【新文速递】2024年8月9日复合材料SCI期刊最新文章

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今日更新：Composite Structures 2 篇，Composites Part A: Applied Science and Manufacturing 3 篇，Composites Science and Technology 1 篇

Composite Structures

Automatic assembly of tensegrity chain structures along axes based on NURBS curves

Yongcan Dong, Xingfei Yuan, Yiqian Chen, Akram Samy, Shilin Dong

doi:10.1016/j.compstruct.2024.118465

基于NURBS曲线的张拉整体链结构轴向自动装配

Tensegrity chain structures (TCS) are emerging as a promising structural form and have gradually garnered increasing attention across a wide range of applications. However, designing large-scale tensegrity chains, particularly those with complex geometric shapes, remains a challenging endeavor. To address this issue, this study proposes a fully parametric design method, termed the Modular Growth Assembly (MGA), to facilitate the automatic construction of TCS. Leveraging Non-Uniform Rational B-Splines (NURBS) curves, this method can directly capture the desired structural shapes and guide the assembly of numerous elementary tensegrity units into the overall structure along their axes. For assembly, some existing tensegrities are exemplarily introduced to serve as the elementary units, forming an elementary unit library. To adopt to various packing spaces, two transformation techniques are employed to explore different shape transformation patterns. Subsequently, the parametric determinations of nodal coordinates, topology, and prestress for the overall structure are investigated, respectively. A number of fascinating design examples, including both 2D and 3D cases, are then presented to demonstrate the effectiveness of the proposed method. This research will pave the way for the convenient production of customized TCS for diverse applications and might be beneficial to provide a comprehensive optimization framework for such systems.

张拉整体链结构(TCS)作为一种新兴的结构形式，在广泛的应用中逐渐受到越来越多的关注。然而，设计大规模的张拉整体链，特别是那些具有复杂几何形状的，仍然是一个具有挑战性的努力。为了解决这一问题，本研究提出了一种全参数化设计方法，称为模块化生长装配(MGA)，以促进TCS的自动构建。利用非均匀有理b样条(NURBS)曲线，该方法可以直接捕获所需的结构形状，并引导许多基本张拉整体单元沿其轴线组装到整体结构中。对于装配，一些现有的张拉整体被范例地引入作为基本单元，形成一个基本单元库。为了适应不同的填充空间，采用了两种变换技术来探索不同的形状变换模式。随后，分别研究了节点坐标、拓扑结构和整体结构预应力的参数确定。一些迷人的设计实例，包括二维和三维的情况下，然后提出，以证明所提出的方法的有效性。本研究将为方便生产各种应用的定制TCS铺平道路，并可能有助于为此类系统提供全面的优化框架。

A micromechanics perspective on the intralaminar and interlaminar damage mechanisms of composite laminates considering ply orientation and loading condition

Zhengtao Qu, Cong Zhao, Luling An

doi:10.1016/j.compstruct.2024.118454

考虑层向和加载条件的复合材料层内和层间损伤机理的细观力学研究

A comprehensive understanding of the complex damage mechanisms in composite laminates is of great importance for establishing material failure models and designing structural damage tolerance. This paper proposed a combined numerical computation and in-situ experimental study to comprehensively investigate the influence of ply orientation and loading conditions on the microscopic damage behaviors of composite laminates. In terms of numerical computation, to overcome the limitations of current monolayer Representative Volume Element (RVE) models, 3-D two-layer RVE models were developed to characterize the intra-ply and inter-ply damage behavior of composite laminates. In-situ tests were conducted on orthotropic laminates under transverse tensile and out-of-plane shear loads, and the physical processes of crack initiation and propagation were analyzed in conjunction with numerical simulation results. The research findings revealed the contributions of the matrix, fibers, and their interfaces to the damage behavior dominated by matrix cracking in composite laminates. The extension processes and final morphologies of matrix cracks were analyzed and a summary of the propagation patterns of matrix cracks was provided. The proposed 3-D two-layer RVE model effectively captured transient failure processes that cannot be observed in in-situ tests, and the numerical computation results were consistent with ex-situ observations after specimen failure.

全面了解复合材料层合板的复杂损伤机理，对于建立材料失效模型和设计结构损伤容限具有重要意义。本文提出了数值计算与现场试验相结合的方法，全面研究了铺层取向和加载条件对复合材料层合板微观损伤行为的影响。在数值计算方面，为了克服现有单层代表体积元(RVE)模型的局限性，建立了表征复合材料层合板层内和层间损伤行为的三维双层代表体积元模型。对正交各向异性层合板进行了横向拉伸和面外剪切试验，并结合数值模拟结果分析了裂纹萌生和扩展的物理过程。研究结果揭示了基体、纤维及其界面对复合材料层合板中以基体开裂为主的损伤行为的影响。分析了基体裂纹的扩展过程和最终形貌，总结了基体裂纹的扩展模式。提出的三维两层RVE模型有效捕捉了原位试验无法观测到的瞬态破坏过程，数值计算结果与试样破坏后的离地观测结果一致。

Composites Part A: Applied Science and Manufacturing

Automatic yarn path extraction of large 3D interlock woven fabrics with confidence estimation

Yuriy Sinchuk, Yanneck Wielhorski, Arturo Mendoza, Samy Blusseau, Santiago Velasco-Forero

doi:10.1016/j.compositesa.2024.108396

基于置信度估计的大型三维互锁机织物纱线路径自动提取

Modeling realistic textile composite structures remains a challenging task due to their complex geometry. In this paper, a novel method for reconstructing yarn paths based on micro-computed tomography is proposed. A deep learning approach is employed to convert μ-CT scan into an appropriate distance map, which is used for extracting yarn paths with a tracking algorithm. An ablation study is performed to understand the hyperparameters that matter the most. This study includes variation of the target images, selection of spatial dimension of the U-Net (2D, 2.5D and 3D), dataset sampling strategies and loss terms weighting. Additionally, a robust method for estimating the quality of the predictions without the need for annotation is introduced. The accuracy of the reconstruction method is demonstrated through the analysis 15 test μ-CT images, with 5 devoted to the optimal post-processing evaluation and 10 for assessing the final test results.

由于复杂的几何形状，现实纺织复合结构的建模仍然是一项具有挑战性的任务。本文提出了一种基于微型计算机断层扫描重建纱线路径的新方法。该方法采用深度学习方法将 μ-CT 扫描转换为适当的距离图，然后利用跟踪算法提取纱线路径。为了解最重要的超参数，进行了一项消融研究。这项研究包括目标图像的变化、U-Net 空间维度的选择（2D、2.5D 和 3D ）、数据集采样策略和损失项加权。此外，还介绍了一种无需注释即可估算预测质量的稳健方法。通过分析 15 张测试 μ-CT 图像（其中 5 张用于优化后处理评估，10 张用于评估最终测试结果），证明了重建方法的准确性。

A deep learning framework based on attention mechanism for predicting the mechanical properties and failure mode of embedded wrinkle fiber-reinforced composites

Chen Liu, Xuefeng Li, Jingran Ge, Xiaodong Liu, Bingyao Li, Zengfei Liu, Jun Liang

doi:10.1016/j.compositesa.2024.108401

基于注意机制的深度学习框架预测嵌入式褶皱纤维增强复合材料力学性能和失效模式

To avoid the expensive computational costs process of high-fidelity simulation, a deep learning (DL) framework based on attention mechanism and three-dimensional stress state is proposed to predict the compressive mechanical properties and failure modes of embedded wrinkle thick-section composites in this paper. The deep learning framework includes strength and stiffness, stress–strain curves and failure mode prediction networks respectively using convolutional neural networks based on wrinkle angle distribution and material distribution. The attention-based loss function is considered in the failure mode network to accurately predict the local high damage areas. The high-fidelity three-dimensional finite element simulations based on progressive damage method are used to compute the datasets for training and validating. The results show that the deep learning framework can accurately predict the compressive mechanical properties and failure modes of embedded wrinkle composites. Meanwhile, the DL framework also reveals the influence rule of wrinkle parameters on mechanical properties and failure modes.

为了避免高保真仿真过程中昂贵的计算成本，本文提出了一种基于注意机制和三维应力状态的深度学习框架来预测嵌入式褶皱厚截面复合材料的压缩力学性能和破坏模式。深度学习框架包括基于皱褶角分布和材料分布的卷积神经网络的强度和刚度、应力-应变曲线和失效模式预测网络。在失效模式网络中考虑基于注意力的损失函数，以准确预测局部高损伤区域。采用基于渐进损伤法的高保真三维有限元模拟，计算训练和验证数据集。结果表明，深度学习框架能够准确预测嵌入褶皱复合材料的压缩力学性能和破坏模式。同时，DL框架还揭示了起皱参数对力学性能和破坏模式的影响规律。

Hierarchical carbonaceous modified carbon fiber reinforced polyether ether ketone and reusing reclaimed carbon fiber for sustainable photocatalysis: An experimental and numerical analysis

R. Sasikumar, Saritha Kanoth, Shubra Singh, Kumaran Rengaswamy, V. Subramanian, R. Jayavel

doi:10.1016/j.compositesa.2024.108403

分级碳基改性碳纤维增强聚醚醚酮及再生碳纤维可持续光催化的实验与数值分析

A strategic one-step design of fiber-film multifunctional carbonaceous (Graphene Nano Platelets (GNPs)/amine-Multiwalled Carbon Nanotubes (MWCNTs) modified carbon fiber reinforced Polyether ether ketone (PEEK) has been fabricated to explore its synergism in mechanical, electromagnetic, and photocatalytic applications. The dispersive surface energy compatibility between PEEK (γsd-36.2 mJ/m2), NH2-MWCNTs (γsd-29.9 mJ/m2), and GNPs (γsd-39 mJ/m2) exhibits unique reinforcement mechanism. The mesoscale modeling using Digimat-FE and Abaqus FEA predicts interlaminar shear behavior, which agrees with the experimental results. The multifarious assembly features of GNP/MWCNT reinforcement enable the improved shielding effectiveness of 42.99 dB. The 0.1 % TiO2-RCF is found to have a degradation efficiency of 99.9 %. A reactor model was developed in COMSOL Multiphysics, and the degradation rate of MB was fitted with the Langmuir-Hinshelwood kinetic model. The estimated parameters included an intrinsic reaction rate of 1.37 × 10−6 mol m−3 min−1 and an adsorption constant of 1.728 × 1018 m3 mol−1.

为了探索其在机械、电磁和光催化应用中的协同作用，我们采用战略性的一步法设计了一种纤维薄膜多功能碳质（石墨烯纳米板（GNPs）/胺-多壁碳纳米管（MWCNTs）改性碳纤维增强聚醚醚酮（PEEK））。聚醚醚酮（PEEK）（γsd-36.2 mJ/m2）、NH2-MWCNTs（γsd-29.9 mJ/m2）和 GNPs（γsd-39 mJ/m2）之间的分散表面能相容性表现出独特的增强机制。利用 Digimat-FE 和 Abaqus FEA 建立的中尺度模型预测了层间剪切行为，与实验结果一致。GNP/MWCNT 增强材料的多种组装特性使屏蔽效果提高了 42.99 dB。0.1 % TiO2-RCF 的降解效率为 99.9 %。在 COMSOL Multiphysics 中开发了反应器模型，并用 Langmuir-Hinshelwood 动力学模型拟合了甲基溴的降解率。估计参数包括 1.37 × 10-6 mol m-3 min-1 的固有反应速率和 1.728 × 1018 m3 mol-1 的吸附常数。

Composites Science and Technology

Experimental and numerical study on failure mechanisms of tapered laminates: Effects of ply thickness and taper ratio

Xin Lu, Ryo Higuchi, Xiawan Hua, Toshio Nagashima, Tomohiro Yokozeki

doi:10.1016/j.compscitech.2024.110784

锥形层压板破坏机理的实验与数值研究:厚度和锥度比的影响

Although the variable ply drop-off strategy in tapered laminates offers design flexibility for composite components, it introduces significant challenges to structural reliability due to the discontinuity and stress concentration caused by ply termination. In light of this, we present an integrated experimental and numerical investigation into the failure mechanisms of tapered composite laminates. Interrupted tensile tests are employed to analyze the progressive damage processes of these laminates, considering the effects of taper ratio and ply thickness. Comprehensive failure examinations are conducted alternately using optical microscopy, X-ray radiography, and X-ray computed tomography. In parallel, a generic failure model is developed within the framework of finite element method. It enables the prediction of failure loads and damage patterns in the laminate specimens, allowing for comparison with test results. A strong correlation between numerical modeling and experimental reference has been achieved, which clarifies the interdependence of failure behavior on ply thickness and taper ratio. For identical structural compositions, it is demonstrated that the utilization of thin plies and shallow tapers enhances the damage resistance of laminate structures with ply drop-offs.

尽管锥形层压板的可变厚度下降策略为复合材料组件提供了设计灵活性，但由于厚度终止引起的不连续和应力集中，它给结构可靠性带来了重大挑战。鉴于此，我们对锥形复合材料层合板的破坏机制进行了综合实验和数值研究。考虑锥度比和厚度的影响，采用间断拉伸试验分析了复合材料的渐进损伤过程。综合故障检查交替使用光学显微镜、x射线摄影和x射线计算机断层扫描进行。同时，在有限元框架内建立了通用的失效模型。它能够预测层压试样的失效载荷和损伤模式，允许与测试结果进行比较。数值模拟结果与实验结果具有较强的相关性，阐明了层厚和锥度比对破坏行为的影响。在相同的结构成分下，薄层和浅锥层的使用均能提高具有层数下降的层压结构的抗损伤能力。

来源：复合材料力学仿真Composites FEM

【新文速递】2024年8月12日固体力学SCI期刊最新文章

今日更新：International Journal of Solids and Structures 2 篇，Mechanics of Materials 1 篇，International Journal of Plasticity 1 篇，Thin-Walled Structures 1 篇International Journal of Solids and StructuresMachine learning applications in sheet metal constitutive Modelling: A reviewArmando E. Marques, Tomás G. Parreira, André F.G. Pereira, Bernardete M. Ribeiro, Pedro A. Pratesdoi:10.1016/j.ijsolstr.2024.113024机器学习在钣金本构建模中的应用综述The numerical simulation of sheet metal forming processes depends on the accuracy of the constitutive model used to represent the mechanical behaviour of the materials. The formulation of these constitutive models, as well as their calibration process, has been an ongoing subject of research. In recent years, there has been a special focus on the application of data-driven techniques, namely Machine Learning, to address some of the difficulties of constitutive modelling. This review explores different methodologies for the application of Machine Learning algorithms to sheet metal constitutive modelling. These methodologies include the use of machine learning algorithms in the identification of constitutive model parameters and the replacement of the constitutive model by a metamodel created by a machine learning algorithm. A discussion about the merits and limitations of the different methodologies is presented, as well as the identification of some possible gaps in the literature that represent opportunities for future research.板料成形过程的数值模拟取决于用来表示材料力学行为的本构模型的准确性。这些本构模型的制定，以及它们的校准过程，一直是一个正在进行的研究课题。近年来，人们特别关注数据驱动技术的应用，即机器学习，以解决本构建模的一些困难。这篇综述探讨了机器学习算法应用于金属板本构建模的不同方法。这些方法包括使用机器学习算法来识别本构模型参数，以及用机器学习算法创建的元模型替换本构模型。讨论了不同方法的优点和局限性，并指出了文献中可能存在的一些空白，这些空白代表了未来研究的机会。On an efficient global/local stochastic methodology for accurate stress analysis, failure prediction and damage tolerance of laminated compositesP. Minigher, A. Arteiro, A. Turon, J. Fatemi, S. Guinard, L. Barrière, P.P. Camanhodoi:10.1016/j.ijsolstr.2024.113026基于有效全局/局部随机方法的层合复合材料精确应力分析、失效预测和损伤容限研究The quantification of uncertainties in the mechanical response of composite structures can be a computationally demanding task. This is due both to the number of uncertain parameters in a real study case and the complexity of the model to be analyzed. In this paper, an efficient global/local approach to estimate the uncertainties of the quantities of interest in specific regions of interest with limited computational effort is proposed. This is achieved by refining only locally the model taking advantage of Refined Structural Theories. At the same time, since the variance of the uncertain parameters is usually relatively small, the stochastic analysis is dealt with a sensitivity study carried out both in the global and in the local model. In this way, it is possible to assess the influence of global and local uncertain parameters in the same submodeling analysis. The methodology presented is applied to several study cases of interest. The results focus on obtaining probabilistic distributions of the stress field that can be later used in failure criteria to evaluate the subsequent distribution of the failure index. Furthermore, a damage tolerance study case is investigated, showing good correlation with the reference Monte Carlo simulations.复合材料结构力学响应的不确定性量化是一项计算要求很高的任务。这是由于实际研究案例中不确定参数的数量和待分析模型的复杂性。本文提出了一种有效的全局/局部方法，在有限的计算量下估计特定兴趣区域中兴趣数量的不确定性。这是通过利用精炼结构理论对模型进行局部精炼来实现的。同时，由于不确定参数的方差通常相对较小，因此对随机分析进行了全局和局部模型的敏感性研究。这样，就可以在同一子模型分析中评估全局和局部不确定参数的影响。所提出的方法被应用于几个感兴趣的研究案例。结果着重于获得应力场的概率分布，该概率分布可用于制定破坏准则，以评估破坏指数的后续分布。此外，还研究了一个损伤容限研究案例，结果与蒙特卡罗模拟结果具有良好的相关性。Mechanics of MaterialsMesoscale modeling of deformations and defects in thin crystalline sheetsLucas Benoit–Maréchal, Ingo Nitschke, Axel Voigt, Marco Salvalagliodoi:10.1016/j.mechmat.2024.105114薄晶片变形和缺陷的中尺度模拟We present a mesoscale description of deformations and defects in thin, flexible sheets with crystalline order, tackling the interplay between in-plane elasticity, out-of-plane deformation, as well as dislocation nucleation and motion. Our approach is based on the Phase-Field Crystal (PFC) model, which describes the microscopic atomic density in crystals at diffusive timescales, naturally encoding elasticity and plasticity effects. In its amplitude expansion (APFC), a coarse-grained description of the mechanical properties of crystals is achieved. We introduce surface PFC and surface APFC models in a convenient height-function formulation encoding deformation in the normal direction. This framework is proven consistent with classical aspects of strain-induced buckling, defect nucleation on deformed surfaces, and out-of-plane relaxation near dislocations. In particular, we benchmark and discuss the results of numerical simulations by looking at the continuum limit for buckling under uniaxial compression and at evidence from microscopic models for deformation at defects and defect arrangements, demonstrating the scale-bridging capabilities of the proposed framework. Results concerning the interplay between lattice distortion at dislocations and out-of-plane deformation are also illustrated by looking at the annihilation of dislocation dipoles and systems hosting many dislocations. With the novel formulation proposed here, and its assessment with established approaches, we envision applications to multiscale investigations of crystalline order on deformable surfaces.我们提出了一个中尺度的变形和缺陷的描述，在薄，柔性片与晶体顺序，处理面内弹性，面外变形，以及位错成核和运动之间的相互作用。我们的方法基于相场晶体(PFC)模型，该模型描述了晶体在扩散时间尺度上的微观原子密度，自然地编码了弹性和塑性效应。在其振幅扩展(APFC)中，实现了晶体力学性能的粗粒度描述。我们以一种方便的高度函数形式引入表面PFC和表面APFC模型，编码在法向上的变形。这一框架被证明与经典的应变诱导屈曲、变形表面上的缺陷成核和位错附近的面外松弛相一致。特别地，我们通过观察单轴压缩下屈曲的连续极限以及缺陷和缺陷排列变形的微观模型的证据，对数值模拟的结果进行了基准测试和讨论，展示了所提出框架的尺度桥接能力。通过观察位错偶极子的湮灭和包含许多位错的系统，还说明了位错处晶格畸变与面外变形之间相互作用的结果。通过本文提出的新公式及其与既定方法的评估，我们设想应用于可变形表面上晶体秩序的多尺度研究。International Journal of PlasticityStrong and Ductile Low Carbon Low Alloy Steels with Multiphase Bimodal MicrostructureChenhe Wang, Ran Chen, Chenyang Wang, Yumeng Zhang, Xiaodong Wang, Mingwei Chendoi:10.1016/j.ijplas.2024.104097 具有多相双峰组织的高韧性低碳低合金钢Restrained by the strength-ductility tradeoff, it is still challenging to develop advanced high-strength low carbon low alloy (LCLA) steels with superior strength-ductility combinations and cost-effectiveness to satisfy industry demands. In this study, an innovative 2-cyclic quenching and partitioning (Q&P) heat treatment was developed to produce a novel LCLA steel with the optimized microstructure, in which a bimodal grain size distribution across various constituent phases was achieved. Tensile test results show that the 2-cyclic Q&P LCLA steel exhibits excellent mechanical properties with a uniform elongation, close to 18%, nearly triple that of conventional Q&P LCLA steel while maintaining a tensile strength above 1 GPa. To reveal the underlying mechanisms of such exceptional strength-elongation synergy, the detailed deformation behaviors of the developed LCLA steel were characterized while the evolution of hetero-deformation-induced (HDI) stress and effective stress was investigated from the perspective of the dislocation model. It is indicated that, with increasing strain, the heterogeneous structures promote strong strain partitioning which leads to extensive geometrically necessary dislocations (GNDs) pile-ups at hetero-interface and persistently strong HDI strengthening effect, and produce the coordinated deformation among constituent phases to realize dislocation forest strengthening, collectively contributing to the enhanced work hardening capacity and hence overcoming the strength-ductility tradeoff. This study provides a new processing strategy for developing strong and ductile LCLA steels.受强度-延性平衡的制约，开发出具有优异强度-延性组合和成本效益的先进高强度低碳低合金(LCLA)钢仍是一项挑战。在本研究中，开发了一种创新的2循环淬火和分配(Q&P)热处理方法，以生产具有优化组织的新型LCLA钢，其中实现了不同组成相的双峰晶粒尺寸分布。拉伸试验结果表明，2循环Q&P LCLA钢具有优异的力学性能，伸长率接近18%，是常规Q&P LCLA钢的近3倍，同时抗拉强度保持在1 GPa以上。为了揭示这种特殊的强度-延伸协同作用的潜在机制，研究了所开发的LCLA钢的详细变形行为，并从位错模型的角度研究了异质变形诱导(HDI)应力和有效应力的演变。结果表明，随着应变的增加，非均质结构促进了强应变分配，导致异质界面上广泛的几何必要位错(GNDs)堆积和持续强的HDI强化效应，并在各组成相之间产生协调变形，实现位错森林强化，共同提高了加工硬化能力，从而克服了强度-塑性平衡。本研究为开发高韧性LCLA钢提供了一种新的加工策略。Thin-Walled StructuresAn investigation of vibration responses for bolted composite flanged-cylindrical shells considering material and joint nonlinearityXiaofeng Liu, Wei Sun, Honghao Liu, Hongwei Ma, Dongxu Du, Hui Lidoi:10.1016/j.tws.2024.112335 考虑材料非线性和节点非线性的螺栓复合法兰-圆柱壳振动响应研究In this paper, a thorough investigation into the vibration response of bolted composite flanged-cylindrical shell structures, considering the material nonlinearity of carbon fiber-reinforced polymer composites (CFRP) and the joint nonlinearity of bolt connections, is presented. Firstly, a general semi-analytical modeling method for bolted composite flanged-cylindrical shell is developed based on the first-order shear deformation theory (FSDT) and the energy method. In this method, material nonlinearity is introduced by accounting for the frequency-strain dependency of material parameters. A joint model with non-uniform distribution parameters and dynamic boundaries is proposed to simulate the interface pressure distribution and nonlinear mechanical behavior of bolted joints. Then, for the general numerical model that incorporates both types of nonlinearities, the ability to accurately predict the nonlinear vibration behavior of a bolted composite flanged-cylindrical shell is demonstrated through experimental testing. Finally, an in-depth discussion is conducted on the influence of fiber layup patterns and bolt numbers on the nonlinear vibration response of the bolted composite flanged-cylindrical shells. The conducted analysis indicates that the proposed method can offer utility to designers, empowering them with the insights necessary for the dynamic optimization of such structures.考虑碳纤维增强聚合物复合材料(CFRP)的材料非线性和螺栓连接的连接非线性，对螺栓复合材料法兰-圆柱壳结构的振动响应进行了深入的研究。首先，基于一阶剪切变形理论(FSDT)和能量法，建立了螺栓复合材料法兰-圆柱壳的通用半解析建模方法;该方法考虑了材料参数的频率-应变关系，引入了材料的非线性。提出了一种具有非均匀分布参数和动态边界的连接模型，用于模拟螺栓连接的界面压力分布和非线性力学行为。然后，通过实验验证了结合两种非线性因素的通用数值模型能够准确预测螺栓复合材料法兰-圆柱壳的非线性振动行为。最后，深入讨论了纤维铺层方式和螺栓数对螺栓复合法兰-圆柱壳非线性振动响应的影响。所进行的分析表明，所提出的方法可以为设计人员提供实用工具，使他们能够对此类结构的动态优化提供必要的见解。来源：复合材料力学仿真Composites FEM