Finite Elements in Analysis and Design最新文献_第3页

Feature-driven topology optimization of continuum structures with tailored octree meshing 基于定制八叉树网格的连续体结构特征驱动拓扑优化

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.2024.104308

Zhen Liu, Liang Xia

To achieve accurate finite element (FE) analysis and to capture intricate geometric features in topology optimization using the feature mapping method, it is essential to apply extreme finely discretized background FE mesh. However, this necessity comes with increased time and memory overheads and may even lead to the failure of solving 3D problems. Consequently, this paper proposes a tailored 2:1 balanced octree meshing algorithm for topology optimization using the feature mapping method. In particular, two strategies are employed to achieve accurate mesh partitioning. The first strategy applies the exact max-min operator, rather than the smooth approximation operator used in the optimization phase, to define union, intersection, and subtraction operations between geometric components. The second strategy combines vertex function evaluation with revised affine arithmetic to rigorously check function transversality. To enhance efficiency in the latter, the function evaluation of the current mesh reuses the evaluation of the identical vertex from the sibling or parent mesh. Concurrently, only active components intersecting the parent mesh undergo checking for the current mesh, eliminating the need to checking all components. Subsequently, only meshes that intersect any one component and whose neighboring meshes share faces (edges in 2D) are balanced and numbered for structural analysis. This measure avoids numerical singularity arising from void elements and reduces extra time and memory requirements. Finally, algorithms for feature-driven topology optimization, including octree meshing, sensitivity analysis, multi-point constraint and the update of design variables using the method of moving asymptotes (MMA), are implemented on an in-house C++ framework. The feasibility and effectiveness of the proposed algorithms are demonstrated by means of benchmark 2D and 3D numerical designs.

为了实现精确的有限元分析和利用特征映射方法捕捉拓扑优化中复杂的几何特征，必须采用极细离散背景有限元网格。然而，这种必要性会增加时间和内存开销，甚至可能导致解决3D问题的失败。因此，本文提出了一种基于特征映射方法的2:1平衡八叉树网格优化算法。特别地，采用了两种策略来实现精确的网格划分。第一种策略应用精确的极大极小运算符，而不是优化阶段使用的光滑近似运算符，来定义几何组件之间的并、交和减法操作。第二种策略将顶点函数计算与修正的仿射算法相结合，以严格检查函数的横向性。为了提高后者的效率，当前网格的函数求值重用了同级或父网格中相同顶点的求值。同时，只有与父网格相交的活动组件才会对当前网格进行检查，从而消除了检查所有组件的需要。随后，只有与任何一个组件相交且相邻网格共享面（2D中的边）的网格才被平衡和编号以进行结构分析。这一措施避免了由空洞元素引起的数值奇点，减少了额外的时间和内存需求。最后，在一个内部c++框架上实现了特征驱动拓扑优化算法，包括八叉树网格划分、灵敏度分析、多点约束和使用移动渐近线（MMA）方法更新设计变量。通过基准二维和三维数值设计，验证了所提算法的可行性和有效性。

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引用次数: 0

An arbitrary Lagrangian-Eulerian corotational formulation for nonlinear dynamic analysis of arbitrarily curved viscoelastic beams 任意弯曲粘弹性梁非线性动力分析的任意拉格朗日-欧拉公式

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.2024.104303

Lanfeng Deng, Mu-Qing Niu, Xin Yang, Yimin Fan, Li-Qun Chen

In this paper, a three-dimensional arbitrary Lagrangian-Eulerian (ALE) formulation based on the consistent corotational method for flexible structures' large deformation problems is proposed. In contrast with the Lagrangian formulations, the proposed formulation can accurately describe moving boundary and load problems using moving nodes. The ALE formulation for flexible structures with an arbitrarily curved initial geometry is derived for the first time. Moreover, internal and external dampings are integrated into the ALE formulation to consider the energy dissipation induced by the structures' deformation and spatial motion. In addition, the rigid-body motion energy dissipation of the internal damping can be avoided by measuring the element's deformation rate in a corotational frame. Kelvin-Voigt model and the interdependent interpolation element are embedded into the element-independent framework of the corotational method. Then, a general beam element model is established to account for the beam's rotary inertia, viscoelasticity, and shear, bending, torsional, and axial deformations in the ALE formulation. Four examples are provided to validate the proposed formulation. The numerical results obtained using the proposed method are compared with those from the commercial software ANSYS and previously published methods. This comparison illustrates the enhanced efficiency in computation time and computer memory.

本文针对柔性结构的大变形问题，提出了一种基于一致矢量法的三维任意拉格朗日-欧拉（ALE）公式。与拉格朗日公式相比，本文提出的公式可以精确描述移动边界和使用移动节点的荷载问题。首次推导出了具有任意弯曲初始几何形状的柔性结构的 ALE 公式。此外，ALE 公式还集成了内部和外部阻尼，以考虑结构变形和空间运动引起的能量耗散。此外，内部阻尼的刚体运动能量耗散可以通过在惯性框架中测量元素的变形率来避免。Kelvin-Voigt 模型和相互依存的插值元素被嵌入到相关性方法的元素无关框架中。然后，建立了一个通用梁元素模型，以在 ALE 公式中考虑梁的旋转惯性、粘弹性以及剪切、弯曲、扭转和轴向变形。本文提供了四个示例来验证所提出的公式。将使用建议方法获得的数值结果与商业软件 ANSYS 和以前发布的方法进行了比较。比较结果表明，计算时间和计算机内存的效率都有所提高。

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引用次数: 0

Time-domain finite element model of level-dependent nonlinear filter earplug 随电平变化的非线性滤波器耳塞时域有限元模型

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-01-29 DOI: 10.1016/j.finel.2025.104313

Cyril Blondé-Weinmann , Christophe Ruzyla , Sébastien Roth , Pascal Hamery

Nonlinear filter earplugs are hearing protection devices that protect against high-level impulse noises while allowing communication and situational awareness. Unlike conventional passive protectors, these devices provide increasing attenuation with the impulse sound pressure level thanks to filters made of one or more small orifices. Their performances are usually assessed with experimental measurements requiring specific high-cost equipment. This study aims to develop a numerical model based on the time-domain finite element method to provide an alternative approach to evaluate these protectors’ performance. Thus, the modeled acoustic pressures in an acoustic test fixture’s ear canal occluded with a simplified nonlinear filter earplug were estimated. The simulations were performed using high-level impulse noises ranging from 116 to 171 dB-peak. The effects of equilibrium temperature and model limitations were also analyzed. The in-ear sound pressure levels and corresponding protector’s attenuation calculated with the numerical model were compared to previous experimental measurements, and good correspondence was found. Regarding the in-ear peak sound level, deviations comprised between 0.5 dB and 1.3 dB were computed. A change in equilibrium temperature did not induce significant variation in peak sound pressure levels. This study and its underlying observations pave the way for optimizing nonlinear filter characteristics and their integration into new hearing protection devices at lower costs.

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引用次数: 0

Improving the computation of forced responses of periodic structures by the wave-based finite element method via a modified generalized Bloch mode synthesis

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-01-29 DOI: 10.1016/j.finel.2025.104314

Vinícius M. de S. Santos , Thiago de P. Sales , Morvan Ouisse

Periodic structures have attracted interest across various fields of science and engineering due to their unique ability to manipulate wave propagation. The Wave-based Finite Element Method (WFEM) is typically employed to model such systems by relying on the dynamic behavior of a single unit cell of the lattice. However, the WFEM can face challenges in handling unit cell finite element (FE) models with several degrees of freedom (DoFs), as it involves operating with large-sized matrices. Therefore, in this work, we combine the WFEM with the Generalized Bloch-Mode Synthesis (GBMS) to offer a highly efficient and accurate method for modeling periodic structures. Three different types of unit cells were investigated in this study, demonstrating that highly reduced unit cell models can be obtained using the Craig-Bampton (CB) and Local-level Characteristic Constraint (L-CC) model reduction methods. By leveraging the advantages of the WFEM and the reduced-order unit cell models, harmonic forced responses were rapidly and accurately computed. Additionally, we showed that combining the WFEM with the GBMS mitigates numerical issues when computing forced responses, as the boundary DoFs are reduced to a smaller number of equations, avoiding the computation of high-order evanescent modes, a task that can be difficult to perform accurately for some unit cells.

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引用次数: 0

Chebyshev polynomials in moving Kriging meshfree method for laminated composite plates 复合材料层合板移动Kriging无网格法中的切比雪夫多项式

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2025-01-19 DOI: 10.1016/j.finel.2025.104312

Lieu B. Nguyen , P. Phung-Van , Chien H. Thai

We propose a new shape function for a meshfree method by combining of moving Kriging (MK) and Chebyshev interpolations, referred to Chebyshev moving Kriging (CMK) interpolations. This approach improves the accuracy of the numerical solutions by using Chebyshev polynomials in place of traditional polynomials. Additionally, Chebyshev polynomials are utilized to represent a higher-order shear deformation theory (HSDT), called the Chebyshev shear deformation theory (CSDT). A key advantage of the CSDT is its ability to automatically satisfy the condition of zero shear stress at both the top and bottom of the plate. This study introduces an integration of the CMK meshfree method and the CSDT to investigate the static and free vibration characteristics of laminated composite plates. Furthermore, the virtual work principle is exploited to derive the weak forms of the governing equations for laminated composite plates. The CMK meshfree method is then used to compute the displacements and natural frequencies. Numerical simulations are conducted to assess the impacts of geometric parameters, boundary conditions, length-to-thickness ratios, and fibre orientation angles on the displacements and natural frequencies of laminated composite plates. The accuracy of the numerical solutions is assessed by comparing them with the results from 3D elasticity and other shear deformation theories.

本文提出了一种结合移动克里格（MK）插值和切比雪夫（Chebyshev）插值的无网格方法的形状函数，称为切比雪夫移动克里格（CMK）插值。该方法用切比雪夫多项式代替传统的多项式，提高了数值解的精度。此外，切比雪夫多项式被用来表示高阶剪切变形理论（HSDT），称为切比雪夫剪切变形理论（CSDT）。CSDT的一个关键优势是它能够自动满足板的顶部和底部的零剪应力条件。将CMK无网格法与CSDT相结合，研究了复合材料层合板的静、自由振动特性。此外，利用虚功原理推导了复合材料层合板控制方程的弱形式。然后使用CMK无网格法计算位移和固有频率。通过数值模拟研究了几何参数、边界条件、长厚比和纤维取向角对复合材料层合板的位移和固有频率的影响。通过与三维弹性和其他剪切变形理论的结果进行比较，评价了数值解的准确性。

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引用次数: 0

Dynamic topology optimization incorporating the material anisotropy feature for 3D printed fiber composite structures 结合材料各向异性特征对 3D 打印纤维复合材料结构进行动态拓扑优化

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2024-11-26 DOI: 10.1016/j.finel.2024.104281

Kaiyuan Meng , Junyu Fu , Dianwei Qu , Lei Li , Jikai Liu

For additive manufacturing of fiber-reinforced composites, integrated structural topology optimization and deposition path planning is critical in capturing the anisotropic material feature for designing dynamic performance-oriented structures. Hence, this paper proposes a concurrent optimization method for simultaneously optimizing the structural topology and the fiber deposition path. The Solid Orthotropic Materials with Penalization (SOMP) is adopted for interpolating the constitutive equation. Double layers of Smoothing and Projection (DSP) are performed to distinguish the contour-offset layer from the zigzag-infilled substrate. For optimization, the dynamic compliance is adopted as the objective function and three types of dynamic forces are involved: the harmonic excitation, the non-harmonic excitation and the frequency band excitation. A wide range of numerical examples are studied to demonstrate the optimization effect. And at the end, two sets of experiments are performed to test the dynamic responses of the topology optimized and 3D printed fiber composite structures. Enhanced dynamic stability through optimization has been proved by both the numerical calculation and physical tests.

对于纤维增强复合材料的增材制造而言，综合结构拓扑优化和沉积路径规划对于捕捉各向异性材料特征以设计动态性能导向结构至关重要。因此，本文提出了一种同时优化结构拓扑和纤维沉积路径的并行优化方法。采用各向同性材料（Solid Orthotropic Materials with Penalization，SOMP）对构成方程进行插值。采用双层平滑和投影（DSP）来区分等高线偏移层和之字形填充基底。在优化过程中，采用动态顺应性作为目标函数，并涉及三种动态力：谐波激励、非谐波激励和频带激励。研究了大量的数值实例，以展示优化效果。最后，还进行了两组实验，测试拓扑优化和 3D 打印纤维复合材料结构的动态响应。数值计算和物理测试都证明了通过优化提高的动态稳定性。

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引用次数: 0

An adaptive mesh refinement algorithm for crack propagation with an enhanced thermal–mechanical local damage model 使用增强型热机械局部损伤模型进行裂纹扩展的自适应网格细化算法

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2024-11-22 DOI: 10.1016/j.finel.2024.104278

Manh Van Pham , Minh Ngoc Nguyen , Tinh Quoc Bui

This paper presents a computationally effective approach for crack propagation under mechanical and thermal loads based on an adaptive mesh refinement (AMR) approach tailored for our recently developed enhanced local damage model. The mesh-dependent issue encountered in the classical local theories is effectively mitigated by incorporation of fracture energy and element characteristic length into the damage evolution function. Our previous research has demonstrated that being equipped by a novel equivalent strain derived from the bi-energy norm concept and a new damage criterion recently proposed by Mazars et al., the model provides results comparable to the reference experimental data as well as other numerical models based on non-local/gradient damage and phase field method. In the framework of computational efficiency using finite elements, we significantly enhance the performance of our enhanced local model by considering adaptive mesh refinement (AMR). The finite element mesh is locally refined in the damaged zone, and the mesh refinement is conducted on-the-fly during the analysis. For that purpose, the damage parameter whose information is stored at integration points is selected as an indicator to mark whether an element should be refined or not after every loading step. For quadrilateral element mesh, a quad-tree technique is utilized, meaning that each marked element is further divided into four smaller quadrilateral elements. The so-called hanging nodes appear during the process, and the elements are thus treated as

n

-gons and are constructed by the Laplace shape functions, instead of the usual Lagranges shape functions. To show the accuracy and effectiveness of the proposed scheme, several numerical examples involving homogeneous and heterogeneous materials are studied. In these examples, the damage is induced either by only mechanical loads or by both mechanical and thermal loads.

本文介绍了一种在机械和热载荷作用下裂纹扩展的有效计算方法，该方法基于自适应网格细化（AMR）方法，专为我们最近开发的增强型局部损伤模型量身定制。通过将断裂能量和元素特征长度纳入损伤演化函数，有效缓解了经典局部理论中遇到的网格依赖问题。我们之前的研究表明，该模型配备了从双能规范概念中衍生出的新型等效应变以及 Mazars 等人最近提出的新损伤准则，其结果可与参考实验数据以及其他基于非局部/梯度损伤和相场方法的数值模型相媲美。在利用有限元提高计算效率的框架下，我们通过考虑自适应网格细化（AMR）显著提高了增强型局部模型的性能。在受损区域局部细化有限元网格，并在分析过程中即时进行网格细化。为此，在每个加载步骤后，都会选择存储在积分点上的损伤参数作为标识元素是否应被细化的指标。对于四边形元素网格，采用了四叉树技术，即每个标记元素进一步划分为四个较小的四边形元素。在这一过程中会出现所谓的悬挂节点，因此这些元素被视为 n 形，并通过拉普拉斯形状函数而不是通常的拉格朗日形状函数来构建。为了证明所提方案的准确性和有效性，我们研究了几个涉及同质和异质材料的数值示例。在这些示例中，损坏要么仅由机械载荷引起，要么由机械载荷和热载荷同时引起。

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引用次数: 0

Difference in dynamic direct tensile failure mechanism between homogeneous mortar and three-dimensional mesoscopic concrete based on the split Hopkinson tension bar 基于分体式霍普金森拉杆的匀质砂浆与三维中观混凝土动态直接拉伸破坏机理的差异

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2024-11-15 DOI: 10.1016/j.finel.2024.104277

Jing He , Dianah Mazlan , Badorul Hisham Abu Bakar , Li Chen

At the mesoscale, concrete is considered a three-phase composite material comprising stone, mortar, and the interfacial transition zone. Even though mortar is an important component of concrete, its material parameters have not been determined systematically, and they are often modeled by assuming that they are weaker versions of the concrete parameters. Therefore, accurately describing the role of mortar in concrete and the failure mechanism of concrete is difficult. The quasi-static and dynamic direct tensile tests were performed to obtain the stress–strain curves and failure modes of mortar specimens and to establish a formula describing the mortar strain-rate effect. Numerical simulations were then performed using the improved Karagozian and Case concrete models, and the obtained experimental data to clarify the differences in the failure mechanisms of mortar and concrete under dynamic tensile loads. Results showed that concrete had a higher tensile strength but a lower strain-rate effect than mortar. This paper provides an important contribution to study the failure analysis of concrete structures under dynamic loads.

在中尺度上，混凝土被认为是由石子、砂浆和界面过渡区组成的三相复合材料。尽管砂浆是混凝土的重要组成部分，但其材料参数尚未得到系统确定，通常是通过假设其为混凝土参数的弱化版本来建立模型。因此，准确描述砂浆在混凝土中的作用和混凝土的破坏机理十分困难。通过准静态和动态直接拉伸试验，获得了砂浆试件的应力-应变曲线和破坏模式，并建立了描述砂浆应变率效应的公式。然后，利用改进的 Karagozian 和 Case 混凝土模型以及获得的实验数据进行了数值模拟，以阐明砂浆和混凝土在动态拉伸荷载下的破坏机制差异。结果表明，与砂浆相比，混凝土的抗拉强度更高，但应变速率效应更低。本文为研究动荷载下混凝土结构的破坏分析做出了重要贡献。

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引用次数: 0

Fracture process zone modelling of a magnesia spinel refractory using phase field fracture model 利用相场断裂模型建立菱镁尖晶石耐火材料的断裂过程区模型

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2024-11-15 DOI: 10.1016/j.finel.2024.104279

Zain Ali , Shengli Jin , Dietmar Gruber

Fracture in quasi-brittle materials, such as refractories and reinforced concrete, involves complex mechanisms due to a progressive micro-cracking process within a fracture process zone (FPZ). This study employs Wu's phase field model (PFM) to simulate fracture behaviour in a magnesia spinel refractory. The PFM integrates fracture mechanics and damage mechanics, predicting tortuous crack patterns when heterogeneous strength distribution is considered. Numerical simulations, including wedge splitting tests typically applied for fracture testing of refractories, demonstrate PFM's effectiveness in capturing fracture behaviour, offering a robust tool for simulation of fracture of refractories with reduced brittleness. Comparative analysis with experimental data confirms the model's accuracy and applicability.

耐火材料和钢筋混凝土等准脆性材料的断裂涉及复杂的机理，其原因是断裂过程区（FPZ）内的渐进微裂纹过程。本研究采用吴氏相场模型（PFM）来模拟菱镁尖晶石耐火材料的断裂行为。相场模型综合了断裂力学和损伤力学，可预测异质强度分布时的曲折裂纹模式。数值模拟（包括通常用于耐火材料断裂测试的楔形劈裂试验）证明了 PFM 在捕捉断裂行为方面的有效性，为模拟脆性降低的耐火材料的断裂提供了一个可靠的工具。与实验数据的对比分析证实了该模型的准确性和适用性。

引用次数: 0

Concurrent multiscale modelling of woven fabrics: Using beam finite elements with contact at mesoscale 编织物的多尺度并行建模：使用带有中尺度接触的梁有限元

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design

Pub Date : 2024-11-09 DOI: 10.1016/j.finel.2024.104274

Celso Jaco Faccio Júnior , Vijay Nandurdikar , Alfredo Gay Neto , Ajay B. Harish

The mechanical behaviour of textile materials, fundamental to textile composites, is critical for designing advanced material solutions. Mechanical modelling of textiles is highly complex due to the interactions between yarns, resulting in distinct nonlinear characteristics for different textile patterns. Therefore, engineering methods are essential for analysing loading scenarios and integrating decisions about textile patterns, their alignment, and other factors into the design process. One potential approach is the use of multiscale analysis. We present a novel approach for multiscale modelling in this context. Our approach models the mesoscale using beam elements and enhanced contact models to capture the interactions between yarns, while the macroscale employs solid elements with material non-linearity. This developed approach is verified by comparing pure mesoscale and multiscale results using uniaxial, biaxial, and picture frame tests. Additionally, the applicability of the multiscale method is demonstrated under more complex loading conditions. This proposal aims to model the overall mechanical response of textile patterns under complex loading conditions and can be used as a tool to evaluate the mechanical behaviour of textiles comprehensively.

纺织材料的机械性能是纺织复合材料的基础，对于设计先进的材料解决方案至关重要。由于纱线之间的相互作用，纺织品的机械建模非常复杂，导致不同纺织图案具有不同的非线性特征。因此，工程方法对于分析加载情况以及在设计过程中整合纺织品图案、排列和其他因素的决策至关重要。多尺度分析是一种可行的方法。在这种情况下，我们提出了一种新的多尺度建模方法。我们的方法使用梁元素和增强型接触模型对中尺度进行建模，以捕捉纱线之间的相互作用，而宏观尺度则使用具有材料非线性的实体元素。通过单轴、双轴和画框测试，比较纯中尺度和多尺度结果，验证了所开发的方法。此外，在更复杂的加载条件下，多尺度方法的适用性也得到了验证。该建议旨在模拟复杂加载条件下纺织品图案的整体机械响应，可用作全面评估纺织品机械性能的工具。

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引用次数: 0