Composite Structures最新文献_第6页

Bayesian uncertainty quantification of residual mechanical properties post lightning strike: Stochastic multi-physical simulations of composite laminates including spatially-random void distribution 雷击后残余力学性能的贝叶斯不确定性量化：包括空间随机空洞分布的复合材料层合板的随机多物理模拟

IF 7.1 2区材料科学 Q1 MATERIALS SCIENCE, COMPOSITES

Composite Structures

Pub Date : 2026-04-15 Epub Date: 2026-01-29 DOI: 10.1016/j.compstruct.2026.120102

R.S. Chahar , T. Mukhopadhyay

Structural integrity of composite laminates can be significantly affected by damage resulting from lightning strikes. Accurately quantifying the residual strength and stiffness post-lightning strike, while accounting for inevitable compound uncertainties in temperature-dependent material properties due to manufacturing irregularities, defects such as random voids and stochastic lightning current parameters, is crucial for ensuring the operational safety of key composite structural components in aircraft. Here, we introduce a Bayesian inference-driven stochastic framework that integrates finite element-based hybrid thermal–electrical–mechanical simulations for uncertainty quantification in residual mechanical properties of composite laminates, wherein the parameters are estimated based on Markov chain Monte Carlo approach along with the Gibbs sampling algorithm. The inherent disadvantages concerning over-fitting and dealing with extraordinarily high-dimensional input parameter space in traditional surrogate-based Monte Carlo simulation methods for uncertainty quantification can be averted through the current approach. To obtain adequate confidence in the presented uncertainty quantification results, the probabilistic descriptions and B-basis design allowable obtained using the current Bayesian approach are compared with full-scale Monte Carlo simulations and classical non-parametric Bootstrap method. The maximum likelihood estimation-based machine learning model is further exploited for global sensitivity analysis to assess the relative influence of various governing parameters on residual mechanical properties post-lightning strike.

复合材料层合板的结构完整性会受到雷击损伤的显著影响。准确量化雷击后的残余强度和刚度，同时考虑由于制造不规范、随机空洞和随机雷击电流参数等缺陷导致的温度相关材料性能不可避免的复合不确定性，对于确保飞机关键复合材料结构部件的运行安全至关重要。在这里，我们引入了一个贝叶斯推理驱动的随机框架，该框架集成了基于有限元的热电力学混合模拟，用于复合材料层合板残余力学性能的不确定性量化，其中参数是基于马尔可夫链蒙特卡罗方法和吉布斯抽样算法估计的。通过该方法可以避免传统的基于代理的蒙特卡罗模拟方法在不确定性量化中存在的过拟合和处理异常高维输入参数空间的固有缺点。为了对所提出的不确定性量化结果获得足够的置信度，将目前贝叶斯方法得到的概率描述和b基设计允许值与全尺寸蒙特卡罗模拟和经典非参数Bootstrap方法进行了比较。进一步利用基于最大似然估计的机器学习模型进行全局敏感性分析，以评估各种控制参数对雷击后残余力学性能的相对影响。

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引用次数: 0

Dynamic tuning of shear horizontal waves in flexoelectric–piezoelectric composites with imperfect interfaces on semiconductor substrates 半导体基板上具有不完美界面的柔性电-压电复合材料剪切水平波的动态调谐

IF 7.1 2区材料科学 Q1 MATERIALS SCIENCE, COMPOSITES

Composite Structures

Pub Date : 2026-04-15 Epub Date: 2026-01-28 DOI: 10.1016/j.compstruct.2026.120061

Shreya Shukla, Sanjeev A. Sahu

Shear horizontal (SH) wave propagation in smart composite structures offers significant potential for acoustic device applications, but current structures with dielectric substrates lack means for active tuning. This study addresses this limitation by analytically identifying new physical regimes that emerge from the combined effects of flexoelectric gradients, mobile semiconductor carriers, and interfacial imperfections. SH wave dispersion and attenuation are investigated for a flexoelectric-piezoelectric layer on an n-type piezoelectric semiconductor half-space with a mechanically imperfect interface. The operator elimination technique is employed to solve the governing differential equations and obtain explicit, closed-form solutions under electrically open and shorted boundary conditions. Results reveal an interfacial compliance range

(m \approx 8 to 12)

beyond which additional stiffness yields limited phase velocity gains and stabilized attenuation. This observation indicates a saturation regime in interface effects. A thickness-dependent crossover also emerges where ultra-thin films are dominated by flexoelectric gradients resulting in higher losses, whereas in thicker films, enhanced carrier dynamics lead to increased phase velocity and reduced attenuation. The analytical formulation is further corroborated through independent numerical validation, confirming the reliability of the proposed multiphysics framework.

剪切水平（SH）波在智能复合材料结构中的传播为声学器件的应用提供了巨大的潜力，但目前的介质基板结构缺乏主动调谐的手段。本研究通过分析确定由柔性电梯度、移动半导体载流子和界面缺陷的综合效应产生的新物理机制来解决这一限制。研究了具有机械缺陷界面的n型压电半导体半空间上挠性压电层的SH波色散和衰减。利用算子消去技术求解控制微分方程，得到电开边界和短路边界条件下的显式闭解。结果表明，界面柔度范围（m≈8 ~ 12）超过该范围，额外的刚度产生有限的相速度增益和稳定的衰减。这一观察结果表明界面效应存在饱和状态。当超薄薄膜由柔性电梯度主导导致更高的损耗时，也会出现厚度相关的交叉，而在较厚的薄膜中，增强的载流子动力学导致相速度增加和衰减减少。通过独立的数值验证进一步证实了解析公式，证实了所提出的多物理场框架的可靠性。

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引用次数: 0

Direct prediction of mechanical energy released by damaged single lap joints using acoustic emission signals combined with finite element analysis 基于声发射信号与有限元分析相结合的损伤单搭接节点机械能直接预测

IF 7.1 2区材料科学 Q1 MATERIALS SCIENCE, COMPOSITES

Composite Structures

Pub Date : 2026-04-01 Epub Date: 2026-01-09 DOI: 10.1016/j.compstruct.2025.119989

Thomas Wolfsgruber, Lukas Heinzlmeier, Martin Schagerl

Adhesively bonded single lap joints are common structures in lightweight design. Despite several advantages, damage initiation and propagation are critical and can be evaluated with structural health monitoring methods. This research combines analytical models and finite element analyses (FEAs) with acoustic emission (AE) measurements to predict the released mechanical energy (RME) during damage evolution.

Two geometries, either with both adherends of constant thickness or with one constant and one tapered adherend, are evaluated. One adherend consists of carbon fibre reinforced polymer, the other one of additively manufactured titanium. The work input during quasi-static loading for the overlap region is calculated based on the longitudinal load and displacement, and based on the longitudinal, lateral, and bending components. For the calculation of the RME, pristine and damaged load–displacement curves are compared. The pristine trends are represented by the extrapolation of an experiment, or an analytical model, or a FEA without failure model. Whereas, the damaged trends are either given by the experimental measurements or a FEA with included failure model. Furthermore, the RME can also be gathered directly from the FEA with failure model. By linking the AE energy with the RME, the RME of a validation sample can be predicted.

粘接单搭接是轻量化设计中常见的结构形式。尽管有一些优点，但损伤的发生和扩展是至关重要的，可以用结构健康监测方法进行评估。本研究将分析模型和有限元分析（FEAs）与声发射（AE）测量相结合，以预测损伤演化过程中释放的机械能（RME）。两种几何形状，要么具有恒定厚度的粘附体，要么具有一个常数和一个锥形粘附体，被评估。一种粘合剂由碳纤维增强聚合物组成，另一种由增材制造的钛组成。重叠区域准静态加载时输入的功是基于纵向载荷和位移，以及基于纵向、横向和弯曲分量计算的。在计算RME时，比较了原始荷载-位移曲线和破坏荷载-位移曲线。原始趋势由实验外推，或分析模型，或无失效模型的有限元分析来表示。而损伤趋势要么由试验测量结果给出，要么由含破坏模型的有限元分析给出。此外，RME也可以直接从具有失效模型的有限元分析中获得。通过将声发射能量与RME联系起来，可以预测验证样品的RME。

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引用次数: 0

Thermal-Oxidative degradation Pathways and lifetime prediction of F881 GFRP: A Multiscale analysis of failure criteria F881 GFRP的热氧化降解途径和寿命预测：失效标准的多尺度分析

IF 7.1 2区材料科学 Q1 MATERIALS SCIENCE, COMPOSITES

Composite Structures

Pub Date : 2026-04-01 Epub Date: 2026-01-16 DOI: 10.1016/j.compstruct.2026.120076

Huilong Wan , Yadong Zhang , Zhengyang Yuan , Yiran Hu

F881 glass fiber reinforced plastic (GFRP) is widely used in coil encapsulation due to its excellent insulation and mechanical properties. However, prolonged exposure to elevated temperatures (up to 150°C) leads to material failure. To elucidate the thermal-oxidative degradation mechanisms, thermal-oxidative aging (TOA) experiments were conducted at 110°C, 130°C, and 150°C for 24–648 h. Multiscale characterization techniques revealed that during TOA, the specimens exhibited progressively severe surface degradation; the weakening of O–H peaks suggested material degradation; the enhanced C=O peaks confirmed oxidative degradation; the reduced C-O peaks demonstrated thermal degradation of the epoxy resin; and the attenuated Si-O peaks indicated interfacial damage. These mechanisms collectively constitute the fundamental causes of mass loss and mechanical strength reduction in F881 GFRP. A 50% reduction in impact strength was identified as the optimal failure criterion, and a lifetime prediction model was established. The predicted service life of F881 GFRP is 453 days at 110°C, 279 days at 130°C, and 179 days at 150°C. These findings provide important insights into the TOA mechanisms and lifetime prediction of GFRP.

F881玻璃纤维增强塑料（GFRP）因其优异的绝缘性能和机械性能而广泛应用于线圈封装。然而，长时间暴露在高温下（高达150°C）会导致材料失效。为了阐明热氧化降解机制，在110°C、130°C和150°C下进行了24-648小时的热氧化老化（TOA）实验。多尺度表征技术表明，在TOA过程中，样品表现出逐渐严重的表面降解；O-H峰减弱表明材料降解；增强的C=O峰证实了氧化降解；C-O峰的降低表明环氧树脂发生了热降解；Si-O峰衰减表明界面损伤。这些机制共同构成了F881玻璃钢质量损失和机械强度降低的根本原因。确定了冲击强度降低50%为最优失效准则，并建立了寿命预测模型。F881 GFRP在110℃下的预测寿命为453天，在130℃下为279天，在150℃下为179天。这些发现为GFRP的TOA机制和寿命预测提供了重要的见解。

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引用次数: 0

An accurate model for nonlinear forced vibrations of higher-order and Timoshenko cantilever beams 高阶和Timoshenko悬臂梁非线性强迫振动的精确模型

IF 7.1 2区材料科学 Q1 MATERIALS SCIENCE, COMPOSITES

Composite Structures

Pub Date : 2026-04-01 Epub Date: 2026-01-02 DOI: 10.1016/j.compstruct.2025.120035

Marco Amabili

An accurate higher-order model for planar nonlinear vibrations of cantilever beams is developed, taking into account nonlinear terms in (i) transverse displacement, (ii) longitudinal displacement, and (iii) rotation, as well as geometric imperfections, shear deformation, and rotary inertia. The model can be reduced to the Timoshenko beam theory, which is a first-order model, when neglecting higher-order terms. It is quite significant that the discretization is obtained by series expansions that satisfy both geometric (essential) and natural boundary conditions. A validation of the present model and a detailed convergence analysis are presented. It is crucial to adopt a proper expansion of the longitudinal displacement, which also satisfies the natural boundary condition of zero longitudinal force at the beam’s tip. Expansions that do not satisfy this boundary condition do not converge and result in over-predicting the system nonlinearity. Results show a very weak hardening-type nonlinearity for cantilever beams. In the case of geometric imperfections in the shape of the fundamental mode, an increase in the natural frequency and in the nonlinearity is observed, as well as differences in the time domain response of the generalized coordinates.

考虑到(i)横向位移、（ii）纵向位移和（iii）旋转以及几何缺陷、剪切变形和旋转惯性等非线性项，建立了悬臂梁平面非线性振动的精确高阶模型。当忽略高阶项时，该模型可简化为一阶模型Timoshenko梁理论。通过同时满足几何（本质）和自然边界条件的级数展开得到离散化是非常重要的。给出了模型的验证和详细的收敛性分析。在满足梁端纵向力为零的自然边界条件下，采用适当的纵向位移展开是至关重要的。不满足此边界条件的展开式不收敛，导致系统非线性的过度预测。结果表明，悬臂梁具有非常弱的硬化型非线性。在基模形状的几何缺陷的情况下，观察到固有频率和非线性的增加，以及广义坐标的时域响应的差异。

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引用次数: 0

Structural characterisation and failure mechanisms of high-performance marine stringers in out-of-plane bending loads 船用高性能弦板在面外弯曲载荷下的结构特征及破坏机制

IF 7.1 2区材料科学 Q1 MATERIALS SCIENCE, COMPOSITES

Composite Structures

Pub Date : 2026-04-01 Epub Date: 2026-01-08 DOI: 10.1016/j.compstruct.2026.120054

Connor Pearson , Mark Battley , John Little , Guillaume Verdier , Tom Allen

Hat stringers are structural components that stiffen and strengthen composite hull panels of high-performance racing yachts. The failure mechanisms of stringer structures are complex, and the relationships between geometric parameters and failure modes are not well understood. This is due to a lack of experimental validation resulting from the cost and complexity in experimentally testing as-designed and in-service load cases. This leads to the reliance on experiential knowledge and coupon data. Experiments based on a 3-point bend provide an alternate method to the testing of full panels to determine structural behaviour and failure mechanisms This can be used to validate designs and better inform design choices. In this work, the structural performance of shear- and bending-dominated marine omega stringer structures are characterised experimentally and numerically under 3-point bending to understand strain states under load, failure mechanisms, and the validity of coupon data when designing complex composite structures. Strain state predictions from the numerical model are well-validated at proof loads, while comparisons at failure are complicated by stochastic laminate defects, geometric features, and discrepancies in predicting based on coupon data. The results of this study highlight the differences between as-designed and actual strengths in marine stringer structures.

帽桁是用于加强高性能赛艇复合船体板的结构部件。弦杆结构的破坏机理复杂，几何参数与破坏模式之间的关系尚不清楚。这是因为缺乏实验验证，这是由于实验测试按设计和在役负载情况的成本和复杂性造成的。这导致了对经验知识和优惠券数据的依赖。基于三点弯曲的实验提供了一种替代全板测试的方法来确定结构行为和破坏机制，这可以用来验证设计并更好地为设计选择提供信息。在这项工作中，以剪切和弯曲为主导的海洋欧米茄弦结构在三点弯曲下的结构性能进行了实验和数值表征，以了解载荷下的应变状态，破坏机制，以及在设计复杂复合结构时联片数据的有效性。数值模型的应变状态预测在验证荷载下得到了很好的验证，而在破坏时的比较由于随机层压缺陷、几何特征和基于优惠券数据预测的差异而变得复杂。本研究的结果突出了设计强度与实际强度之间的差异。

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引用次数: 0

Tunable topological edge states of Rayleigh waves in composite piezoelectric half-space 复合压电半空间中瑞利波的可调谐拓扑边缘态

IF 7.1 2区材料科学 Q1 MATERIALS SCIENCE, COMPOSITES

Composite Structures

Pub Date : 2026-04-01 Epub Date: 2026-01-02 DOI: 10.1016/j.compstruct.2025.120027

Chengjun Sha , Zheng Wu , Shixuan Shao , Jiyue Chen , Mehrdad Negahban , Zheng Li

Topological insulators (TIs) have shown great potential in the manipulation of elastic wave propagation with defect immune characteristics. In this paper, a composite piezoelectric half-space is designed by covering piezoelectric patch arrays with shunt negative capacitance circuits on the surface. By tuning the negative capacitance circuits, one can easily manipulate the topological edge states of Rayleigh waves in half-space. Based on the Su-Schrieffer-Heeger (SSH) model and the valley Hall effect, topological edge states of Rayleigh waves are obtained in one-dimensional and two-dimensional piezoelectric patch arrays attached on half-spaces. This allows energy concentration and facilitates the design of tailored concentration paths for Rayleigh waves. A universal design is proposed for topologically protected Rayleigh waveguides, which is further used to achieve straight-line, L-shaped and Z-shaped waveguides. This study not only propels advancements in the field of elastic wave control, but also enables the practical application of tunable topological edge states in the fabrication of smart devices, thereby addressing complex real-world engineering challenges.

拓扑绝缘体在控制具有缺陷免疫特性的弹性波传播方面显示出巨大的潜力。本文通过在压电贴片阵列表面覆盖并联负电容电路，设计了复合压电半空间。通过调整负电容电路，可以很容易地控制半空间中瑞利波的拓扑边缘状态。基于Su-Schrieffer-Heeger （SSH）模型和谷霍尔效应，得到了附着在半空间上的一维和二维压电贴片阵列中瑞利波的拓扑边缘态。这允许能量集中，并有利于为瑞利波设计量身定制的集中路径。提出了一种拓扑保护瑞利波导的通用设计，并进一步用于实现直线、l形和z形波导。这项研究不仅推动了弹性波控制领域的进步，而且使可调谐拓扑边缘状态在智能设备制造中的实际应用成为可能，从而解决了复杂的现实世界工程挑战。

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引用次数: 0

Laser-textured polymer-metal bonding: A combined experimental and computational approach to enhanced mechanical bond strength 激光织构聚合物-金属键合：一种增强机械键合强度的实验与计算相结合的方法

IF 7.1 2区材料科学 Q1 MATERIALS SCIENCE, COMPOSITES

Composite Structures

Pub Date : 2026-04-01 Epub Date: 2026-01-07 DOI: 10.1016/j.compstruct.2026.120038

O.A. Taqatqa , Omar Al Osman , Maen Alkhader , Wael Abuzaid , Ali S. Alnaser

Polymer–metal interfaces play a key role in many sectors, including aerospace, biomedical, energy, and electronics. Their use has grown with the increased utilization of fiber-reinforced composites, soft polymers, and thin films. Strong interfaces are essential to reliable performance. Unlike adhesives or conventional joining, micro-interlocking provides strength without relying on temperature-sensitive materials. This study uses laser surface texturing to bond acrylic to Al-7075. A nanosecond laser is used to create a texture with a square pattern on the Al-7075 substrate to promote interlocking and bonding with acrylic. Experiments were used to characterize the strength of the developed bond under shear loading. A Finite Element model was developed and utilized to provide insights into the stress distribution in the interlocked phases and to investigate the effects of polymeric infills and laser-induced microstructures. Experiments and simulations were conducted to investigate the effect of four pattern spacings, namely 0.5 mm, 0.75 mm, 1 mm, and 1.5 mm. Results showed that reducing groove spacing considerably increases the bond strength. A maximum bond strength of 27 MPa was achieved. The combined experimental and computational study confirms that nanosecond laser-based texturing can develop interlocking-based bonds with strengths comparable to those of commercial epoxies.

聚合物-金属界面在许多领域发挥着关键作用，包括航空航天、生物医学、能源和电子。它们的使用随着纤维增强复合材料、软聚合物和薄膜的使用增加而增长。强大的接口对于可靠的性能至关重要。与粘合剂或传统连接不同，微联锁提供强度，而不依赖于温度敏感材料。本研究使用激光表面变形将丙烯酸与Al-7075粘合在一起。纳秒激光用于在Al-7075基板上创建具有方形图案的纹理，以促进与丙烯酸的联锁和粘合。通过实验表征了在剪切荷载作用下发育的粘结体的强度。开发了一个有限元模型，并利用该模型来深入了解联锁相中的应力分布，并研究聚合物填充物和激光诱导微观结构的影响。通过实验和模拟研究了0.5 mm、0.75 mm、1 mm和1.5 mm四种模式间距对叶片生长的影响。结果表明，减小槽间距可显著提高粘结强度。最大粘结强度达到27 MPa。实验和计算相结合的研究证实，纳秒激光织构可以形成与商业环氧树脂强度相当的互锁键。

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引用次数: 0

Finite element modeling and crushing energy absorption analysis of AA6063/CFRP hybrid thin-walled tube subjected to quasi-static load 准静态载荷作用下AA6063/CFRP复合薄壁管的有限元建模及破碎吸能分析

IF 7.1 2区材料科学 Q1 MATERIALS SCIENCE, COMPOSITES

Composite Structures

Pub Date : 2026-04-01 Epub Date: 2026-01-10 DOI: 10.1016/j.compstruct.2026.120058

Shenhua Li , Jinheng Zhang , Lihao Hou , Feng Xiong

AA6063/CFRP hybrid thin-walled tube represents a novel lightweight structural configuration characterized by high energy absorption efficiency and broad application scenarios. However, the numerical simulation methods and crushing energy absorption mechanisms for AA6063/CFRP hybrid thin-walled tubes remain in the exploratory phase. Consequently, this study focuses on finite element modeling and the crushing energy absorption characteristics of AA6063/CFRP hybrid thin-walled tubes subjected to quasi-static load. The main contributions and innovations of this paper are as follows: ① A finite element modeling strategy for AA6063/CFRP hybrid structures was proposed, leading to the development of a best fit simulation model for the hybrid thin-walled tube, achieving numerical simulation errors of less than 1 % for all five crashworthiness performance metrics；② Research findings reveal that AA6063/CFRP hybrid thin-walled tubes exhibit a competitive energy absorption mechanism between dissimilar materials under axial compressive loading, where an optimal cross-sectional design can fully activate the potential of this competitive energy absorption within the hybrid tubes；③ Under multi-angle oblique compressive loading, multi-cell AA6063/CFRP hybrid thin-walled tubes demonstrate a coupled enhancement effect, within the oblique pressure range of [0°, 35°], the maximum energy absorption enhancement ratio reached 21.05 %.

AA6063/CFRP复合薄壁管是一种新型的轻量化结构形式，具有吸能效率高、应用场景广泛等特点。然而，AA6063/CFRP复合薄壁管的数值模拟方法和破碎吸能机理仍处于探索阶段。因此，本研究重点研究了准静态载荷下AA6063/CFRP复合薄壁管的有限元建模和破碎吸能特性。本文的主要贡献和创新点如下：①提出了AA6063/CFRP复合材料结构的有限元建模策略，建立了该复合材料薄壁管的最佳拟合仿真模型，实现了5项抗撞性能指标的数值模拟误差小于1%；②研究结果表明，在轴向压缩载荷作用下，AA6063/CFRP复合材料薄壁管表现出不同材料间的竞争吸能机制；③在多角度斜向压缩载荷作用下，多芯AA6063/CFRP复合薄壁管表现出耦合增强效应，在[0°，35°]斜向压力范围内，复合薄壁管的最大吸能增强率达到21.05%。

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引用次数: 0

Intelligent design of the bonded patch repairs for damaged composite laminates via conditional generative models 基于条件生成模型的复合材料层合板粘结修补智能设计

IF 7.1 2区材料科学 Q1 MATERIALS SCIENCE, COMPOSITES

Composite Structures

Pub Date : 2026-04-01 Epub Date: 2026-01-02 DOI: 10.1016/j.compstruct.2025.120033

Ziyi Li , Qingfeng Wang , Liyong Jia , Yushu Li , Yilun Liu

Bonded patch repair is a rapid and cost-effective technique for repairing the local damage of composite laminates. However, determining the repair solution is ‌usually time-consuming and relies on the experience of engineers due to the complex relations among an extensive set of parameters, like damage states, patch configurations, adhesive layers, repair performance, and lightweight demands. In this work, an intelligent design method integrating the conditional variational autoencoder-generative adversarial network is developed to autonomously generate repair solutions for damaged laminates under tension, compression, or both. Given the geometry and layup of damaged laminates, material properties of both adhesive layers and patches, our method can directly generate geometric parameters and layup of patches and adhesive thicknesses that meet the repair performance and lightweight demands under tension or compression. In addition, the balanced solutions for the damaged laminates under mixed compression and tension are also provided through additional criteria screening and overall repair performance evaluation. Initial and ultimate failure strains of the repaired laminates are calculated by the finite element method, showing the validity of the generated repair solutions.

粘结修补是一种快速、经济的修复复合材料层合板局部损伤的技术。然而，确定修复方案通常是耗时的，并且依赖于工程师的经验，因为大量参数之间的复杂关系，如损伤状态、贴片配置、粘合剂层、修复性能和轻量化要求。在这项工作中，开发了一种集成条件变分自编码器生成对抗网络的智能设计方法，用于在拉伸，压缩或两者同时存在的情况下自动生成损坏层压板的修复方案。考虑到受损层压板的几何形状和叠层、粘接层和贴片的材料特性，我们的方法可以直接生成满足拉伸或压缩下修复性能和轻量化要求的几何参数、贴片的叠层和粘接厚度。此外，还通过附加标准筛选和整体修复性能评估，给出了复合材料在压缩和拉伸混合作用下的平衡解。采用有限元法对修复后的层合板进行了初始和最终破坏应变计算，验证了修复解的有效性。

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引用次数: 0