Finite Elements in Analysis and Design最新文献_第4页

Behavior of cohesive stresses in embedded finite elements based on the strong discontinuity approach 基于强不连续方法的内嵌有限元内聚应力行为

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-11-18 DOI: 10.1016/j.finel.2025.104485

Danilo Cavalcanti , Cristian Mejia , Caio Souza , Carlos A. Mendes , Ignasi de-Pouplana , Guillermo Casas , Deane Roehl

Embedded finite element formulations have gained increased attention for modeling strong discontinuities in solid mechanics problems, as they eliminate the need for mesh conformity required by discrete fracture models. While several such formulations have been extensively studied, particularly regarding strategies to mitigate stress locking, less is understood about the causes and possible remedies to the spurious stress oscillations along cohesive discontinuities. In this work, we employ the Enhanced Assumed Strain framework to derive two of the most popular formulation types: the Kinematically Optimal Symmetric (KOS) and the Statically and Kinematically Optimal Nonsymmetric (SKON). We investigate their performance in a broad range of scenarios, including stick and slip contact conditions, in both two and three dimensions, using linear and quadratic finite elements. Our results show that the SKON formulation consistently yields smoother cohesive stress fields by enforcing local equilibrium in a strong sense. While spurious oscillations are effectively eliminated under stick conditions, small-amplitude oscillations may persist under slip conditions; however, they are significantly reduced compared to the KOS formulation. Finally, we demonstrate the application of the SKON formulation to a fault reactivation problem, confirming its capability to accurately capture stress evolution and assess fault reactivation risk.

嵌入式有限元公式在模拟固体力学问题中的强不连续面方面得到了越来越多的关注，因为它们消除了离散断裂模型所需的网格一致性。虽然已经对几种这样的公式进行了广泛的研究，特别是关于减轻应力锁定的策略，但对沿着内聚不连续的虚假应力振荡的原因和可能的补救措施了解较少。在这项工作中，我们采用增强假设应变框架来推导两种最流行的公式类型：运动最优对称（KOS）和静态和运动最优非对称（SKON）。我们研究了它们在广泛的场景下的性能，包括粘和滑接触条件，在二维和三维，使用线性和二次元有限元。我们的结果表明，SKON配方通过在强意义上强制局部平衡，始终产生更平滑的内聚应力场。虽然在粘滞条件下可以有效地消除伪振荡，但在滑移条件下可能会持续存在小振幅振荡；然而，与KOS配方相比，它们明显减少了。最后，我们演示了SKON公式在断层再激活问题中的应用，证实了其准确捕获应力演化和评估断层再激活风险的能力。

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引用次数: 0

Assessment of the Spalart–Allmaras turbulence model in a stabilized finite element framework for hypersonic turbulent flows using pressure-primitive variables 基于压力原变量的高超声速湍流稳定有限元框架下的Spalart-Allmaras湍流模型评估

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-11-08 DOI: 10.1016/j.finel.2025.104473

Rahul Verma , David Codoni , Craig Johansen , A. Korobenko

This study evaluates the performance of the Spalart–Allmaras (SA) turbulence model within a finite element framework. The streamline upwind Petrov–Galerkin (SUPG) method is employed as a stabilization technique to provide numerical stability. The proposed formulation solves the three-dimensional Navier–Stokes (N-S) equations expressed in primitive variables. The robustness and accuracy of the stabilized framework, incorporating the one-equation SA turbulence model, are assessed across a wide range of Mach numbers using benchmark test cases. The results demonstrate the effectiveness of the present approach in modeling high-speed turbulent flows, including separated boundary layers and shock wave interactions.

本研究在有限元框架内评估了Spalart-Allmaras （SA）湍流模型的性能。采用流线迎风彼得罗夫-伽辽金（SUPG）方法作为稳定技术来提供数值稳定性。该公式求解了以原始变量表示的三维Navier-Stokes （N-S）方程。结合单方程SA湍流模型的稳定框架的鲁棒性和准确性，使用基准测试用例在广泛的马赫数范围内进行了评估。结果证明了该方法在模拟高速湍流流动时的有效性，包括分离边界层和激波相互作用。

引用次数: 0

The adaptive thermo-mechanical-electro-magnetic enriched finite element method for statics analysis of functionally graded magneto-electro-elastic structures 功能梯度磁电弹性结构静力分析的自适应热-机-电磁富集有限元法

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-11-08 DOI: 10.1016/j.finel.2025.104476

Liming Zhou , Guangyu Liang , Jiye Wang , Panpan Zhu

In this paper, the thermo-mechanical-electro-magnetic enriched finite element method (TMEM-EFEM) is proposed to analyze static models of magneto-electro-elastic smart structures. An improvement over the traditional finite element method (FEM) is that the displacement, electric and magnetic fields are fitted by interpolation covering functions. The support domain of the node is constructed by a series of triangular elements. Although the concept of support domain is used, the proposed method does not require high computational cost to solve the extent of the support domain. The feasibility of TMEM-EFEM is demonstrated by a series of numerical examples. The proposed method is proven to be efficient under coarse and distorted meshes. Besides, the adaptive mesh refinement (AMR) technology is used to locally refine functionally graded magneto-electro-elastic smart structures in interested areas under a coarse mesh. The generalized strain energy criterion is used in the AMR technology. Through a series of numerical examples, the high accuracy of the proposed method under the AMR partitioning scheme is demonstrated. The results show that the values of displacement u_z, electric potential Φ and magnetic potential Ψ decrease with the increase of exponential factors. The computational efficiency of TMEM-EFEM is significantly higher than that of FEM, which verifies the correctness and effectiveness of this method.

本文提出了热-机-电磁富集有限元法（TMEM-EFEM）来分析磁-电弹性智能结构的静态模型。对传统有限元法的改进是利用插值覆盖函数拟合位移场、电场场和磁场。节点的支持域由一系列三角形元素构成。虽然采用了支撑域的概念，但该方法求解支撑域范围的计算成本不高。通过一系列数值算例验证了该方法的可行性。在粗糙和变形网格下，该方法是有效的。此外，采用自适应网格细化（AMR）技术在粗网格下对感兴趣区域的功能梯度磁电弹性智能结构进行局部细化。AMR技术采用广义应变能准则。通过一系列的数值算例，证明了该方法在AMR划分方案下具有较高的精度。结果表明：位移uz、电势Φ和磁势Ψ随指数因子的增大而减小；TMEM-EFEM的计算效率明显高于FEM，验证了该方法的正确性和有效性。

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引用次数: 0

PGD-based local surrogate models via overlapping domain decomposition: A computational comparison 基于重叠域分解的pgd局部代理模型：计算比较

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-11-07 DOI: 10.1016/j.finel.2025.104475

Marco Discacciati , Ben J. Evans , Matteo Giacomini

An efficient strategy to construct physics-based local surrogate models for parametric linear elliptic problems is presented. The method relies on proper generalized decomposition (PGD) to reduce the dimensionality of the problem and on an overlapping domain decomposition (DD) strategy to decouple the spatial degrees of freedom. In the offline phase, the local surrogate model is computed in a non-intrusive way, exploiting the linearity of the operator and imposing arbitrary Dirichlet conditions, independently at each node of the interface, by means of the traces of the finite element functions employed for the discretization inside the subdomain. This leads to parametric subproblems with reduced dimensionality, significantly decreasing the complexity of the involved computations and achieving speed-ups up to 100 times with respect to a previously proposed DD-PGD algorithm that required clustering the interface nodes. A fully algebraic alternating Schwarz method is then formulated to couple the subdomains in the online phase, leveraging the real-time (less than half a second) evaluation capabilities of the computed local surrogate models, that do not require the solution of any additional low-dimensional problems. A computational comparison of different PGD-based local surrogate models is presented using a set of numerical benchmarks to showcase the superior performance of the proposed methodology, both in the offline and in the online phase.

提出了一种构造参数线性椭圆问题的基于物理的局部代理模型的有效方法。该方法采用适当的广义分解（PGD）来降低问题的维数，采用重叠域分解（DD）策略来解耦空间自由度。在离线阶段，局部代理模型以非侵入式的方式计算，利用算子的线性，并通过用于子域中离散化的有限元函数的轨迹，在界面的每个节点独立地施加任意的狄利克雷条件。这导致了维度降低的参数子问题，显著降低了所涉及计算的复杂性，并且相对于先前提出的需要聚集接口节点的DD-PGD算法实现了高达100倍的加速。然后制定了一个完全代数交替Schwarz方法来耦合在线阶段的子域，利用计算的局部代理模型的实时（不到半秒）评估能力，不需要解决任何额外的低维问题。使用一组数值基准对不同的基于pgd的局部代理模型进行了计算比较，以展示所提出的方法在离线和在线阶段的优越性能。

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引用次数: 0

A generic tomography-based conforming finite elements model 基于层析成像的通用有限元模型

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-11-05 DOI: 10.1016/j.finel.2025.104472

Chandrashekhar M. Pilgar , Jean-Luc Bouvard , Teddy Fixy , Daniel Pino-Munoz

This study presents a novel, automated pipeline to transform Micro-computed tomography (

μ

CT) images into conformal Finite element analysis (FEA) models with high-quality tetrahedral elements. The proposed methodology uses image separation techniques and levelset methods to isolate distinct material components while avoiding overlaps and voids. A graph-based algorithm further optimizes the separation by grouping components into minimal non-overlapping level sets, enhancing computational efficiency and ensuring geometric fidelity. Subsequent mesh adaptation and remeshing procedures produce conformal meshes that accurately represent complex geometries and boundaries. The framework is validated through three case studies: woven composites, polycrystals, and dental implants, demonstrating its applicability across diverse material systems. This approach provides a robust solution for bridging tomographic imaging and high fidelity simulations, enabling more precise predictions of mechanical behavior and material performance.

本研究提出了一种新的自动化流水线，将微计算机断层扫描（μCT）图像转换为具有高质量四面体单元的共形有限元分析（FEA）模型。所提出的方法使用图像分离技术和水平集方法来隔离不同的材料成分，同时避免重叠和空隙。基于图的算法通过将组件分组到最小的不重叠水平集来进一步优化分离，提高了计算效率并保证了几何保真度。随后的网格适应和网格重新划分程序产生的保形网格，准确地表示复杂的几何形状和边界。该框架通过三个案例研究进行了验证：编织复合材料、多晶体和牙科植入物，证明了它在不同材料系统中的适用性。这种方法为层析成像和高保真模拟提供了一个强大的解决方案，可以更精确地预测机械行为和材料性能。

引用次数: 0

One-way coupled staggered implementation of gradient-enhanced damage models coupled to thermoplasticity 热塑性梯度增强损伤模型的单向耦合交错实现

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-10-31 DOI: 10.1016/j.finel.2025.104471

Johannes Friedlein, Paul Steinmann, Julia Mergheim

Gradient-enhancement of the damage variable for the regularisation of coupled plasticity-damage constitutive models leads to a coupled system of equations. This is mostly solved monolithically due to the strong coupling and often implemented by a thermomechanical substitution approach into commercial finite element solvers. Therewith the analogy between implicit gradient theory and heat equation is utilised. This avoids the implementation of a separate element formulation and is compatible with many existing finite element solvers. However, for some commercial solvers only a staggered thermomechanical approach is available. Therefore, a method is introduced to use a staggered solver for gradient-enhanced damage formulations. The strong coupling is thereby only approximated, but the size and symmetry of the subsystems can be preserved. Moreover, the staggered approach leads to a modular implementation, which enables to stack multiple subsystems without permanently occupying the thermal solver by a single monolithic coupling. This easily extendable multi-purpose use of the thermal solver is demonstrated by a three-field problem solving coupled thermo-plasticity-gradient-damage. The staggered and monolithic approach are compared and investigated by numerical examples.

为了正则化耦合塑性-损伤本构模型，损伤变量的梯度增强导致了一个耦合方程组。由于强耦合，这主要是整体解决的，并且通常通过热机械替代方法实现到商业有限元求解器中。利用隐式梯度理论与热方程的类比。这避免了单独的单元公式的实现，并与许多现有的有限元求解器兼容。然而，对于一些商业解决方案，只有交错的热机械方法是可用的。因此，引入了一种使用交错求解器求解梯度增强损伤公式的方法。因此，强耦合只是近似的，但子系统的大小和对称性可以保持。此外，交错方法导致模块化实现，这使得可以堆叠多个子系统，而无需通过单个单片耦合永久占用热求解器。通过求解耦合热塑性-梯度-损伤的三场问题，证明了热求解器的这种易于扩展的多用途用途。通过数值算例对交错法和整体法进行了比较和研究。

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引用次数: 0

Temperature response bounds analysis for heat conduction problems with spatial uncertainties 空间不确定性热传导问题的温度响应界分析

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-10-30 DOI: 10.1016/j.finel.2025.104474

Weiwei Chen , Wanyi Tian , Bingyu Ni , Rong Wang , Qun Wang , Shouhua Yi

Spatial uncertainties in heat conduction problems, such as uncertain heat sources and boundary condition parameters, significantly influence the temperature response within the control domain. Constructing reliable probabilistic random fields for these uncertainties is often infeasible due to the scarcity of experimental data, particularly in the early design stages. To address this challenge, this paper develops a temperature response bounds analysis method based on the concept of the interval field, enabling the uncertainty analysis of structural temperature responses under limited sample data conditions. For one-dimensional heat conduction problems, analytical formulations of temperature response bounds are derived under three typical boundary conditions. For multi-dimensional problems, a semi-analytical formulation is proposed by integrating the interval field approach with the interval finite element method. The effectiveness and efficiency of the proposed approach are demonstrated through three numerical examples, highlighting its potential for practical engineering applications under data-scarce conditions.

热传导问题中的空间不确定性，如热源和边界条件参数的不确定性，会显著影响控制域中的温度响应。由于实验数据的缺乏，特别是在早期设计阶段，为这些不确定性构建可靠的概率随机场往往是不可行的。针对这一挑战，本文提出了基于区间场概念的温度响应界分析方法，实现了有限样本数据条件下结构温度响应的不确定性分析。对于一维热传导问题，导出了三种典型边界条件下温度响应边界的解析表达式。对于多维问题，将区间域法与区间有限元法相结合，提出了一种半解析式。通过三个数值算例证明了该方法的有效性和效率，突出了其在数据稀缺条件下的实际工程应用潜力。

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引用次数: 0

Multi-objective topological structure design using a modified adaptive weighted sum method 基于改进自适应加权和法的多目标拓扑结构设计

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-10-27 DOI: 10.1016/j.finel.2025.104469

Hyunseung Ryu , Jeonghoon Yoo

This study presents a topological design methodology for thermoelastic structures based on bi-objective and tri-objective optimization formulations. The design objectives are to simultaneously minimize elastic compliance and thermal compliance, while maximizing the first natural frequency. To obtain multi-objective optimization solutions approaching the utopia point, a novel modified adaptive weighted sum method is proposed, where the weight vector is dynamically adjusted using scale factors to effectively generate new Pareto optimal solutions. The effectiveness of the proposed method is validated through quantitative comparisons of optimal solutions obtained using the conventional weighted sum method, the adaptive scaling strategy, and the proposed adaptive weighted sum method. The proposed approach is further validated through its application to both two- and three-dimensional topology optimization problems.

本文提出了一种基于双目标和三目标优化公式的热弹性结构拓扑设计方法。设计目标是同时最小化弹性顺应性和热顺应性，同时最大化第一固有频率。为了获得接近理想点的多目标优化解，提出了一种改进的自适应加权和法，利用尺度因子动态调整权向量，有效地生成新的Pareto最优解。通过对传统加权和方法、自适应缩放策略和自适应加权和方法的最优解进行定量比较，验证了所提方法的有效性。通过对二维和三维拓扑优化问题的应用，进一步验证了该方法的有效性。

引用次数: 0

A novel interpolation scheme using partition-of-unity mapping for multi-material topology optimizations with compliance-based and stress-based designs 基于柔度和应力设计的多材料拓扑优化新插值方法

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-10-23 DOI: 10.1016/j.finel.2025.104470

Tinh Quoc Bui, Minh Ngoc Nguyen

This paper presents an enhanced computational framework for multi-material topology optimization using a novel interpolation scheme with the partition-of-unity (PU) mapping. Inspired by the recent

p

-norm mapping scheme by Yi et al., (2023) the developed scheme inherits the easy-to-implement property, as the interpolation is written in a SIMP-like manner, and the sensitivity with respect to each material phase takes the same form. More importantly, the current scheme addresses the lack of PU property of the

p

-norm scheme, that is, the sum of volume fraction of all material phases within each element must be equal to one. In the

p

-norm scheme setting, the case when the physical densities of the materials are all equal to one is theoretically possible. This phenomenon means the duplication of the element volume. In the developed scheme, the mapping functions are computed in rational form, explicitly satisfying the PU property. The performance of the present method is investigated through six numerical examples: the first three are for the compliance-based designs and the other three are for the stress-based designs including the design of periodic meta-material with high bulk modulus. It is demonstrated in the numerical examples that although the lack of PU property in

p

-norm scheme does not seem to cause problematic issue in compliance-based design with only fixed load, erroneous patterns may appear in more complicated problems, e.g., in compliance-based design with consideration of self-weight load, and in stress-based design. The issue is successfully removed in the proposed PU mapping scheme.

本文提出了一种改进的多材料拓扑优化计算框架，该计算框架采用了一种新颖的统一分割（PU）映射插值方案。受Yi等人（2023）最近的p-范数映射方案的启发，开发的方案继承了易于实现的特性，因为插值是以类似simp的方式编写的，并且相对于每个材料相的灵敏度采用相同的形式。更重要的是，目前的方案解决了p-范数方案缺乏PU特性的问题，即每个单元内所有材料相的体积分数之和必须等于1。在p-范数方案设置中，材料的物理密度都等于1的情况在理论上是可能的。这种现象意味着元素体积的重复。在开发的方案中，映射函数以有理形式计算，显式地满足PU性质。通过六个数值算例研究了该方法的性能：前三个是基于柔度的设计，另外三个是基于应力的设计，包括高体积模量的周期性超材料的设计。数值算例表明，虽然在p范数方案中缺乏PU特性似乎不会导致仅固定荷载的基于柔度的设计出现问题，但在更复杂的问题中，例如在考虑自重荷载的基于柔度的设计中，以及在基于应力的设计中，可能会出现错误模式。在提出的PU映射方案中成功地消除了该问题。

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引用次数: 0

Analytical solutions for Cook’s membrane inferred by open-source learning algorithms: A critical assessment of the expressivity-complexity trade-off 由开源学习算法推断的库克膜的解析解：对表达性-复杂性权衡的关键评估

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-10-13 DOI: 10.1016/j.finel.2025.104466

Huijian Cai, Nhon N. Phan, WaiChing Sun

Cook’s membrane is one of the most popular boundary value problems used to benchmark the performance of finite element models. Despite its popularity, the analytical solution to this boundary value problem remains unknown. As such, Richardson’s extrapolation, which provides a highly accurate displacement at the tip, is often used in verification exercises for finite element software used for analyses and designs. This paper introduces machine learning algorithms, particularly (1) the family of neural additive models and their subsequent symbolic approximations, (2) Kolmogorov-Arnold networks, (3) physics-informed neural networks as well as (4) the classical finite element method, (5) physics-informed polynomials and (6) brute-force symbolic regression algorithm to obtain new analytical solutions that may supplement Richardson’s extrapolation for the verification exercise. We consider two cases: one with a compressible linear elastic model and the other with an incompressible neo-Hookean model, where analytical solutions are unknown. Due to the floating-point representation, we did not seek an analytical solution with no error. Instead, we compare the accuracy, complexity, and interpretability of the solutions of the displacement field obtained from these methods and seek solutions with the optimal trade-off. We find that the best analytical solutions for the linear elastic and incompressible neo-Hookean cases are both obtained via the projected neural additive models followed by a post-processing step, with (1) errors in the orders of

1 0^{- 7}

and

1 0^{- 5}

respectively and (2) complexities an order less than the counterparts obtained from Kolmogorov-Arnold networks. The training algorithms and results are open-source to facilitate third-party verification and further efforts to surpass the benchmark performance established in this paper.

库克膜是最流行的边界值问题之一，用于基准性能的有限元模型。尽管它很流行，但这个边值问题的解析解仍然是未知的。因此，理查德森的外推法提供了尖端高度精确的位移，经常用于分析和设计的有限元软件的验证练习。本文介绍了机器学习算法，特别是(1)神经加性模型家族及其后续符号逼近，(2)Kolmogorov-Arnold网络，(3)物理信息神经网络以及(4)经典有限元法，(5)物理信息多项式和(6)暴力符号回归算法，以获得新的解析解，可以补充理查森的外推验证练习。我们考虑两种情况：一种是可压缩的线弹性模型，另一种是不可压缩的新胡克模型，其中解析解是未知的。由于采用浮点表示，我们没有寻求没有错误的解析解。相反，我们比较了这些方法得到的位移场解的精度、复杂性和可解释性，并寻求最优权衡的解。我们发现线性弹性和不可压缩新hookean情况的最佳解析解都是通过投影神经相加模型和后处理步骤得到的，(1)误差分别在10−7和10−5数量级，(2)复杂性比从Kolmogorov-Arnold网络得到的对应解小一个数量级。训练算法和结果是开源的，方便第三方验证和进一步努力超越本文建立的基准性能。

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引用次数: 0