Computers & Structures最新文献_第10页

A framework for simulation-based transfer path analysis using dynamic substructuring and component mode synthesis 基于动态子结构和构件模态综合的仿真传递路径分析框架

IF 4.8 2区工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computers & Structures

Pub Date : 2026-01-15 Epub Date: 2026-01-19 DOI: 10.1016/j.compstruc.2026.108097

Said El Kadmiri Pedraza , Hans Peter Monner , Stephan Algermissen

This paper presents a simulation-based framework for Transfer Path Analysis (TPA) using Dynamic Substructuring (DS) and Component Mode Synthesis (CMS) in the context of Finite Element Analysis. A new CMS method is introduced, which combines fixed-interface and constraint modes within a dual assembly formulation, referred to as the Fixed-dual Craig-Bampton Method.

The framework enables the application of DS and CMS techniques for Multilevel TPA, offering a structured approach to trace vibration transmission through hierarchical vibrating sublevels. Two families of TPA are defined and investigated: displacement-based (primal) and force-based (dual). A detailed structural example is provided to benchmark several CMS methods and to evaluate the trade-offs between computational efficiency and accuracy in numerical TPA.

The results highlight the advantages of Multilevel TPA in isolating critical substructures. The benchmark analysis establishes the Craig-Bampton Method (primal) and the novel Fixed-dual Craig-Bampton Method (dual) as the most suitable CMS approaches for numerical TPA. Finally, displacement-based and force-based TPA results are compared. Both approaches exhibit different contribution results, leading to different interpretations of the Transfer Path Analysis.

本文在有限元分析的背景下，提出了一种基于仿真的基于动态子结构（DS）和构件模态综合（CMS）的传递路径分析（TPA）框架。介绍了一种新的CMS方法，该方法将固定接口和约束模式结合在一个双装配公式中，称为固定-对偶克雷格-班普顿方法。该框架使DS和CMS技术应用于多级TPA，提供了一种结构化的方法来跟踪通过分层振动子级的振动传输。定义和研究了两类TPA：基于位移的（原始）和基于力的（双重）。给出了一个详细的结构示例，对几种CMS方法进行了基准测试，并评估了数值TPA中计算效率和精度之间的权衡。结果突出了多层TPA在隔离关键子结构方面的优势。基准分析确定Craig-Bampton方法（原始）和新型固定对偶Craig-Bampton方法（对偶）是最适合数值TPA的CMS方法。最后，比较了基于位移和基于力的TPA结果。两种方法表现出不同的贡献结果，导致对传递路径分析的不同解释。

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引用次数: 0

Multi-material topology optimization of negative thermal expansion metamaterial structures based on element-free Galerkin method 基于无单元伽辽金法的负热膨胀超材料结构多材料拓扑优化

IF 4.8 2区工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computers & Structures

Pub Date : 2026-01-15 Epub Date: 2025-12-29 DOI: 10.1016/j.compstruc.2025.108080

Jianping Zhang, Jiahong Chen, Ruiyuan Gao, Yafei Yang, Wang Kuang, Shuying Wu, Zhiqiang Zhang, Zhijian Zuo

A novel multi-material topology optimization framework based on element-free Galerkin method is developed for designing novel symmetric and chiral negative thermal expansion (NTE) metamaterial structures. A meshless multi-material interpolation model is established by using discrete material optimization to design multi-material NTE metamaterial structures and the equivalent properties of microstructures are evaluated by the numerical homogenization method. The framework is evaluated through numerical examples at both macroscopic and microscopic scales. The effective performance of the optimized structures is verified through simulation analysis and additive manufacturing. The effects of material volume fraction, thermal expansion ratio of the constituent materials and the number of materials on optimal NTE metamaterial structures are evaluated. The results indicate that when two materials are utilized, setting the ratio of the coefficients of thermal expansion between 1:30 and 1:10, along with maintaining the volume fraction ratio of the material with low coefficient of thermal expansion to the material with high coefficient of thermal expansion within the range of 1:1 to 2:1, structures with more excellent negative thermal expansion performance can be obtained. It is suggested that the number of materials constituting the NTE metamaterial structure be 2 or 3, which can balance the structural performance and manufacturability.

提出了一种基于无单元伽辽金方法的多材料拓扑优化框架，用于设计新型对称手性负热膨胀（NTE）超材料结构。采用离散材料优化方法建立了无网格多材料插值模型，设计多材料NTE超材料结构，并采用数值均匀化方法评估微观结构的等效性能。通过宏观和微观尺度的数值算例对该框架进行了评价。通过仿真分析和增材制造验证了优化结构的有效性能。考察了材料体积分数、组成材料的热膨胀比和材料数量对最佳NTE超材料结构的影响。结果表明：当两种材料同时使用时，将热膨胀系数之比设置在1:30 ~ 1:10之间，同时保持热膨胀系数低的材料与热膨胀系数高的材料的体积分数比在1:1 ~ 2:1之间，可以得到具有更优异的负热膨胀性能的结构。建议构成NTE超材料结构的材料数量为2或3种，以平衡结构性能和可制造性。

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引用次数: 0

Path-independent sensitivity-driven topology optimization for continuum structures with combined nonlinearities 组合非线性连续体结构的路径无关灵敏度驱动拓扑优化

IF 4.8 2区工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computers & Structures

Pub Date : 2026-01-01 Epub Date: 2025-11-17 DOI: 10.1016/j.compstruc.2025.108044

Leijia Wang, Hui Xia, Huzhi Zhang, Mingqiao Zhu

This work presents an Evolutionary Structural Optimization (ESO) based topology optimization methodology for continuum structures subjected to combined material and geometric nonlinearities. The objective is compliance minimization, wherein stress constraints are implicitly addressed via the material constitutive model. The methodology integrates ESO with nonlinear Finite Element Analysis (FEA) introduces a novel sensitivity scheme derived from elemental strain energy densities at the final converged state, enhancing theoretical consistency and computational simplicity for path-dependent problems compared to conventional adjoint approaches. An efficient computational strategy couples MATLAB optimization logic with commercial FEA software using element birth–death techniques, achieving significant data transfer reduction. The methodology’s effectiveness and robustness are validated using benchmark examples involving compliance minimization for structures under static loads with combined material yielding and large deformations. Furthermore, the use of an ideal elastoplastic material model is shown to inherently manage stress constraints, leveraging the yield strength as a natural limiter, thereby providing a practical approach for designing structures under complex nonlinear conditions without requiring explicit stress constraints. This contribution advances the field by providing a theoretically consistent sensitivity analysis for path-dependent problems and offering a robust, and readily implementable methodology for nonlinear topology optimization in engineering practice.

本文提出了一种基于演化结构优化（ESO）的连续体结构拓扑优化方法。目标是顺应最小化，其中应力约束通过材料本构模型隐含地解决。该方法将ESO与非线性有限元分析（FEA）相结合，引入了一种新的灵敏度格式，该格式由最终收敛状态的元素应变能密度导出，与传统的伴随方法相比，增强了路径相关问题的理论一致性和计算简单性。一种有效的计算策略将MATLAB优化逻辑与商业有限元软件结合，采用元素生-死技术，实现了显著的数据传输减少。该方法的有效性和鲁棒性通过基准示例进行验证，该示例涉及在静态载荷下具有复合材料屈服和大变形的结构的柔度最小化。此外，使用理想弹塑性材料模型固有地管理应力约束，利用屈服强度作为自然限制，从而为复杂非线性条件下设计结构提供了一种实用的方法，而不需要明确的应力约束。这一贡献通过为路径相关问题提供理论上一致的灵敏度分析，并为工程实践中的非线性拓扑优化提供鲁棒且易于实现的方法，从而推动了该领域的发展。

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引用次数: 0

A peridynamic-lattice Boltzmann-immersed boundary hybrid model for fluid interactions with low-density flexible structures 流体与低密度柔性结构相互作用的周动力-晶格玻尔兹曼-浸入边界混合模型

IF 4.8 2区工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computers & Structures

Pub Date : 2026-01-01 Epub Date: 2025-11-24 DOI: 10.1016/j.compstruc.2025.108043

Ya Zhang , Tian Bao , Yu Yang , Yonghao Zhang , Dongyang Chen , Qiaogao Huang , Guang Pan

The coupling of peridynamics model and lattice Boltzmann method using immersed boundary method can effectively simulate strong fluid structure interactions. However, the current hybrid models fail to describe flow-induced large deformation, fracture and damage of low-density structures, which restricts their applications in engineering design simulations. To overcome this restriction, we propose an advanced algorithm that implements velocity correction points throughout the solid subdomains, where strong coupling through simultaneous velocity corrections in both solid structures modelled with peridynamics and fluid domains solved with lattice Boltzmann method is implemented at each time step, utilizing an implicit velocity correction scheme. Consequently, this method enables the simulation of large deformation and fracture of low-density flexible structures, as validated by a range of benchmark cases. Therefore, the proposed peridynamic-lattice Boltzmann-immersed boundary hybrid model is capable of simulating strong fluid structure interactions across a range of structural densities—whether greater than, less than, or equal to the fluid density. In addition, the present scheme significantly improves computational accuracy for fluid structure interactions with rotational structures.

采用浸入边界法将周动力模型与晶格玻尔兹曼方法耦合，可以有效地模拟强流体结构相互作用。然而，目前的混合模型无法描述低密度结构的大变形、断裂和损伤，限制了其在工程设计模拟中的应用。为了克服这一限制，我们提出了一种先进的算法，该算法在整个实体子域实现速度校正点，其中在每个时间步上，利用隐式速度校正方案，通过在用周动力学建模的实体结构和用晶格玻尔兹曼方法求解的流体域同时进行速度校正来实现强耦合。因此，该方法能够模拟低密度柔性结构的大变形和断裂，并通过一系列基准案例进行了验证。因此，所提出的周动力-晶格玻尔兹曼-浸入边界混合模型能够在一定的结构密度范围内模拟强流体-结构相互作用，无论结构密度是大于、小于还是等于流体密度。此外，该方案显著提高了流体结构与旋转结构相互作用的计算精度。

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引用次数: 0

A phase-field regularized cohesive zone model to bridge pore architecture and R-curve behavior in geopolymer composites 一种相场正则化黏结带模型来桥接地聚合物复合材料的孔隙结构和r曲线行为

IF 4.8 2区工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computers & Structures

Pub Date : 2026-01-01 Epub Date: 2025-11-14 DOI: 10.1016/j.compstruc.2025.108034

Reshmi Maria Jose, Sudakshina Dutta

Micropores are prevalent in composite materials that play a decisive role in their overall macroscopic behavior. Determining the mechanical response accurately demands a detailed consideration of the pore characteristics such as volume fraction and size distribution. The present study focuses on the prediction of the nucleation and propagation of damage from pores in geopolymer composites, a new class of sustainable construction materials. A numerical model, realistically representing the pore features, is developed based on the images obtained from SEM analysis. Using the phase-field regularized cohesive zone model, the fracture of the material under uniaxial tension and flexure is studied. The variation of the crack pattern and the macroscopic response with different microstructural features, such as pore morphology, elastic properties, and matrix fracture energy are explored through an extensive parametric study. The model is capable of capturing the complex crack trajectories stemming from the statistical distribution of the pores in the material. The study offers a detailed view of the toughening mechanisms and fracture resistance inherent in geopolymer composites under tensile loads. The findings provide significant insight into how microstructural design can optimize the fracture performance of this class of materials.

微孔在复合材料中普遍存在，对复合材料的宏观性能起着决定性的作用。准确地确定力学响应需要详细考虑孔隙特征，如体积分数和尺寸分布。地聚合物复合材料是一种新型的可持续建筑材料，对其孔隙损伤的成核和扩展进行了研究。基于扫描电镜图像，建立了能真实反映孔隙特征的数值模型。采用相场正则内聚区模型，研究了材料在单轴拉伸和弯曲作用下的断裂。通过广泛的参数化研究，探讨了不同微观结构特征（如孔隙形态、弹性性能和基体断裂能）下裂纹模式和宏观响应的变化。该模型能够捕捉材料中孔隙的统计分布所产生的复杂裂纹轨迹。该研究提供了在拉伸载荷下地聚合物复合材料固有的增韧机制和抗断裂性的详细视图。这些发现为微观结构设计如何优化这类材料的断裂性能提供了重要的见解。

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引用次数: 0

Data-driven modeling of the plastic anisotropy of sheet metal with an investigation of its material symmetry based on cylindrical cup drawing experiments 基于圆柱杯拉伸实验的金属薄板塑性各向异性数据驱动建模及其材料对称性研究

IF 4.8 2区工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computers & Structures

Pub Date : 2026-01-01 Epub Date: 2025-11-05 DOI: 10.1016/j.compstruc.2025.108011

Stefan C. Soare , Seonghwan Choi , Myoung-Gyu Lee

Predicting the outcome of a cylindrical cup drawing experiment is one of the most difficult challenges for both the constitutive model of the sheet and the finite element simulation of the experiment. Results using conventional yield functions are often limited to qualitative predictions (number of ears and their locations). Here we retain the standard phenomenology of metal plasticity and use instead a data-driven approach to the modeling of its constitutive elements—yielding and flow. For better quantitative predictions, the issue of the asymmetries of the cup height profiles observed in many cupping experiments needs to be addressed. For this, we construct a weakly orthotropic modeling function, based on a feed-forward neural network. Central to such data-driven constitutive modeling is the data generating scheme. For sheet metal plasticity we propose an enhanced interpolation scheme allowing for a thorough control of the yielding and flow properties in the drawing regime. The interpolation scheme is ideally suited for inferring data from complex experiments such as cup drawing. We demonstrate our methodology by performing simulations of two cupping experiments, with aluminum alloys AA2090T3 and AA6016T4. By comparison with orthotropic models, the weakly orthotropic neural network model shows the best quantitative agreement with the outcome of the experiments.

圆柱杯拉伸实验结果的预测是板料本构模型和实验有限元模拟的难点之一。使用传统产量函数的结果通常局限于定性预测（耳数及其位置）。在这里，我们保留了金属塑性的标准现象学，并使用数据驱动的方法来建模其本构元素-屈服和流动。为了更好的定量预测，在许多拔罐实验中观察到的杯子高度轮廓的不对称问题需要解决。为此，我们构造了一个基于前馈神经网络的弱正交各向异性建模函数。这种数据驱动的本构建模的核心是数据生成方案。对于钣金塑性，我们提出了一种增强的插值方案，允许在拉伸状态下彻底控制屈服和流动特性。该插值方案非常适合于从诸如杯形图等复杂实验中推断数据。我们通过模拟AA2090T3和AA6016T4铝合金的拔罐实验来验证我们的方法。通过与正交各向异性模型的比较，弱正交各向异性神经网络模型与实验结果的定量一致性最好。

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引用次数: 0

Flexoelectricity effects on smart piezoelectric nanoplates using an isogeometric analysis-based Chebyshev shear deformation theory 基于切比雪夫剪切变形理论的智能压电纳米片挠性电效应研究

IF 4.8 2区工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computers & Structures

Pub Date : 2026-01-01 Epub Date: 2025-11-20 DOI: 10.1016/j.compstruc.2025.108033

P.T. Hung , H. Nguyen-Xuan , M. Abdel-Wahab , Chien H. Thai , P. Phung-Van

This study conducts a comprehensive investigation into free vibration and static behaviors of smart piezoelectric nanoplates, incorporating electromechanical coupling phenomena, particularly the flexoelectric effect. The flexoelectric effect, which characterizes the interaction between electric polarization and strain gradient, is considered by capturing size-dependent properties at the nanoscale. To enhance modeling accuracy, the third-order Chebyshev shear deformation theory is employed, naturally fulfilling the zero-shear stress conditions on the top and bottom surfaces of the plate without requiring supplementary constraints. For the computation of nanoplate displacement and natural frequency, isogeometric analysis is utilized to discretize the problem domain, offering superior geometric representation and computational efficiency. The present study systematically investigates the effects of flexoelectricity boundary conditions and material properties on structural behaviors of smart piezoelectric nanoplates. Numerical results demonstrate that the flexoelectric effect significantly enhances the stiffness and natural frequency of piezoelectric nanoplates, particularly for thinner structures. As thickness increases, this influence diminishes and the results converge toward classical predictions. The findings provide valuable insights for the design of nanoscale piezoelectric and flexoelectric devices in smart structural applications.

本研究对智能压电纳米片的自由振动和静态行为进行了全面的研究，并考虑了机电耦合现象，特别是挠曲电效应。挠曲电效应表征了电极化和应变梯度之间的相互作用，通过捕获纳米尺度上的尺寸相关特性来考虑。为提高建模精度，采用三阶切比雪夫剪切变形理论，自然满足板的上下表面零剪应力条件，无需补充约束。对于纳米板位移和固有频率的计算，采用等几何分析对问题域进行离散化，提供了优越的几何表示和计算效率。本研究系统地研究了柔性电边界条件和材料性能对智能压电纳米板结构性能的影响。数值结果表明，挠曲电效应显著提高了压电纳米片的刚度和固有频率，特别是对于较薄的结构。随着厚度的增加，这种影响减小，结果向经典预测收敛。这些发现为智能结构中纳米级压电和柔性电器件的设计提供了有价值的见解。

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引用次数: 0

Parallel topology optimization introducing enclosed cavity manufacturing constraints based on graph search algorithms 引入封闭腔制造约束的并行拓扑优化

IF 4.8 2区工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computers & Structures

Pub Date : 2026-01-01 Epub Date: 2025-11-24 DOI: 10.1016/j.compstruc.2025.108041

David Herrero-Pérez , Javier Principe

We present a distributed method based on Graph Theory for detecting enclosed cavities in density-based topology optimization using the traditional material penalization scheme. We integrate the enclosed cavity detection method into a distributed topology optimization framework that utilizes domain decomposition to leverage parallel computing resources. We introduce enclosed cavities as a manufacturing constraint in a modified topology optimization formulation to control unwanted designs based on the number of enclosed holes. Removing enclosed holes is essential for many additive manufacturing techniques because they can complicate the manufacturing process. The cavity detection method generates a graph with the subdomain design variables represented as nodes and their connections as arcs. The enclosed cavity detection method only uses the void phase part of the corresponding subdomain graph, which is divided into disconnected graphs using a Graph Search algorithm. We then classify them based on the connections between subdomain void graphs. The proposal minimizes inter-node communications by generating a hierarchical distributed graph to obtain a coherent representation of the void phase connectivity during the optimization process. Finally, we evaluate the feasibility and scalability of the computational framework using two- and three-dimensional problems with symmetric and asymmetric simplifications using multi-core computing.

在基于密度的拓扑优化中，采用传统的材料惩罚方案，提出了一种基于图论的分布方法来检测封闭腔。我们将封闭腔检测方法集成到分布式拓扑优化框架中，该框架利用域分解来利用并行计算资源。我们在改进的拓扑优化公式中引入封闭腔作为制造约束，以控制基于封闭孔数量的不必要设计。对于许多增材制造技术来说，去除封闭孔是必不可少的，因为它们会使制造过程复杂化。空腔检测方法生成一个图，其中子域设计变量表示为节点，它们的连接表示为弧。封闭空腔检测方法仅利用相应子域图的空洞相位部分，通过图搜索算法将子域图划分为不相连的图。然后，我们根据子域空图之间的连接对它们进行分类。在优化过程中，通过生成分层分布图来获得空洞相位连通性的连贯表示，从而最大限度地减少节点间通信。最后，我们通过使用多核计算对对称和非对称简化的二维和三维问题评估了计算框架的可行性和可扩展性。

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引用次数: 0

An efficient computational approach for generating synthetic data to train neural networks in concrete bridge monitoring 混凝土桥梁监测中生成综合数据训练神经网络的有效计算方法

IF 4.8 2区工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computers & Structures

Pub Date : 2026-01-01 Epub Date: 2025-11-06 DOI: 10.1016/j.compstruc.2025.107995

D. Fusco, C. Rinaldi, D. Addessi, V. Gattulli

Machine-learning tools can automate inspection and monitoring of concrete bridges, but they require large, labeled datasets that encompass many damage scenarios. Conventional two-dimensional and three-dimensional nonlinear finite element models involve a high computational burden, which limits their practicality for generating large-scale datasets. This study proposes an efficient physics-based framework that couples a force-based fiber beam element with an enhanced damage-plasticity constitutive law accounting for partial crack closure, thus reproducing both nonlinear static responses and frequency shifts associated with beam cracking that underpin vibration-based Structural Health Monitoring. Validation against a prestressed beam laboratory test and the full-scale Alveo Vecchio viaduct demonstrates that the model matches load-displacement curves and crack-related frequency variations, while significantly reducing the computational burden compared to two-dimensional and three-dimensional finite element models. The resulting efficiency enables the execution of a large number of nonlinear simulations spanning elastic, cracking and yielding regimes. These synthetic responses train two neural networks for damage identification: (i) a Nonlinear AutoRegressive network that performs unsupervised novelty detection and (ii) a Long Short-Term Memory for supervised time series classification. Together the networks detect and classify damage with high accuracy in real time, illustrating how simulation-driven datasets can accelerate physics-informed Structural Health Monitoring of ageing bridge infrastructure.

机器学习工具可以自动检查和监测混凝土桥梁，但它们需要包含许多损坏场景的大型标记数据集。传统的二维和三维非线性有限元模型计算量大，限制了其在大规模数据集生成中的实用性。本研究提出了一种有效的基于物理的框架，该框架将基于力的纤维梁单元与考虑部分裂纹闭合的增强损伤塑性本构律耦合在一起，从而再现与梁裂纹相关的非线性静态响应和频移，从而支持基于振动的结构健康监测。通过预应力梁实验室试验和全尺寸Alveo Vecchio高架桥的验证表明，该模型符合荷载-位移曲线和裂纹相关频率变化，同时与二维和三维有限元模型相比，显著减少了计算量。由此产生的效率使执行大量的非线性模拟跨越弹性，开裂和屈服的制度。这些综合响应训练了两个用于损伤识别的神经网络：(i)执行无监督新颖性检测的非线性自回归网络和（ii）用于监督时间序列分类的长短期记忆网络。这些网络一起以高精度实时检测和分类损伤，说明了仿真驱动的数据集如何加速老化桥梁基础设施的物理信息结构健康监测。

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引用次数: 0

Study on the nonlinear effects of rail cracks based on non-collinear mixing ultrasound 基于非共线混合超声的钢轨裂纹非线性效应研究

IF 4.8 2区工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computers & Structures

Pub Date : 2026-01-01 Epub Date: 2025-11-25 DOI: 10.1016/j.compstruc.2025.108045

Zhiqiang Xue , Meng Hu , Siyi Chen , Yude Xu , Shaozheng Li

Conventional ultrasonic testing shows limited sensitivity to rail microcracks. Accordingly, a non-collinear mixing ultrasonic numerical model based on FEM-SEM coupling and nonlinear acoustics is proposed for high-sensitivity detection of rail microcracks. The results indicate that the intensity of the mixing components generated by crack contact nonlinearity increases monotonically with crack size. The amplitude ratio of the first and last echoes and the −6 dB wave-packet width can be used for qualitative identification of crack presence, while the proportions of high- and low-frequency energy and the nonlinear parameter enable quantitative characterization of crack size. The proportion of high-frequency energy at or above 2.0 MHz increases from 0.21 % to 38.63 %, while the proportion of low-frequency energy at or below 0.25 MHz increases from 0.01 % to 10.63 %. The bispectrum exhibits pronounced sum-frequency and second-harmonic peaks. As crack length increases from 1 mm to 8 mm, the nonlinear parameter increases by 95 % in simulations and by 102 % in experiments, and the nonlinear ultrasonic factor increases by 43 % and by 46 % respectively. The strong agreement between numerical and experimental results verifies the accuracy of the model and the feasibility of applying non-collinear mixing ultrasonics for the quantitative detection of rail microcracks.

常规超声检测对钢轨微裂纹的灵敏度有限。基于此，提出了一种基于FEM-SEM耦合和非线性声学的非共线混合超声数值模型，用于钢轨微裂纹的高灵敏度检测。结果表明：裂纹接触非线性产生的混合分量强度随裂纹尺寸的增大而单调增加；首末回波振幅比和- 6 dB波包宽度可用于裂纹存在的定性识别，高低频能量比和非线性参数可用于裂纹大小的定量表征。2.0 MHz及以上的高频能量占比从0.21%增加到38.63%，0.25 MHz及以下的低频能量占比从0.01%增加到10.63%。双谱表现出明显的和频峰和二次谐波峰。当裂纹长度从1 mm增加到8 mm时，非线性参数在模拟中增加95%，在实验中增加102%，非线性超声因子分别增加43%和46%。数值结果与实验结果吻合较好，验证了模型的准确性和应用非共线混合超声定量检测钢轨微裂纹的可行性。

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引用次数: 0