and allowing for local solution updates. This discretization also generalizes the description of boundary conditions for PFC models. We showcase the framework capabilities through two-dimensional benchmark simulations. We also show that the proposed formulation allows for overcoming the limitations of the APFC model in describing large-angle grain boundaries.

相场晶体（PFC）模型通过一个周期的微观密度场来描述晶体在扩散时间尺度上的结构。它已经被提出来模拟晶体生长中的弹性，并编码大多数与晶体力学性能相关的现象，如位错成核和运动、晶界、弹性或界面能量各向异性。为了克服小系统的局限性，以前的研究引入了一种粗粒度公式，专注于微观密度场缓慢变化的复杂振幅。这种振幅- pfc （APFC）模型能很好地描述弹性和位错，同时接近微观特征，但在描述大角度晶界时受到限制。我们在这里提出了混合多尺度PFC-APFC框架的基本概念，该框架结合了块状晶体中APFC模型的粗粒度描述，同时利用了位错、晶界和界面或表面的PFC分辨率。这是通过基于傅里叶谱方法的高级离散化耦合两个模型并允许局部解决方案更新来实现的。这种离散化也推广了PFC模型边界条件的描述。我们通过二维基准模拟展示了框架的功能。我们还表明，所提出的公式可以克服APFC模型在描述大角度晶界方面的局限性。

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引用次数: 0

Exploring energy minimization to model strain localization as a strong discontinuity using Physics Informed Neural Networks 探索能量最小化模型应变局部化作为强不连续使用物理通知神经网络

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-01-11 DOI: 10.1016/j.cma.2024.117724

Omar León , Víctor Rivera , Angel Vázquez-Patiño , Jacinto Ulloa , Esteban Samaniego

We explore the possibilities of using energy minimization for the numerical modeling of strain localization in solids as a sharp discontinuity in the displacement field. For this purpose, we consider (regularized) strong discontinuity kinematics in elastoplastic solids. The corresponding mathematical model is discretized using Artificial Neural Networks (ANNs), aiming to predict both the magnitude and location of the displacement jump from energy minimization, i.e., within a variational setting. The architecture takes care of the kinematics, while the loss function takes care of the variational statement of the boundary value problem. The main idea behind this approach is to solve both the equilibrium problem and the location of the localization band by means of trainable parameters in the ANN. As a proof of concept, we show through both 1D and 2D numerical examples that the computational modeling of strain localization for elastoplastic solids using energy minimization is feasible.

我们探索了在位移场中使用能量最小化进行应变局部化数值模拟的可能性。为此，我们考虑弹塑性固体中的（正则化的）强不连续运动学。利用人工神经网络（ann）对相应的数学模型进行离散化，旨在从能量最小化，即在变分设置下预测位移跳变的大小和位置。体系结构负责运动学，而损失函数负责边值问题的变分表述。该方法的主要思想是利用人工神经网络中的可训练参数来解决平衡问题和定位带的定位问题。作为概念的证明，我们通过一维和二维数值实例表明，使用能量最小化的弹塑性固体应变局部化的计算建模是可行的。

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引用次数: 0

A fully decoupled, iteration-free, unconditionally stable fractional-step scheme for dispersed multi-phase flows 离散多相流的完全解耦、无迭代、无条件稳定的分步格式

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-01-10 DOI: 10.1016/j.cma.2024.117712

Douglas R.Q. Pacheco

Volume-averaged flow equations model fluid systems with two or more interpenetrating phases, as used in various engineering and science applications. Each fluid obeys its own set of Navier–Stokes equations, and the interphase coupling occurs via mass conservation, drag forces, and a common pressure shared by all phases. Therefore, designing decoupling schemes to avoid costly monolithic solvers is a complex, yet very relevant task. In particular, it requires treating the pressure explicitly in a stable way. To accomplish that, this article presents an incremental pressure-correction method built upon the fact that the mean (volume-averaged) flow field is incompressible, even though each individual phase may have a non-solenoidal velocity. To completely and stably decouple the phase equations, the drag is made implicit–explicit (IMEX). Furthermore, by treating all nonlinear terms in a similar IMEX fashion, the new method completely eliminates the need for Newton or Picard iterations. At each time step, only linear advection–diffusion–reaction and Poisson subproblems need to be solved as building blocks for the multi-phase system. Unconditional temporal stability is rigorously proved for the method, i.e., no CFL conditions arise. The stability and first-order temporal accuracy of the scheme are confirmed via two-phase numerical examples using finite elements for the spatial discretisation.

体积平均流动方程模拟具有两个或多个互穿相的流体系统，用于各种工程和科学应用。每种流体都遵循自己的一套Navier-Stokes方程，并且通过质量守恒、阻力和所有相共享的共同压力来实现相间耦合。因此，设计解耦方案以避免昂贵的单片求解器是一项复杂但非常相关的任务。特别是，它要求以稳定的方式明确地处理压力。为了实现这一目标，本文提出了一种增量压力校正方法，该方法建立在平均（体积平均）流场不可压缩的事实之上，即使每个单独的相可能具有非螺线线速度。为了完全稳定地解耦相位方程，将阻力进行隐式显式（IMEX）处理。此外，通过以类似的IMEX方式处理所有非线性项，新方法完全消除了牛顿或皮卡德迭代的需要。在每个时间步，只需要解决线性平流-扩散-反应和泊松子问题，作为多相系统的基础。严格证明了该方法的无条件时间稳定性，即不存在CFL条件。利用有限元进行空间离散的两相数值算例验证了该方案的稳定性和一阶时间精度。

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引用次数: 0

A multi-GPU based high-performance computing framework in elastodynamics simulation using octree meshes 基于多gpu的八叉树网格弹性动力学仿真高性能计算框架

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-01-10 DOI: 10.1016/j.cma.2024.117723

Shayan Mohammadian, Ankit S. Kumar, Chongmin Song

This paper proposes a high-performance computing framework for large-scale elastodynamic analysis utilizing Graphics Processor Units (GPUs). The study adopts an octree algorithm for automatic mesh generation. The scaled boundary finite element method (SBFEM) is employed with the octree mesh, eliminating hanging nodes between octree cells with different sizes. This approach significantly reduces the computational cost and memory requirement by exploiting the limited number of master cells in a balanced octree grid, and is advantageous for GPU computation. The parallelization is achieved through mesh-partitioning techniques and message-passing-interface (MPI) directives, complemented by the NVIDIA Collective Communication Library (NCCL) for optimal point-to-point communication between GPUs in high-performance computing (HPC) facilities. The HPC framework is implemented for both explicit and implicit dynamic analysis. The preconditioned conjugate gradient method is employed for the equation solution in the implicit analysis. Numerical examples are presented for validation of the implementation and for demonstrating the capabilities of the GPU implementation. An image-based 3D model representing a portion of the Moon’s complex surface is simulated with a layered structure comprising of approximately 440 million degrees of freedom. Using the explicit solver, a speed-up of 865 is achieved on a single computational node equipped with eight NVIDIA A100 GPUs in parallel. A 3D virtual city comprising of approximately 61 million degrees of freedom is modelled using the implicit solver.

本文提出了一种利用图形处理器单元（gpu）进行大规模弹性动力学分析的高性能计算框架。本研究采用八叉树算法自动生成网格。八叉树网格采用缩放边界有限元法（SBFEM），消除了不同大小的八叉树单元之间的挂节点。该方法利用平衡八叉树网格中有限的主单元，大大降低了计算成本和内存需求，有利于GPU计算。并行化是通过网格划分技术和消息传递接口（MPI）指令实现的，辅以NVIDIA集体通信库（NCCL），以实现高性能计算（HPC）设施中gpu之间的最佳点对点通信。HPC框架实现了显式和隐式动态分析。隐式分析中，采用预条件共轭梯度法求解方程。给出了数值实例来验证该实现，并演示了GPU实现的能力。一个基于图像的3D模型代表了月球复杂表面的一部分，模拟了一个由大约4.4亿个自由度组成的分层结构。使用显式求解器，在并行配置8个NVIDIA A100 gpu的单个计算节点上实现了865的加速。利用隐式求解器对一个包含约6100万个自由度的三维虚拟城市进行建模。

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引用次数: 0

Intermediate flexural crack debonding of externally bonded FRP in RC beams through a FEM formulation based on positions 基于位置的FRP外粘钢筋混凝土梁中间弯曲裂缝的有限元解缝方法

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-01-10 DOI: 10.1016/j.cma.2024.117716

Danilo Silva Bomfim, Humberto Breves Coda, Rodrigo Ribeiro Paccola

This study presents a new strategy for simulating the coupling of internal and external reinforcements in continuum media, accounting for large translations and rotations, using High Aspect Ratio (HAR) interface elements combined with a tailored technique. In the proposed approach, a J2 damage model is applied to HAR interface elements to simulate the bond–slip behavior of reinforcements. Crack growth in concrete is modeled using the Mesh Fragmentation Technique (MFT), a novel discrete method that employs HAR solid elements to represent cracks via a continuous tension damage model. Additionally, a specialized objective strain measure is proposed to allow large translations and rotations in HAR elements for general analyses. These strategies are specifically applied to simulate reinforced concrete (RC) structures with steel bars and fiber-reinforced polymer (FRP) reinforcements. Notably, HAR interface elements have not previously been applied to FRP reinforcement coupling, nor have MFT and HAR elements been used in large displacement simulations. The results indicate that the combination of these techniques effectively represents the behavior of externally reinforced RC beams with FRP plates or sheets, capturing the brittle failure mode associated with the intermediate debonding of FRP induced by flexural cracks.

本研究提出了一种新的策略来模拟连续介质中内部和外部增强的耦合，考虑到大的平移和旋转，使用高纵横比（HAR）界面元素结合定制技术。该方法将J2损伤模型应用于HAR界面单元，模拟增强材料的粘结滑移行为。采用网格破碎技术（MFT）对混凝土中的裂缝扩展进行建模，这是一种新颖的离散方法，通过连续拉伸损伤模型使用HAR实体单元来表示裂缝。此外，提出了一种专门的客观应变测量，以允许在HAR元素中进行一般分析的大平移和旋转。这些策略特别适用于模拟钢筋和纤维增强聚合物（FRP）增强的钢筋混凝土（RC）结构。值得注意的是，HAR界面单元以前没有应用于FRP加固耦合，也没有MFT和HAR单元用于大位移模拟。结果表明，这些技术的结合有效地代表了FRP板或板的外部增强RC梁的行为，捕捉了与受弯裂缝引起的FRP中间剥离相关的脆性破坏模式。

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引用次数: 0