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GUI-based hybrid ML model for predicting ultimate strength of FRP-confined UHPC with CTGAN-augmented data 基于gui的混合ML模型与ctgan增强数据预测frp约束的UHPC极限强度
IF 7.1 2区 材料科学 Q1 MATERIALS SCIENCE, COMPOSITES Pub Date : 2025-11-29 DOI: 10.1016/j.compstruct.2025.119905
Ibrahim A Tijani , Cheng Jiang
Fiber-reinforced polymer (FRP)-confined ultra-high-performance concrete (UHPC) is a promising form for advanced structural applications because of its superior mechanical performance and resilience. Meanwhile, consistent prediction models for the ultimate strength of FRP-confined UHPC stays limited, specifically due to the scarcity of sufficient experimental data. Hence, the current study proposes innovative machine learning (ML)-based framework that combines a conditional tabular generative adversarial network (CTGAN) with Optuna, a cutting-edge hyperparameter optimization algorithm, to address limitations of datasets and improve model generality. A processed experimental data consisting of 145 FRP-confined UHPC samples was assembled from the literature and utilized to train the model. Using the augmented dataset, a stacked hybrid ML model integrating multiple algorithms with ridge regression as the meta-learner was developed. The proposed model demonstrated superior predictive performance compared to individual ML models, achieving a correlation coefficient of 0.984 for the entire dataset, along with consistently low performance error metric. SHapley Additive exPlanations (SHAP) analysis shown that feature hierarchies between original and augmented datasets were strongly correlated, confirming that CTGAN preserved the input–output relationships. Furthermore, the leave-one-study-out validation demonstrated robust cross-study generalization, with CTGAN-generated data achieving error levels comparable to experimental datasets. Finally, a user-friendly graphical user interface (GUI) was developed for structural design applications.
纤维增强聚合物(FRP)约束的高性能混凝土(UHPC)由于其优异的力学性能和弹性,在高级结构应用中具有广阔的应用前景。同时,由于缺乏足够的实验数据,对于frp约束下的超高性能混凝土的极限强度的一致预测模型仍然有限。因此,本研究提出了基于机器学习(ML)的创新框架,该框架将条件表格生成对抗网络(CTGAN)与Optuna(一种前沿的超参数优化算法)相结合,以解决数据集的局限性并提高模型的通用性。从文献中收集了145个frp约束的UHPC样品的处理实验数据,并用于训练模型。利用增强的数据集,开发了一个集成多种算法和脊回归的堆叠混合ML模型作为元学习器。与单个ML模型相比,所提出的模型显示出优越的预测性能,整个数据集的相关系数为0.984,并且性能误差指标始终较低。SHapley加性解释(SHAP)分析表明,原始数据集和增强数据集之间的特征层次具有强相关性,证实了CTGAN保留了输入-输出关系。此外,遗漏一项研究验证显示了稳健的交叉研究泛化,ctgan生成的数据达到了与实验数据集相当的误差水平。最后,开发了面向结构设计应用的图形用户界面(GUI)。
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引用次数: 0
Utilizing multi-step plastic deformation in negative stiffness metastructures for superior energy absorption 利用负刚度元结构的多步塑性变形来获得更好的能量吸收
IF 7.1 2区 材料科学 Q1 MATERIALS SCIENCE, COMPOSITES Pub Date : 2025-11-29 DOI: 10.1016/j.compstruct.2025.119909
Shun Wang, Hai-Tao Liu
The use of soft materials with large elastic strains and rigid support frameworks that do not participate in deformation greatly limits the energy absorption of negative stiffness metastructures. 3D printing technology provides an effective means to design high energy absorbing metastructures with complex geometrical configurations. Here, we propose negative stiffness metastructures by leveraging the superior energy absorption of multi-step plastic deformation and fabricated by selective laser sintering. Its deformation mechanisms and mechanical responses are analyzed through experiments and simulations. Negative stiffness and tunable stress fluctuation phenomena are simultaneously observed in multi-step metastructures. Compared with the existing single-stage negative stiffness metastructures, the new metastructures simultaneously have negative stiffness, tunable ordered multi-step deformation, and multi-stress plateau. The energy-absorbing stroke is extended while the energy absorption per unit mass is enhanced by nearly 8 times, and the average compressive stress is raised by nearly 6 times. These excellent properties come from the multi-step plastic deformation of the deformable support frameworks, which dramatically improves the material utilization of the negative stiffness metastructures. We design the deformation sequence utilizing the strength difference between the substructures, along with a staged arrangement of the negative stiffness characteristics formed under the snap-through buckling and rotational deformation mechanisms. The integration of negative stiffness and plastic deformation provides a new approach for designing metastructures with high energy absorption efficiency and promotes widespread applications of additive manufacturing in the field of protection.
采用弹性应变大的软质材料和不参与变形的刚性支撑框架,极大地限制了负刚度元结构的能量吸收。3D打印技术为设计具有复杂几何形态的高能量吸收元结构提供了有效手段。在这里,我们提出了利用多步塑性变形的优越能量吸收和选择性激光烧结制备的负刚度元结构。通过实验和仿真分析了其变形机理和力学响应。在多阶元结构中同时观察到负刚度和可调应力波动现象。与现有的单阶段负刚度元结构相比,新元结构同时具有负刚度、可调有序多步变形和多应力平台。吸能行程延长,单位质量吸能提高近8倍,平均压应力提高近6倍。这些优异的性能来自于可变形支撑框架的多步塑性变形,极大地提高了负刚度元结构的材料利用率。我们利用子结构之间的强度差异来设计变形序列,以及在卡通屈曲和旋转变形机制下形成的负刚度特征的阶段性安排。负刚度和塑性变形的集成为设计高能量吸收效率的元结构提供了新的途径,促进了增材制造在防护领域的广泛应用。
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引用次数: 0
A two-scale constitutive model for steel-confined ultra-high-performance concrete (UHPC) considering fibre–confinement interactions 考虑纤维约束作用的钢约束超高性能混凝土(UHPC)双尺度本构模型
IF 7.1 2区 材料科学 Q1 MATERIALS SCIENCE, COMPOSITES Pub Date : 2025-11-29 DOI: 10.1016/j.compstruct.2025.119904
Shack Yee Hiew , Keat Bin Teoh , Chung-Chan Hung , Doo-Yeol Yoo , Shanaka Kristombu Baduge , Daniel Kong , Sudharshan N. Raman
Defining a comprehensive constitutive law for designing steel fibre-reinforced ultra-high-performance concrete (UHPC) structural members necessitates a complete understanding of steel fibres’ contributions to both confined and unconfined behaviours under compression and tension regimes. This study introduces a complete set of stress–strain (constitutive) models tailored for the simulation of reinforced UHPC columns subjected to varying levels of confinement and incorporating commonly used types of steel fibres within practical volumetric ranges. The proposed models integrate critical modifications to conventional confinement models for reinforced concrete columns, calibrated to better reflect the actual fibre orientation, improved ductility (through actual stress levels in transverse reinforcement at peak strength), and the elevated peak and residual strengths characteristic of steel-confined UHPC. Validation against independently tested specimens through both analytical and numerical approaches confirms the reliability and generalisability of the models, establishing them as effective tools for predicting the structural performance of UHPC members across a diverse range of fibre parameters and confinement conditions.
为设计钢纤维增强高性能混凝土(UHPC)结构构件定义一个全面的本构律,需要完全理解钢纤维在压缩和拉伸状态下对约束和无约束行为的贡献。本研究介绍了一套完整的应力-应变(本构)模型,专门用于模拟受不同程度约束的增强UHPC柱,并在实际体积范围内纳入常用类型的钢纤维。所提出的模型整合了对钢筋混凝土柱传统约束模型的关键修改,经过校准以更好地反映实际纤维方向,改进的延性(通过横向钢筋峰值强度的实际应力水平),以及钢约束UHPC的峰值和残余强度特性。通过分析和数值方法对独立测试样本进行验证,证实了模型的可靠性和通用性,并将其建立为预测不同纤维参数和约束条件下UHPC构件结构性能的有效工具。
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引用次数: 0
Multi-axis 3D printing of L-shaped honeycomb sandwich structure with continuous carbon fiber reinforced composites 连续碳纤维增强复合材料多轴3D打印l型蜂窝夹层结构
IF 7.1 2区 材料科学 Q1 MATERIALS SCIENCE, COMPOSITES Pub Date : 2025-11-28 DOI: 10.1016/j.compstruct.2025.119901
Wudan Li , Xiaoyong Tian , Peng Liu , Yiming Huang , Tengfei Liu , Weiyi Kong , Liming Lei , Muhammad Jawad Ahmad , Dichen Li
Continuous carbon fiber reinforced composites (CCFRCs) sandwich structures are renowned for their exceptional bending stiffness and strength, making them ideal for aerospace and automotive applications. However, the design and fabrication of curved honeycomb composite structures remain challenging due to limitations of traditional mold-based manufacturing techniques. In this study, a multi-axis robotic 3D printing process for CCFRCs was established to fabricate curved honeycomb sandwich structure with variable reference surfaces, by taking L-shaped beam as an example. Two path planning strategies, normal offset and coaxial projection, were proposed for the top/bottom facesheets and honeycomb cores with controllable gestures of printing head. Three-point bending tests were conducted to analyze the bending behavior of L-shaped curved honeycomb sandwich structures with different curvature radii and path planning strategies. The results indicate both strategies effectively ensure bonding between the core and facesheets, and the bending stiffness increases with the curvature radius. Notably, the bending strength of structure formed by coaxial projection is more sensitive to curvature changes. When the curvature radius changes from 30 mm to 6 mm, the bending strength difference between the two strategies reaches 51.55 %. These studies provide valuable insights for the design and fabrication of curved honeycomb sandwich structures.
连续碳纤维增强复合材料(CCFRCs)夹层结构以其卓越的抗弯刚度和强度而闻名,使其成为航空航天和汽车应用的理想选择。然而,由于传统的基于模具的制造技术的限制,弯曲蜂窝复合材料结构的设计和制造仍然具有挑战性。本研究以l型梁为例,建立了一种多轴机器人3D打印CCFRCs工艺,用于制造具有可变参考面的弯曲蜂窝夹层结构。针对打印头姿态可控的上下面片和蜂窝芯,提出了法向偏移和同轴投影两种路径规划策略。通过三点弯曲试验,分析了不同曲率半径和路径规划策略下l型弯曲蜂窝夹层结构的弯曲性能。结果表明,两种策略均能有效保证芯板与面板的粘结,且弯曲刚度随曲率半径增大而增大。值得注意的是,同轴投影结构的抗弯强度对曲率变化更为敏感。当曲率半径从30 mm变化到6 mm时,两种策略的抗弯强度差异达到51.55%。这些研究为弯曲蜂窝夹层结构的设计和制造提供了有价值的见解。
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引用次数: 0
An origami-inspired N-type core for all-composite sandwich construction: Enhanced mechanical performance and failure mechanisms 用于全复合材料夹层结构的折纸启发的n型芯:增强的机械性能和失效机制
IF 7.1 2区 材料科学 Q1 MATERIALS SCIENCE, COMPOSITES Pub Date : 2025-11-27 DOI: 10.1016/j.compstruct.2025.119903
Zengxian Wang , Xiaojian Chen , Shubin Tian , Zhe Wang , Qiang Liu , Guocai Yu , Jian Deng , Tian Jian Lu
An origami-inspired N-type (ON) corrugated core was proposed to enhance the load-bearing capacity of an ultralight all-composite sandwich panel having the traditional V-type corrugation core (folded plate). A combined theoretical and experimental approach was employed to evaluate systematically the equivalent elastic modulus and ultimate compressive strength of ON corrugated composite sandwich panels. Subsequently, a dedicated manufacturing process was developed to fabricate the ON corrugated sandwich specimens; traditional corrugated composite sandwich panels were also fabricated. Comparative analysis between ON and V-type corrugated sandwiches was conducted, with particular focus placed upon failure processes, elastic modulus, and strength. It is demonstrated that ON corrugation combined the structural advantages of both the traditional I-type and V-type configurations. Unique failure modes were observed, and the maximum load capacity achieved when the I- and V-type substructures buckle simultaneously. Finally, it is demonstrated that the specific strength/stiffness and energy absorption of the proposed ON corrugation was superior to alternative constructions reported in existing literature, providing valuable insights for the optimal design of ultralight composite sandwich structures.
为了提高具有传统v型波纹芯(折叠板)的超轻型全复合材料夹层板的承载能力,提出了一种折纸型n型波纹芯(ON)。采用理论与实验相结合的方法对ON波纹复合材料夹层板的等效弹性模量和极限抗压强度进行了系统的评估。随后,开发了专门的制造工艺来制造ON波纹夹层试件;还制作了传统的波纹复合夹层板。对ON型和v型波纹夹层进行了对比分析,重点研究了破坏过程、弹性模量和强度。结果表明,ON型波纹结合了传统i型和v型结构的优点。观察到独特的破坏模式,当I型和v型子结构同时屈曲时,其承载能力达到最大。最后,证明了所提出的ON波纹结构的比强度/刚度和能量吸收优于现有文献报道的替代结构,为超轻复合材料夹层结构的优化设计提供了有价值的见解。
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引用次数: 0
Trade-offs between load-bearing capability and ionic conductivity of composite polymer electrolytes 复合聚合物电解质的承载能力和离子电导率之间的权衡
IF 7.1 2区 材料科学 Q1 MATERIALS SCIENCE, COMPOSITES Pub Date : 2025-11-27 DOI: 10.1016/j.compstruct.2025.119875
Maryam Niazi , Federico Danzi , Pedro P. Camanho
Composite polymer electrolytes show strong potential for load-bearing energy storage systems, such as structural batteries, due to their high mechanical strength, flexibility, interfacial compatibility, low interfacial resistance, ease of manufacturing, and improved safety. However, literature often reports an inverse relationship between mechanical performance and ionic conductivity, requiring careful trade-offs to achieve optimal multifunctionality. This review discusses the thermal (e.g., glass transition temperature, melting point), mechanical (e.g., stiffness, strength), and ionic conductivity properties of commonly used thermoplastic polymers in electrolytes. It examines how viscoelastic behavior, molecular weight, and temperature influence these thermo-electro-mechanical properties and the need for balancing them. The role of additives—including salts, ionic liquids, nano-fillers, and thermoset polymers like epoxy—is evaluated, with a focus on their impact on electrochemical and mechanical performance trade-offs. Additionally, current manufacturing techniques along with their advantages and limitations are discussed. Eventually, the paper highlights strategies to overcome the mechanical–ionic conductivity trade-off, including the use of self-healing networks, functional fillers, and engineered architectures.
复合聚合物电解质由于其高机械强度、柔韧性、界面兼容性、低界面阻力、易于制造和提高安全性,在结构电池等承载能量存储系统中显示出强大的潜力。然而,文献经常报道机械性能和离子电导率之间的反比关系,需要仔细权衡以实现最佳的多功能。本文讨论了常用的热塑性聚合物在电解质中的热(如玻璃化转变温度、熔点)、机械(如刚度、强度)和离子电导率等性能。它研究了粘弹性行为、分子量和温度如何影响这些热-电-机械性能以及平衡它们的必要性。评估了添加剂的作用,包括盐、离子液体、纳米填料和热固性聚合物,如环氧树脂,重点是它们对电化学和机械性能权衡的影响。此外,目前的制造技术及其优点和局限性进行了讨论。最后,论文强调了克服机械-离子电导率权衡的策略,包括使用自修复网络、功能性填料和工程结构。
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引用次数: 0
Recent advances in graphene origami structures: A review 石墨烯折纸结构研究进展综述
IF 7.1 2区 材料科学 Q1 MATERIALS SCIENCE, COMPOSITES Pub Date : 2025-11-26 DOI: 10.1016/j.compstruct.2025.119898
Yi Wang , Yihe Zhang , Shaoyu Zhao , Bin Dong , Jie Yang , Yingyan Zhang
Graphene and its derivatives have attracted huge attention due to their excellent physical properties such as high in-plane Young’s modulus, extraordinary electrical and thermal properties. Graphene has been widely used as reinforcing nanofiller for high-performance polymer or metal nanocomposites. However, owing to its two-dimensional (2D) structure, graphene is brittle and cannot withstand large deformation under external loading, which limits its application in load bearing components. Recently, origami and kirigami structures have been introduced in nanotechnology and they are able to effectively tailor the properties of graphene. This work aims to review and summarize recent advances on graphene with origami or kirigami structures, graphene reinforced polymer nanocomposites and graphene origami (GOri) reinforced nanocomposites. The influence of graphene configuration including origami and kirigami structures, layer number, defects and functionalization on the properties of nanocomposites reinforced by graphene or GOri is critically reviewed. Emphasis will be placed on the mechanical and thermal properties, and their applications in nanocomposites. Research challenges and future work will also be discussed to provide a constructive guidance for further work in this emerging area.
石墨烯及其衍生物由于其优异的物理性能,如高的面内杨氏模量、非凡的电学和热学性能,引起了人们的广泛关注。石墨烯作为增强纳米填料被广泛应用于高性能聚合物或金属纳米复合材料中。然而,由于石墨烯的二维(2D)结构,它很脆,不能承受外部载荷下的大变形,这限制了它在承重部件中的应用。最近,在纳米技术中引入了折纸和基叠结构,它们能够有效地调整石墨烯的性质。本文综述了近年来石墨烯折纸结构、石墨烯增强聚合物纳米复合材料和石墨烯折纸增强纳米复合材料的研究进展。本文综述了石墨烯结构(包括折纸结构和基叠结构、层数、缺陷和功能化)对石墨烯或GOri增强纳米复合材料性能的影响。重点将放在机械和热性能,以及它们在纳米复合材料中的应用。还将讨论研究挑战和未来的工作,为这一新兴领域的进一步工作提供建设性的指导。
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引用次数: 0
Eccentrically loaded corroded RC columns repaired with advanced composites: Experimental testing and analytical modeling 用先进复合材料修复偏心加载腐蚀RC柱:试验测试和分析模型
IF 7.1 2区 材料科学 Q1 MATERIALS SCIENCE, COMPOSITES Pub Date : 2025-11-26 DOI: 10.1016/j.compstruct.2025.119899
Feras AbuObaida , Tamer El Maaddawy , Farid Abed , Ahmed ElRefai
This study provides direct experimental evidence comparing carbon fiber-reinforced polymer (C-FRP) and carbon fabric-reinforced cementitious matrix (C-FRCM) systems for rehabilitation of short reinforced concrete (RC) columns. Fifteen RC columns were tested under eccentricity-to-depth ratios (e/h) of 0.0–0.3. Corroded columns were pre-damaged through accelerated corrosion, resulting in steel losses of 22% in longitudinal bars and 42% in ties. Corrosion reduced the load capacity by 41% under concentric loading and by an average of 17% under eccentric loading. Both repair systems effectively restored the load capacity of the corroded columns. C-FRP repairs increased the load capacity by 80–167%, while C-FRCM achieved load capacity gains of 49–86%. The lower effectiveness of C-FRCM was ascribed to a premature debonding at the fabric–mortar interface. A new analytical model was developed to predict the load capacity, incorporating material nonlinearities, corrosion-induced degradation, and combined confinement from internal steel ties and external composite wraps. Model predictions were validated using experimental results from this study and additional literature data. The model produced P–M interaction diagrams consistent with experimental trends, confirming its reliability and practical use as a simple, accurate tool for structural evaluation and retrofit design.
本研究提供了直接的实验证据,比较碳纤维增强聚合物(C-FRP)和碳纤维增强胶凝基质(C-FRCM)系统修复短钢筋混凝土(RC)柱。15根钢筋混凝土柱在偏深比(e/h)为0.0 ~ 0.3的条件下进行了试验。腐蚀柱通过加速腐蚀进行预损伤,导致纵筋和扎筋的钢损分别为22%和42%。在同心加载下,腐蚀降低了41%的承载能力,在偏心加载下平均降低了17%。两种修复系统都有效地恢复了腐蚀柱的承载能力。C-FRP修复的承载能力提高了80-167%,而C-FRCM修复的承载能力提高了49-86%。C-FRCM较低的有效性归因于织物-砂浆界面的过早脱粘。开发了一种新的分析模型来预测载荷能力,该模型考虑了材料非线性、腐蚀引起的退化以及内部钢系带和外部复合包裹层的联合约束。使用本研究的实验结果和其他文献数据验证了模型预测。该模型生成的P-M相互作用图与实验趋势一致,证实了其可靠性和作为结构评估和改造设计的简单、准确工具的实用性。
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引用次数: 0
Criterion-free and model-free data-driven framework for failure prediction of composites 复合材料失效预测的无准则、无模型数据驱动框架
IF 7.1 2区 材料科学 Q1 MATERIALS SCIENCE, COMPOSITES Pub Date : 2025-11-26 DOI: 10.1016/j.compstruct.2025.119900
Liang Li , Jie Yang , Xiaowei Bai , Qun Huang , Gaetano Giunta , Salim Belouettar , Huicui Li , Heng Hu
Often, a failure prediction relies on criteria that evaluate current deformation state satisfying both conservation law and material law. To achieve this, two challenges arise: (1) it is difficult to obtain the material law when the constitutive behavior is complex, especially near or beyond the critical state, and (2) it is difficult to establish the failure criterion that performs well in the case of new failure modes. Based on data-driven computational mechanics, a criterion-free and model-free framework is proposed to predict the failure of composites. Data-driven computational mechanics minimizes the distance function between material data and admissible state satisfying the conservation law. After failure occurs, the admissible state is beyond the material database regime, leading to a high value of distance function. Thus, the proposed framework predicts failure by significant increase in value of the distance function. The failure predicting results based on the proposed framework are compared with those of other failure criteria. Moreover, the test data from the First World-Wide Failure Exercise are considered to evaluate the proposed framework. Different from classical failure prediction where the material models and failure criteria are calibrated based on test data, the proposed framework can predict failure directly with test data.
通常,失效预测依赖于评估当前变形状态同时满足守恒定律和物质定律的准则。为了实现这一目标,出现了两个挑战:(1)当本构行为复杂时,特别是接近或超过临界状态时,很难获得材料规律;(2)很难建立在新破坏模式下表现良好的破坏准则。基于数据驱动的计算力学,提出了一种无准则、无模型的复合材料失效预测框架。数据驱动计算力学将材料数据与满足守恒律的容许状态之间的距离函数最小化。故障发生后,容许状态超出材料数据库范围,导致距离函数值较高。因此,所提出的框架通过距离函数值的显著增加来预测故障。将基于该框架的失效预测结果与其他失效准则的预测结果进行了比较。此外,还考虑了来自第一次世界范围失效演习的测试数据来评估所提出的框架。与传统的基于试验数据标定材料模型和失效准则的失效预测不同,该框架可以直接利用试验数据进行失效预测。
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引用次数: 0
From bistable Geometry to acoustic Functionality: A Data-Driven study of Kresling origami bandgaps 从双稳几何到声学功能:Kresling折纸带隙的数据驱动研究
IF 7.1 2区 材料科学 Q1 MATERIALS SCIENCE, COMPOSITES Pub Date : 2025-11-25 DOI: 10.1016/j.compstruct.2025.119896
Ji Zhang , Shuai Liu , Jintong Chen , Tianyu Gao , Changguo Wang
The Kresling origami structure, a geometric construction with folding deformation characteristics, exhibits significant research potential in the domains of deformable structures and phononic crystals. This research presents a novel approach for precise bandgap modulation of Kresling origami structures through geometric design. Gradient Boosting Regression (GBR) and Lasso Regression (LR) are employed for the first time to predict bandgap frequencies, capturing the nonlinear relationship between geometric parameters and bandgaps. The models, trained on experimental and simulation data, provide reliable statistical support, significantly enhancing prediction accuracy, with a maximum sampling error of only 1.28%, while structural optimization efficiency is greatly improved. The findings indicate that the bandgap frequency can be precisely adjusted by modifying parameters like height, diameter, relative angle, and number of layers of the origami structure, hence enabling vibration isolation over a wide frequency range. The effectiveness of the regression models in handling complex nonlinear data was evaluated through prediction errors and bandgap analysis, with data-driven modeling providing theoretical and statistical support for the design optimization of Kresling origami structures.
Kresling折纸结构是一种具有折叠变形特性的几何结构,在可变形结构和声子晶体领域具有重要的研究潜力。本文提出了一种通过几何设计实现克雷斯林折纸结构精确带隙调制的新方法。首次采用梯度增强回归(GBR)和Lasso回归(LR)预测带隙频率,捕捉几何参数与带隙之间的非线性关系。该模型经过实验和仿真数据的训练,提供了可靠的统计支持,预测精度显著提高,最大抽样误差仅为1.28%,结构优化效率大大提高。研究结果表明,通过改变折纸结构的高度、直径、相对角度和层数等参数,可以精确地调节带隙频率,从而在较宽的频率范围内实现隔振。通过预测误差和带隙分析,评价了回归模型处理复杂非线性数据的有效性,数据驱动模型为Kresling折纸结构的设计优化提供了理论和统计支持。
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引用次数: 0
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Composite Structures
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