Finite Elements in Analysis and Design最新文献

Application of zonal Reduced-Order-Modeling to tire rolling simulation

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-02-22 DOI: 10.1016/j.finel.2025.104330

D. Danan , R. Meunier , T. Dairay , T. Homolle , M. Yagoubi

Physic-based simulation remains a key enabler for real-world ever-growing complex industrial systems especially when crucial decisions are needed. While classical approaches have proven their accuracy and robustness over the years and come with a rich mathematical foundation, they suffer from several limitations depending of the underlying physics and use cases. For instance, especially concerning the resolution of Partial Differential Equations (PDEs) in 3 dimensions (3D), classical approaches are known to be computationally expensive. However, it turns out that simple pure data-driven approaches, while allegedly much more efficient from a computational point of view, do not necessarily hold up well regarding physical considerations. In this work, our aim is to investigate the tradeoff between accuracy and computational cost to design efficient and robust physical simulation methods under industrial constraints. In particular, as it is not easy to generate a large dataset through numerical simulations for such a problem, our aim is to design an approach addressing the data scarcity issue. To do so, we propose to hybridize a standard Finite Element Method (FEM) physics-based solver with a zonal Reduced Order Model (ROM) approach to simulate a rolling tire.

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引用次数: 0

An enhanced single Gaussian point continuum finite element formulation using automatic differentiation

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-02-19 DOI: 10.1016/j.finel.2025.104329

Njomza Pacolli , Ahmad Awad , Jannick Kehls , Bjorn Sauren , Sven Klinkel , Stefanie Reese , Hagen Holthusen

This contribution presents an improved low-order 3D finite element formulation with hourglass stabilization using automatic differentiation (AD). Here, the former Q1STc formulation is enhanced by an approximation-free computation of the inverse Jacobian. To this end, AD tools automate the computation and allow a direct evaluation of the inverse Jacobian, bypassing the need for a Taylor series expansion. Thus, the enhanced version, Q1STc+, is introduced. Numerical examples are conducted to compare the performance of both element formulations for finite strain applications, with particular focus on distorted meshes. Moreover, the performance of the new element formulation for an elasto-plastic material is investigated. To validate the obtained results, a volumetric locking-free element based on scaled boundary parametrization is used. Both the implementation of the element routine Q1STc+ and the corresponding material subroutine are made accessible to the public at https://doi.org/10.5281/zenodo.14259791.

本文提出了一种改进的低阶三维有限元计算方法，利用自动微分法（AD）实现沙漏稳定。在这里，前 Q1STc 公式通过无近似计算逆 Jacobian 得到了增强。为此，自动微分工具实现了计算自动化，并允许直接评估逆雅各比，而无需泰勒级数展开。因此，引入了增强版 Q1STc+。通过数值示例，比较了两种元素公式在有限应变应用中的性能，尤其侧重于扭曲网格。此外，还研究了弹塑性材料的新元素公式的性能。为了验证所获得的结果，使用了基于比例边界参数化的体积无锁定元素。元素例程 Q1STc+ 的实现和相应的材料子例程均可通过 https://doi.org/10.5281/zenodo.14259791 公开获取。

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引用次数: 0

Robust multi-physical-material topology optimization with thermal-self-weight uncertain loads

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-02-13 DOI: 10.1016/j.finel.2025.104319

Minh-Ngoc Nguyen , Joowon Kang , Soomi Shin , Dongkyu Lee

Most topology optimization techniques for enhanced designs rely on the premise of deterministic loads. Nevertheless, in actuality, variables such as placements, weights, and orientations of applied loads may inadvertently fluctuate. Deterministic load-based designs may exhibit suboptimal structural performance in the presence of loading uncertainties. Uncertain aspects must be considered in topological optimization to provide robust outcomes. This work introduces an innovative robust multi-physics topology optimization technique for the design of multi-materials in response to unforeseen load variations. A combination of thermo-mechanical and self-weight loads, along with loading uncertainties, is provided based on the extended SIMP technique to achieve resilient designs. The optimized structures can be concurrently refined by minimizing the weighted sum of predicted compliance and standard deviation. The impact of self-weight and heat loads is examined through various cases to validate the proposed strategy.

引用次数: 0

An assumed enhanced strain finite element formulation for modeling hydraulic fracture growth in a thermoporoelastic medium

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-02-11 DOI: 10.1016/j.finel.2025.104320

Fushen Liu

This paper presents an assumed enhanced strain finite element framework for simulating hydraulic fracture propagation in saturated thermoporoelastic media, considering the influence of thermal effects. The proposed approach combines classical thermoporoelasticity theory with a cohesive fracture model to describe the coupled behaviors of fluid flow, rock deformation and fracture propagation. Within this framework, fractures are represented using constant strain triangular elements enriched with constant displacement jumps. The mechanical response of fractures is governed by a trilinear cohesive law, and fracture initiation and propagation are both determined by using standard Newton’s method while maintaining global equilibrium. The numerical framework is verified through a series of examples, including cases without fractures, cases with rigid and deformable fractures, and hydraulic fracture propagation with thermal effects. The results show that thermal stress primarily affects the region near the injection point but has limited impact on fracture length evolution and fluid pressure distribution within the fracture. In contrast, temperature-dependent viscosity can significantly influence hydraulic fracture propagation. This work can be beneficial to our understanding of hydraulic fracture modeling in thermoporoelastic media and provide a potential useful numerical tool for simulating hydraulic fracturing processes with consideration of thermal effects.

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引用次数: 0

Sequential sensor placement for damage detection under frequency-domain dynamics

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-02-11 DOI: 10.1016/j.finel.2025.104315

Mark J. Chen , Kavinayan Sivakumar , Gregory A. Banyay , Brian M. Golchert , Timothy F. Walsh , Michael M. Zavlanos , Wilkins Aquino

Identification and monitoring of damage have a growing importance in the maintenance of structures. A robust active sensing framework that integrates model-based inference and optimal sensor placement is proposed. By tightly coupling measured data and data acquisition scenarios, a simultaneous approach of damage estimation and sensor placement can be used to continuously and accurately assess a structure. In this work, a partial differential equation-constrained formulation for damage estimation is first developed using a conventional model-updating approach with a penalization damage parameter. Then, this formulation is linearized around the damage estimator to produce an Optimal Experimental Design (OED) problem for desirable sensor locations. Hence, the simultaneous sensing framework is postulated using a Fisher Information Matrix (FIM)-based approach as follows: given a current candidate damage state associated with the most up-to-date sensor information, find the next sensor location that minimizes some metric of the FIM and update the damage estimator. The sensing framework is also enhanced by introducing a Modified Error in Constitutive Equations (MECE) functional in the damage estimator. Adding MECE makes the framework more robust by limiting the damage estimator from being trapped in local minima. Through numerical examples, we show that our approach produces accurate damage estimators using a small number of sensor locations. In addition, we compare our results to those obtained using random sensor selections and expertly selected locations.

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引用次数: 0

Stress-related topology optimization based on Isogeometric Analysis and global stress measures

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-02-05 DOI: 10.1016/j.finel.2025.104317

Yupeng Huang, Song Yao, Xing Chen

This paper presents a robust isogeometric topology optimization (ITO) framework that integrates Isogeometric Analysis (IGA) with global stress measures to enhance both accuracy and stability in stress-related structural optimization. Non-Uniform Rational B-Splines (NURBS)-based IGA is employed to ensure higher-order continuity and refined topology representation, enabling precise stress evaluation. The p-norm stress aggregation approximates maximum stress, while incorporating average stress into ITO mitigates oscillations for large p-norm parameters and further reduces sensitivity to

P

. Notably, this approach eliminates stress concentrations even when

P = 3

, and maintains stable convergence as

P

increases up to 40 or more, thereby extending the feasible range of

P

-values. By examining various weight combinations of p-norm and average stress, we reveal how controlling both amplitude and mean stress leads to more uniform and lower stress levels. Additionally, an adaptive continuous scheme for stress constraints further improves convergence stability by gradually tightening stress limits from a relaxed state to the target value. Numerical results confirm that the proposed method consistently delivers accurate, stable, and efficient solutions for stress-related isogeometric topology optimization, marking a significant advancement in the field.

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引用次数: 0

Computational modeling of a residually stressed thick-walled cylinder under the combined action of axial extension and inflation 轴向扩展和膨胀联合作用下残余应力厚壁圆筒的计算模型

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-02-01 DOI: 10.1016/j.finel.2024.104309

Murtadha J. Al-Chlaihawi , Dariel Desena-Galarza , Heiko Topol , José Merodio

Previous studies have shown that the mechanical response of incompressible hyperelastic materials is affected by the occurrence of residual stresses. In the context of biological soft tissues, such residual stresses result from factors that include growth and development processes. The detailed effect of these initial stresses on mechanical behavior remains to be explored in detail. The magnitude and distribution of residual stresses in arterial wall tissue affect the location of the occurrence of instabilities such as bulges. This study aims to develop a new approach to assess material behavior during bifurcation instability in the presence of residual stresses, especially non-planar stresses. A finite element protocol is developed for bifurcation and post-bifurcation of residually stressed thick-walled hyper-elastic circular hollow tubes subjected to axial stretches and internal pressure, incorporating three-dimensional residual stresses. A constitutive equation based on the strain energy function for these tubes is formulated and implemented in ABAQUS, using the Modified Riks method and a user-defined material subroutine (UMAT). Results indicate that bending bifurcation is likely for small axial stretches but becomes less probable with larger axial stretches while bulging bifurcation is expected for all axial stretch values. Pressures associated with pure bulging modes are higher than those for bulging induced by bending, suggesting aneurysms can be delayed by avoiding bending bifurcation. The bulging from bending bifurcation occurs on one side of the tubes, reflecting abdominal aortic aneurysm (AAA) conditions. The unsymmetrical bulge development aligns with the methodology used, whereas balloon-like bulging in pure modes is linked to arterial rupture.

以往的研究表明，不可压缩超弹性材料的力学响应受到残余应力的影响。在生物软组织的情况下，这种残余应力是由生长和发育过程等因素引起的。这些初始应力对力学行为的具体影响还有待进一步探讨。动脉壁组织内残余应力的大小和分布影响着动脉壁内不稳定现象发生的位置。本研究旨在开发一种新的方法来评估材料在残余应力，特别是非平面应力存在时的分岔失稳行为。建立了考虑三维残余应力的厚壁超弹性圆空心管在轴向拉伸和内压作用下的分岔和后分岔有限元方案。利用改进的Riks方法和用户定义的材料子程序（UMAT），在ABAQUS中建立了基于应变能函数的本构方程并实现了该方程。结果表明，当轴向拉伸值较小时，有可能发生弯曲分岔，但当轴向拉伸值较大时，发生弯曲分岔的可能性减小，而在所有轴向拉伸值下均有可能发生胀形分岔。单纯胀形模式下的压力高于弯曲引起的胀形，提示通过避免弯曲分叉可以延缓动脉瘤的发生。管的一侧出现弯曲分叉引起的肿胀，反映了腹主动脉瘤（AAA）的情况。不对称凸起的发展与使用的方法一致，而纯模式下的气球状凸起与动脉破裂有关。

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引用次数: 0

A hybrid stress finite element for the efficient nonlinear analysis of masonry walls based on a multi-failure strength domain 基于多破坏强度域的混合应力有限元对砌体墙体进行有效的非线性分析

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-02-01 DOI: 10.1016/j.finel.2024.104310

G. Bertani , A. Bilotta , A.M. D’Altri , S. de Miranda , F.S. Liguori , A. Madeo

A novel 8-node hybrid stress finite element (FE) is proposed for the efficient nonlinear analysis of in-plane loaded masonry walls. To provide a robust, easy-to-characterize mechanically, and computationally efficient practice-oriented numerical framework, masonry is idealized as an elasto-plastic homogeneous continuum. Elasto-plasticity is considered at the FE level by means of a dual-decomposition approach, with plasticity controlled at Gauss–Lobatto points. A state-of-the-art single-surface multi-failure anisotropic strength domain specifically dedicated to masonry is employed. Multiple limit surfaces are considered and condensed into a unique surface through the RealSoftMax function, preserving the distinction between failure modes and the level of activation of each failure thanks to specific weights. The present numerical framework is tested though several structurally meaningful examples with available numerical and experimental reference solutions, comparing the efficiency of the proposed FE with standard displacement-based FEs, as well as other mixed FEs. As a result, the novel 8-node hybrid stress FE shows superior performance with respect to the other FEs, in terms of accuracy and convergence rate. Accordingly, the present numerical framework allows to simulate accurately the nonlinear response of masonry walls and to track realistically the evolution of the considered failure modes even with a few FEs per wall, so being particularly efficient and appealing in engineering common practice.

本文提出了一种新型的 8 节点混合应力有限元（FE），用于对平面荷载砌体墙进行高效的非线性分析。为了提供一个稳健、易于机械表征且计算效率高的面向实践的数值框架，砌体被理想化为弹塑性均质连续体。弹塑性是通过双重分解方法在 FE 层面上考虑的，塑性受控于高斯-洛巴托点。采用了专门针对砌体的最先进的单面多破坏各向异性强度域。考虑了多个极限曲面，并通过 RealSoftMax 功能将其浓缩为一个独特的曲面，通过特定权重保留了失效模式之间的区别以及每个失效的激活水平。本数值框架通过几个具有结构意义的示例与现有的数值和实验参考解进行了测试，比较了所提出的 FE 与基于位移的标准 FE 以及其他混合 FE 的效率。结果表明，新型 8 节点混合应力 FE 在精度和收敛速度方面都优于其他 FE。因此，本数值框架可以精确模拟砌体墙的非线性响应，即使每面墙只有几个 FE，也能真实跟踪所考虑的破坏模式的演变，因此在工程实践中特别有效和有吸引力。

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引用次数: 0

Advancing industrial finite element software: Developing Model Order Reduction for nonlinear transient thermal problems 工业有限元软件的发展：非线性瞬态热问题的模型降阶

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-02-01 DOI: 10.1016/j.finel.2024.104299

Pierre-Eliot Malleval , Ronan Scanff , David Néron

Over the past two decades, non-intrusive techniques have been used to develop reduced-order models for nonlinear structures in industrial environments. These techniques have placed a significant emphasis on a posteriori methods, which often rely on solutions derived from computationally expensive full-order models. Using a priori methods not relying on the full order model might be preferred as they reduce the computational burden upfront. The intrusiveness of the algorithms associated with these methods limits their introduction into commercial finite element software. Integrating robust and reliable approaches into a certified product is necessary for these methods to spread at an industrial level. This work aligns with this ambition, extending a weakly-intrusive implementation of the LATIN-PGD already embedded into commercial finite element software to transient thermal problems. The novelty of the approach stems from its extensive applicability, enabling the PGD method to address not just specific applications but also to seamlessly handle any nonlinearities, diverse element types, various boundary conditions, and other features inherent in such software. This results in a new comprehensive industrial nonlinear solver, including a priori model order reduction.

在过去的二十年里，非侵入式技术被用于开发工业环境中非线性结构的降阶模型。这些技术非常重视后验方法，后验方法通常依赖于计算成本高昂的全阶模型求解。使用不依赖全阶模型的先验方法可以减轻前期计算负担，因此可能更受欢迎。与这些方法相关的算法的复杂性限制了它们在商业有限元软件中的应用。要想在工业领域推广这些方法，就必须将稳健可靠的方法集成到认证产品中。这项工作正是为了实现这一目标，将已嵌入商用有限元软件的 LATIN-PGD 的弱侵入式实现扩展到瞬态热问题。该方法的新颖之处在于其广泛的适用性，使 PGD 方法不仅能解决特定的应用问题，还能无缝处理任何非线性问题、各种元素类型、各种边界条件以及此类软件固有的其他功能。这就产生了一种新的综合性工业非线性求解器，包括先验模型阶次缩减。

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引用次数: 0

Plate finite elements with arbitrary displacement fields along the thickness 具有沿厚度任意位移场的板有限元

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-02-01 DOI: 10.1016/j.finel.2024.104296

E. Carrera , D. Scano , E. Zappino

The present paper introduces a methodology for formulating two-dimensional structural theories featuring arbitrary kinematic fields. In the proposed approach, each displacement variable can be examined through an independent expansion function, enabling the integration of both classical and higher-order theories within a unified framework. The Carrera Unified Formulation is used to derive the governing equations in a unified form, independent of the expansion adopted for each displacement component. In this paper, plate structural theories are constructed by using polynomial expansions. The finite element method is used to discretize the structure in the reference plane of the plate, utilizing Lagrange-based elements. The Mixed Interpolation of Tensorial Components is adopted to alleviate the shear locking issues. In this study, isotropic plate structures are investigated under various loadings, boundary conditions, and different length-to-thickness ratios. Whenever possible, the present results are compared with analytical and literature solutions. The accuracy of the presented models is evaluated for both displacements and stress components. The findings indicate that the selection of the most appropriate model is strongly dependent on the specific parameters of the individual problem, however, choosing the right model can significantly enhance the efficiency of the numerical analysis.

本文介绍了一种以任意运动场为特征的二维结构理论的表述方法。在所提出的方法中，每个位移变量都可以通过一个独立的扩展函数进行研究，从而在一个统一的框架内整合经典理论和高阶理论。卡雷拉统一公式（Carrera Unified Formulation）用于以统一的形式推导控制方程，与每个位移分量所采用的扩展函数无关。本文采用多项式展开构建板结构理论。利用基于拉格朗日元素的有限元法，在板的参考平面上对结构进行离散化。采用张量成分混合插值法来缓解剪切锁定问题。本研究对各向同性板结构在各种载荷、边界条件和不同长厚比下的情况进行了研究。在可能的情况下，将目前的结果与分析和文献解决方案进行比较。针对位移和应力成分，对所提出模型的准确性进行了评估。研究结果表明，选择最合适的模型在很大程度上取决于各个问题的具体参数，然而，选择正确的模型可以显著提高数值分析的效率。

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引用次数: 0