Advances in Engineering Software最新文献_第8页

Numerical investigation on fretting wear in steel wires by introducing system stiffness and dissipated friction energy 引入系统刚度和耗散摩擦能的钢丝微动磨损数值研究

IF 5.7 2区工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Advances in Engineering Software

Pub Date : 2025-07-30 DOI: 10.1016/j.advengsoft.2025.103999

Zhen Hu , Kai Liang , Enyuan Wang , Xiaofei Liu , Fuyin Jia

In the mining hoisting system, the reliability of wire ropes has a significant influence on the safety of the entire system. Subjected to coupled alternating stresses and small cyclic motions, fretting wear occurs in the internal steel ropes, leading to fatigue damage and reduced service life. Studying fretting behaviour through experiments is economically costly and cumbersome. This study numerically investigated the effects of system tangential stiffness (Ks), Crossing Angle (CA), and contact load (P) on fretting contact and wear behaviours of steel wires. Firstly, the fretting wear model for contact wires was established based on Archard’s wear model, and the accuracy of the model was compared with the published literature. Then, the fretting characteristics, such as wear morphology, relative slip amplitude (δ_a), and hysteresis loop, were investigated, and the action mechanism on wear depth was analysed. Finally, a more streamlined approach was proposed to predict wear depth by using dissipated friction energy. The results show that with an increase in the number of cycles, the relative slip amplitude gradually decreases, and non-Coulomb friction behaviour intensifies. The wear depth is influenced by the crossing angle and system stiffness mainly through the contact pressure and relative slip amplitude. Specifically, larger crossing angles and system stiffness result in more severe wear. An increase in contact load lead to a competition between contact pressure and relative slip, resulting in the initially increasing and then decreasing of wear depth. The effective dissipated friction energy, for the first time, was employed in wear prediction of steel wires. Compared to Archard's model, the prediction accuracy of the proposed model improves with the increasing system stiffness and the decreasing contact load. The proposed method offers a practical tool for wear prediction of steel wires, greatly enhancing the efficiency of wear calculations.

在矿山提升系统中，钢丝绳的可靠性对整个系统的安全有着重要的影响。在交变应力和小周期运动耦合作用下，钢索内部发生微动磨损，导致疲劳损伤，降低使用寿命。通过实验研究微动行为在经济上既昂贵又繁琐。本文研究了系统切向刚度（Ks）、交叉角（CA）和接触载荷(P)对钢丝微动接触和磨损行为的影响。首先，基于Archard磨损模型建立了接触导线微动磨损模型，并与已有文献进行了精度比较；研究了微动磨损形态、相对滑移幅值（δa）和磁滞回线等微动特性，分析了微动对磨损深度的作用机理。最后，提出了一种利用耗散摩擦能预测磨损深度的简化方法。结果表明：随着循环次数的增加，相对滑移幅值逐渐减小，非库仑摩擦行为加剧；磨损深度主要通过接触压力和相对滑移幅值受交叉角和系统刚度的影响。具体来说，较大的交叉角和系统刚度会导致更严重的磨损。接触载荷的增大导致接触压力和相对滑移之间的竞争，导致磨损深度先增大后减小。首次将有效耗散摩擦能用于钢丝的磨损预测。与Archard模型相比，该模型的预测精度随着系统刚度的增大和接触载荷的减小而提高。该方法为钢丝的磨损预测提供了实用工具，大大提高了磨损计算的效率。

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引用次数: 0

As-scanned point cloud generation using structured-light simulation and machine learning-based coverage prediction 使用结构光模拟和基于机器学习的覆盖预测生成扫描点云

IF 5.7 2区工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Advances in Engineering Software

Pub Date : 2025-07-29 DOI: 10.1016/j.advengsoft.2025.103996

Tingcheng Li , Ruding Lou , Arnaud Polette , Manon Jubert , Dominique Nozais , Jean-Philippe Pernot

Although several methods have been proposed for generating as-scanned point clouds, i.e. point clouds incorporating various realistic artefacts that would appear if the corresponding real objects were digitized for real, most of them still fail to take into account the complex phenomena that occur in a real acquisition devices. This paper presents a new way of artificially generating point clouds by combining simulation and machine learning. Starting from the CAD model of the object to be virtually scanned and from a scan configuration, structured light simulation first allows reconstructing a preliminary 3D point cloud. Then, a coverage prediction network is used to predict the regions that would be acquired if a real acquisition was to be done. The prediction model has been trained from a large database of scan configurations and point clouds scanned for real. Finally, filtering and cropping are performed to fine-tune the generated point cloud. Experiments confirm that this method can generate point clouds very close to those that a real scanner would acquire, as shown by several metrics characterizing both local and global similarity. Such a virtual scanning technique enables the rapid generation of large quantities of realistic point clouds, especially when compared to the time-consuming and costly processes involved in using physical acquisition systems. This opens up new perspectives in terms of access to realistic point cloud databases, in particular for the development of various AI-based approaches.

虽然已经提出了几种方法来生成扫描点云，即包含各种逼真的人工制品的点云，如果相应的真实物体被真实数字化，就会出现这些人工制品，但大多数方法仍然没有考虑到真实采集设备中发生的复杂现象。本文提出了一种将仿真与机器学习相结合的人工生成点云的新方法。从要虚拟扫描的对象的CAD模型和扫描配置开始，结构光模拟首先允许重建初步的3D点云。然后，使用覆盖预测网络来预测如果要进行实际采集将被采集的区域。预测模型的训练来自于一个大型的扫描配置数据库和真实扫描的点云。最后进行滤波和裁剪，对生成的点云进行微调。实验证实，该方法可以生成非常接近真实扫描仪所获得的点云，如几个表征局部和全局相似性的指标所示。这种虚拟扫描技术能够快速生成大量逼真的点云，特别是与使用物理采集系统所涉及的耗时和昂贵的过程相比。这在访问现实点云数据库方面开辟了新的视角，特别是对于各种基于人工智能的方法的开发。

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引用次数: 0

Solar-induced thermal effects on steel-concrete composite beams: A meteorological data-driven analysis for long-span bridges 钢-混凝土组合梁的太阳热效应：大跨度桥梁的气象数据驱动分析

IF 4 2区工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Advances in Engineering Software

Pub Date : 2025-07-26 DOI: 10.1016/j.advengsoft.2025.103995

Yonghao Chu , Yuping Zhang , Chuanxi Li , Junliang Xie , Jiaping Jiang , Xing Tang

To investigate the effects of solar radiation temperature on steel-concrete composite beams in long-span bridges, a temperature analysis method based on meteorological parameters is proposed. First, an accurate thermal analysis model was established based on the principles of heat conduction and finite element computation theory. The model’s accuracy was validated using measured data. Subsequently, the representative values of temperature differences for the composite beam were calculated based on the analysis of historical meteorological data. The calculation method integrated the finite element temperature field model with the generalized extreme value distribution function. Finally, the simulated solar radiation temperature field was applied to the overall finite element model of the long-span bridge. The comprehensive influence of solar radiation temperature effects on long-span bridges was then evaluated. The results indicate that the finite element analysis results are in good agreement with the measured values. The 50-year return period representative value (T_d) for the maximum vertical positive temperature difference in the composite beam is 17.613 °C. The compressive stress induced in the concrete bridge deck of the composite beam by temperature loads during the operational phase exceeds twice that caused by lane loads. By analyzing seven different load effect combinations, the impact of the most unfavorable load effect combination on the bridge structure was determined. This provides an important reference for bridge design and assessment. This research offers a novel method for understanding and predicting the temperature response of long-span bridges. Additionally, it provides theoretical foundations and technical support for achieving the lightweight goals of bridge health monitoring.

为了研究太阳辐射温度对大跨度桥梁钢-混凝土组合梁的影响，提出了一种基于气象参数的温度分析方法。首先，基于热传导原理和有限元计算理论，建立了精确的热分析模型；利用实测数据验证了模型的准确性。随后，在分析历史气象资料的基础上，计算出复合梁温差的代表值。该计算方法将有限元温度场模型与广义极值分布函数相结合。最后，将模拟的太阳辐射温度场应用于该大跨度桥梁的整体有限元模型。然后评价了太阳辐射温度效应对大跨度桥梁的综合影响。结果表明，有限元分析结果与实测值吻合较好。组合梁竖向正温差最大值的50年回归期代表值（Td）为17.613℃。在运行阶段，温度荷载在组合梁混凝土桥面产生的压应力超过车道荷载的两倍。通过对7种不同荷载效应组合的分析，确定了最不利荷载效应组合对桥梁结构的影响。这为桥梁设计和评估提供了重要参考。该研究为理解和预测大跨度桥梁的温度响应提供了一种新的方法。为实现桥梁健康监测的轻量化目标提供了理论基础和技术支持。

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引用次数: 0

A stochastic linear neural network-based differential evolution algorithm for optimizing reluctance actuator 基于随机线性神经网络的磁阻执行器优化差分进化算法

IF 4 2区工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Advances in Engineering Software

Pub Date : 2025-07-15 DOI: 10.1016/j.advengsoft.2025.103983

Yunlang Xu , Datong Pan , Longbin Jiang , Haibo Zhou

Reluctance actuators encounter significant challenges in active gravity compensation due to nonlinear effects including dynamic stiffness, leakage flux, and fringing flux, which cause unstable thrust output during operation. This study focuses on suppressing thrust fluctuations in open-loop reluctance actuator gravity compensation systems through design parameter optimization. We first establish a parametric optimization model based on equivalent magnetic circuit principles to characterize nonlinear thrust dynamics. To address limitations in conventional optimization approaches, we develop a differential evolution algorithm enhanced by a stochastic linear neural network (DE-SLNN). This hybrid method combines conventional linear neural networks (CLNN) with a stochastic dynamic opposite learning mechanism (SDOLM) to strengthen DE’s search capability. Comprehensive validation using CEC 2014 benchmark confirms DE-SLNN’s accelerated convergence speed and superior search performance. Application to reluctance actuator optimization demonstrates DE-SLNN’s ability to maintain full-stroke thrust output with a small deviation of less than 2.69% for stable gravity compensation, as confirmed by thrust distribution analysis. Comparative validation with finite element analysis (FEA) reveals thrust error control within 0.16%, verifying the optimization model’s precision. Experimental results demonstrate the framework’s effectiveness in mitigating nonlinearities and achieving stable thrust output within the actuator’s operational stroke.

由于动刚度、泄漏磁通和边缘磁通等非线性影响，磁阻执行器在运行过程中推力输出不稳定，因此在主动重力补偿中遇到了很大的挑战。通过设计参数优化，研究了开环磁阻作动器重力补偿系统中推力波动的抑制问题。首先建立了基于等效磁路原理的参数优化模型来表征非线性推力动力学。为了解决传统优化方法的局限性，我们开发了一种由随机线性神经网络（DE-SLNN）增强的微分进化算法。该方法将传统线性神经网络（CLNN）与随机动态反向学习机制（SDOLM）相结合，增强了神经网络的搜索能力。使用CEC 2014基准的综合验证证实了DE-SLNN的加速收敛速度和优越的搜索性能。在磁阻执行器优化中的应用表明，DE-SLNN能够保持全行程推力输出偏差小于2.69%，实现稳定的重力补偿，推力分布分析证实了这一点。与有限元分析（FEA）对比验证表明，推力误差控制在0.16%以内，验证了优化模型的精度。实验结果表明，该框架在减轻非线性和实现执行器工作行程内稳定的推力输出方面是有效的。

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引用次数: 0

Integrated software platform for the structural health control of historical constructions and numerical model calibration (HH-Structures) 历史建筑结构健康控制与数值模型标定集成软件平台（HH-Structures）

IF 4 2区工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Advances in Engineering Software

Pub Date : 2025-07-11 DOI: 10.1016/j.advengsoft.2025.103994

Y. Cruz, B. Conde, M. Cabaleiro, B. Riveiro

Currently, BIM systems applied to new building construction are highly developed, standardised and widely implemented. However, this situation contrasts with the existing difficulties in their application to the field of built heritage, where important limitations persist. Among the main shortcomings is the lack of commercial or end-user tools to efficiently structure the information needed for the management and assessment of structural health in historic bridges. In this context, it is essential to enable robust bi-directional communication between 3D models generated in Building Information Modelling (BIM) environments and structural analysis software based on the Finite Element Method (FEM), thus promoting interoperability between platforms. Furthermore, to reduce the impact of uncertainties inherent in the modelling of in-service structures, it is essential to complement numerical models with experimental data and to apply advanced calibration methodologies. In response to these challenges, HH-Structures, a comprehensive platform for structural health monitoring of historic bridges, is presented. This platform combines non-destructive techniques with automated numerical model calibration processes, and enables the interoperable exchange of information between BIM environments and FEM analysis software, in order to provide rigorous support for structural analysis of heritage constructions.

目前，BIM系统在新建建筑施工中的应用已经高度发达、标准化和广泛实施。然而，这种情况与它们在建筑遗产领域的应用存在的困难形成了鲜明对比，在建筑遗产领域仍然存在重要的局限性。主要缺点之一是缺乏商业或最终用户工具来有效地组织管理和评估历史桥梁结构健康所需的信息。在这种情况下，在建筑信息建模（BIM）环境中生成的3D模型与基于有限元法（FEM）的结构分析软件之间实现强大的双向通信至关重要，从而促进平台之间的互操作性。此外，为了减少在役结构建模中固有的不确定性的影响，有必要用实验数据补充数值模型并应用先进的校准方法。为了应对这些挑战，HH-Structures，一个用于历史桥梁结构健康监测的综合平台，被提出。该平台将非破坏性技术与自动化数值模型校准过程相结合，实现BIM环境与FEM分析软件之间的信息互操作交换，为遗产建筑结构分析提供严格的支持。

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引用次数: 0

Prediction of the limiting uniform normal pressure in deep contiguous piled walls using soft computing techniques 用软计算技术预测深层连续桩墙极限均布正压

IF 4 2区工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Advances in Engineering Software

Pub Date : 2025-07-09 DOI: 10.1016/j.advengsoft.2025.103993

Divesh Ranjan Kumar , Warit Wipulanusat , Duy Tan Tran , Suraparb Keawsawasvong

In urban civil engineering projects, deep contiguous piled walls are crucial for support and stability, particularly in limited spaces. This study employs advanced soft computing techniques, integrating FELA simulations, XGBoost, and optimization algorithms (PSO, GWO, and WOA), to predict the limiting uniform normal pressure behind circular and I-shaped contiguous piled walls in cohesive soil. The key factors in the prediction model include the soil properties, pile wall geometry, and soil strength parameters such as the spacing-to-width ratio (S/B or S/D), adhesion factor (m), height-to-width ratio of the I-section (H/B), and friction angle (φ). The sensitivity analysis reveals that for circular-shaped piles, φ is the most influential parameter (R = 0.69, R_i = 47 %), followed by the m and S/D, with moderate impacts (R = 0.49 and 0.28, R_i = 34 % and 19 %, respectively). For I-shaped piles, the m has the highest effect (R = 0.52, R_i = 28 %) followed by the S/B (R = 0.49, R_i = 26 %), H/B (R = 0.45, R_i = 24 %) and φ (R = 0.41, R_i = 22 %). The predictive performance of the constructed model was assessed using several performance metrics, regression plot, residual error histogram and regression error characteristic (REC) curve. The hybrid XGBoost-WOA model is identified as the most effective for both circular and I-shaped piles based on various performance metrics (R², RMSE, MAE, WMAPE, VAF, and PI) and error analyses. This approach aims to improve prediction accuracy and address the limitations of traditional methods in deep contiguous piled wall design.

在城市土木工程项目中，深层连续桩墙对于支撑和稳定至关重要，特别是在有限的空间中。本研究采用先进的软计算技术，集成FELA模拟、XGBoost和优化算法（PSO、GWO和WOA），预测了粘性土中圆形和i形连续桩墙后的极限均匀法向压力。预测模型的关键因素包括土体性质、桩壁几何形状和土体强度参数，如间距比（S/B或S/D）、黏附系数(m)、工字段高宽比（H/B）、摩擦角（φ）等。敏感性分析表明，对于圆形桩，φ是影响最大的参数（R = 0.69, Ri = 47%），其次是m和S/D，影响中等（R = 0.49和0.28，Ri分别= 34%和19%）。对于工字形桩，m的影响最大（R = 0.52, Ri = 28%），其次是S/B （R = 0.49, Ri = 26%）、H/B （R = 0.45, Ri = 24%）和φ (R = 0.41, Ri = 22%)。采用多个性能指标、回归图、残差直方图和回归误差特征（REC）曲线对构建模型的预测性能进行评估。基于各种性能指标（R2、RMSE、MAE、WMAPE、VAF和PI）和误差分析，XGBoost-WOA混合模型被认为对圆形和i形桩都是最有效的。该方法旨在提高预测精度，解决传统方法在深层连续桩墙设计中的局限性。

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引用次数: 0

Effect of distributed DVAs on stochastic dynamic behaviors of FG-GPLRC annular plates 分布DVAs对FG-GPLRC环形板随机动力行为的影响

IF 4 2区工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Advances in Engineering Software

Pub Date : 2025-07-08 DOI: 10.1016/j.advengsoft.2025.103982

Haochen Hu , Rui Zhong , Qingshan Wang

Based on dynamic vibration absorber (DVA) technology, a hybrid numerical method combining the spectro-geometric method (SGM) and the pseudo-excitation method (PEM) is proposed to analyze the free vibration characteristics and stochastic dynamic behavior of functionally graded graphene platelet-reinforced composites (FG-GPLRC) annular plates under various stationary and nonstationary stochastic excitations. The dynamic model of the DVA is simplified as a spring–mass system. Within the theoretical framework of the first-order shear deformation theory (FSDT), the Lagrangian energy functional of the coupled structure is constructed, and the dynamic response of the coupled system is obtained using the Rayleigh-Ritz variational method. The numerical accuracy of the proposed method is validated by comparing the results with those from existing literature and the finite element method (FEM). On this basis, the effectiveness of DVAs in suppressing structural vibration is demonstrated, and the effects of structural dimensions, material properties, and DVA installation parameters on the dynamic behavior of the coupled system are examined.

基于动态吸振器（DVA）技术，提出了一种结合光谱几何法（SGM）和伪激励法（PEM）的混合数值方法，分析了功能梯度石墨烯平板增强复合材料（FG-GPLRC）环形板在各种平稳和非平稳随机激励下的自由振动特性和随机动力行为。将DVA的动力学模型简化为弹簧-质量系统。在一阶剪切变形理论（FSDT）的理论框架下，构建了耦合结构的拉格朗日能量泛函，并采用瑞利-里兹变分方法得到了耦合系统的动力响应。通过与已有文献和有限元法计算结果的比较，验证了所提方法的数值精度。在此基础上，论证了DVA抑制结构振动的有效性，并考察了结构尺寸、材料性能和DVA安装参数对耦合系统动力性能的影响。

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引用次数: 0

From density to CAD: Automatic and robust CAD model generation of topology optimization results via sparse optimization 从密度到CAD：通过稀疏优化实现拓扑优化结果的自动鲁棒CAD模型生成

IF 4 2区工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Advances in Engineering Software

Pub Date : 2025-07-02 DOI: 10.1016/j.advengsoft.2025.103977

Zepeng Wen , Xiaoya Zhai , Hongmei Kang

Topology optimization (TO) is a mature design technique that provides a conceptual design with the desired structural performance. However, the raw TO results cannot be interactively fine-tuned for conceptual design or further post-processing. This paper proposes an automatic and effective framework that can convert TO results into editable CAD models. The marching cubes algorithm is utilized to obtain discrete boundary points, which are subsequently transformed into CAD format via the sparse curve fitting technique. The proposed framework ensures robust and automatic reconstruction of the TO results of macrostructures and microstructures, especially complex small-scale structures with tiny holes and a few extracted points. We developed a Rhino plug-in, facilitating designers to modify the structural layout and intuitively assess the performance of the editable structures. Furthermore, we address stress concentrations by editing the reconstructed CAD models to illustrate the application of the proposed method.

拓扑优化（TO）是一种成熟的设计技术，它可以提供具有理想结构性能的概念设计。然而，原始的TO结果不能交互式地对概念设计或进一步的后处理进行微调。本文提出了一个自动有效的框架，可以将TO结果转换为可编辑的CAD模型。采用移动立方体算法获得离散边界点，然后通过稀疏曲线拟合技术将其转换为CAD格式。该框架保证了宏观结构和微观结构，特别是具有微小孔洞和少量提取点的复杂小尺度结构的TO结果的鲁棒性和自动重建。我们开发了一个Rhino插件，方便设计人员修改结构布局并直观地评估可编辑结构的性能。此外，我们通过编辑重建的CAD模型来解决应力集中问题，以说明所提出方法的应用。

引用次数: 0

Effect of frequency content of ground motion on seismic response of buildings with variable aspect ratio including soil-structure interaction 地震动频率含量对含土-结构相互作用变宽比建筑物地震反应的影响

IF 4 2区工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Advances in Engineering Software

Pub Date : 2025-06-30 DOI: 10.1016/j.advengsoft.2025.103981

Dilek Kaya , Tufan Cakir , Kasif Furkan Ozturk , Onur Araz

Soil-structure interaction (SSI) may lead to reduction, amplification or negligible change in structural responses depending on the relationship between the nature of excitations and subsoil conditions. Since neglecting SSI effects may cause uncertainties in seismic design, it is crucial to consider them during the design process. Another important factor affecting the dynamic behavior of structures interacting with the ground is the dynamic properties of the structures. To consider this effect, three buildings with 4, 8, and 12 stories designed in accordance with the Turkish Building Earthquake Code (TBEC-2018) are analyzed. The aspect ratios of these structures are 2, 4, and 6, corresponding to squat, ordinary, and slender structures, respectively. The primary objective of this study is to simulate the combined effects of these key parameters on the dynamic response of reinforced concrete structures. In the time history analyses, six ground motions classified by three different frequency contents are considered. 3D finite element models of SSI systems are established using ANSYS software. The usability of the numerical models is demonstrated for both SSI and fixed-base cases through three different analytical approaches. The displacement, acceleration, and stress responses are examined through time history analyses. The results indicate that the SSI is not negligible and neglecting the SSI is an oversimplification that does not lead to always-conservative predictions. Moreover, both the frequency content of the excitation and the structural aspect ratio are found to be decisive parameters in seismic response.

土-结构相互作用（SSI）可能导致结构响应的减小、放大或可忽略不计的变化，这取决于激励性质和底土条件之间的关系。由于忽略SSI效应可能会在抗震设计中造成不确定性，因此在设计过程中考虑SSI效应至关重要。影响结构与地面相互作用动力性能的另一个重要因素是结构的动力特性。为了考虑这种影响，根据土耳其建筑地震规范（tbc -2018）对三栋分别为4层、8层和12层的建筑进行了分析。这些结构的纵横比分别为2、4和6，分别对应于深、普通和细长结构。本研究的主要目的是模拟这些关键参数对钢筋混凝土结构动力响应的综合影响。在时程分析中，考虑了按三种不同频率分量分类的六种地震动。利用ANSYS软件建立了SSI系统的三维有限元模型。通过三种不同的分析方法，证明了数值模型在SSI和固定基数情况下的可用性。位移、加速度和应力响应通过时间历史分析进行检验。结果表明，SSI是不可忽略的，忽略SSI是一种过度简化，不会导致总是保守的预测。此外，发现激励频率含量和结构长径比是地震反应的决定性参数。

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引用次数: 0

Bilinear-inverse-mapper: Analytical solution and algorithm for inverse mapping of bilinear interpolation of quadrilaterals 双线性逆映射：四边形双线性插值逆映射的解析解和算法

IF 4 2区工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Advances in Engineering Software

Pub Date : 2025-06-26 DOI: 10.1016/j.advengsoft.2025.103975

Indrajeet Sahu

The challenge of finding parametric coordinates of bilinear interpolation of a point with respect to a quadrilateral in 2D or 3D frequently arises as a subproblem in various applications, e.g. finite element methods, computational geometry, and computer graphics. The accuracy and efficiency of inverse mapping in such cases are critical, as the accumulation of errors can significantly affect the quality of the overall solution to the broader problem. This mapping is nonlinear and typically solved with Newton’s iterative method, which is not only prone to convergence issues but also incurs high computational cost. This paper presents an analytical solution to this inverse mapping, along with a comprehensive geometric analysis covering all possible quadrilateral configurations. It describes the invertibility of all points and extends the discussion to 3D and concave quadrilaterals. The proposed algorithm is robust, free from failure due to convergence issues or oscillations in iterative methods, and achieves approximately

2.4 \times

higher computational speed compared to Newton’s method for quadrilaterals with non-parallel opposite edges. This enables an efficient calculation of shape functions or interpolation functions at all invertible spatial points. The high-accuracy, high-speed computational solution will be particularly advantageous in applications involving high spatial or temporal discretisation (i.e. fine mesh and small timesteps) where iterative methods will be computationally expensive. The analytical solution based algorithm is available as an open-source library at https://github.com/sahu-indrajeet/Bilinear-Inverse-Mapper.

在二维或三维四边形中寻找点的双线性插值参数坐标的挑战经常作为子问题出现在各种应用中，例如有限元方法，计算几何和计算机图形学。在这种情况下，逆映射的准确性和效率是至关重要的，因为误差的积累会显著影响更广泛问题的整体解决方案的质量。这种映射是非线性的，通常采用牛顿迭代法求解，不仅容易出现收敛问题，而且计算成本高。本文给出了这种逆映射的解析解，并给出了涵盖所有可能的四边形构型的全面几何分析。它描述了所有点的可逆性，并将讨论扩展到三维和凹四边形。该算法具有鲁棒性，不会因迭代方法的收敛性问题或振荡而失效，并且对于非平行对边四边形的计算速度比牛顿方法提高了约2.4倍。这使得在所有可逆空间点上有效地计算形状函数或插值函数成为可能。高精度、高速计算解决方案在涉及高空间或时间离散化（即精细网格和小时间步长）的应用中将特别有利，其中迭代方法的计算成本很高。基于解析解的算法可以在https://github.com/sahu-indrajeet/Bilinear-Inverse-Mapper上作为开源库获得。

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引用次数: 0