今日更新：Journal of the Mechanics and Physics of Solids 1 篇，Mechanics of Materials 1 篇，International Journal of Plasticity 2 篇，Thin-Walled Structures 6 篇Journal of the Mechanics and Physics of SolidsMultimaterial topology optimization of elastoplastic composite structuresYingqi Jia, Weichen Li, Xiaojia Shelly Zhangdoi:10.1016/j.jmps.2024.106018弹塑性复合材料结构的多材料拓扑优化Plasticity is indispensable for wide-ranging structures as a protection mechanism against extreme loads. Tailoring elastoplastic behaviors such as stiffness, yield force, and energy dissipation to optimal states is therefore crucial for safety and economics. Recent studies have optimized either geometry or material phase for desired energy dissipating capacities; however, integrating both in design optimization is essential but thus far not achieved, impeding a comprehensive understanding of the interplay among structural geometry, material heterogeneity, and plasticity. Here, we propose a general topology optimization framework for discovering lightweight, multimaterial structures with optimized elastoplastic responses under small deformations. This framework features a multiobjective optimization formulation that simultaneously enhances initial stiffness, delays plastic yielding, and maximizes energy absorption/dissipation. The approach is built upon rigorous elastoplasticity theory and the celebrated return mapping algorithm, incorporating both isotropic and kinematic hardening. We analytically derive the history-dependent sensitivities using the reversed adjoint method and automatic differentiation. Employing the proposed framework, we investigate several composite structures and demonstrate the non-intuitive optimized geometries and material distributions that deliver diverse superior elastoplastic performances, including maximized plastic energy dissipation and various degrees of yield resistance. Furthermore, our findings reveal underlying mechanisms that enhance structural elastoplastic performance, such as leveraging sequential yielding to prolong post-yielding resistance and prevent catastrophic failure. These optimized designs and discovered mechanisms reveal the principles for creating the next generation of resilient engineering structures accounting for elastoplastic behaviors.塑性是广泛的结构不可缺少的保护机制，对极端载荷。因此，将弹塑性行为（如刚度、屈服力和能量耗散）调整到最佳状态对于安全性和经济性至关重要。最近的研究已经优化了几何或材料相所需的能量耗散能力；然而，将两者整合到设计优化中是必不可少的，但到目前为止还没有实现，这阻碍了对结构几何、材料异质性和塑性之间相互作用的全面理解。在这里，我们提出了一个通用的拓扑优化框架，用于发现在小变形下具有优化弹塑性响应的轻质多材料结构。该框架具有多目标优化公式，可同时提高初始刚度，延迟塑性屈服，并最大化能量吸收/耗散。该方法建立在严格的弹塑性理论和著名的返回映射算法的基础上，结合了各向同性和运动硬化。利用逆伴随法和自动微分法，分析推导了历史相关灵敏度。采用提出的框架，我们研究了几种复合材料结构，并展示了非直观的优化几何形状和材料分布，这些几何形状和材料分布提供了各种优越的弹塑性性能，包括最大的塑性能量耗散和不同程度的屈服阻力。此外，我们的研究结果揭示了增强结构弹塑性性能的潜在机制，例如利用顺序屈服来延长屈服后阻力并防止灾难性破坏。这些优化设计和发现的机制揭示了创造下一代弹性工程结构的原则，这些结构考虑了弹塑性行为。Mechanics of MaterialsThe bending-buckling coupled model for blistering behavior in anti-corrosion coatingsLiangji Ma, Yin Yao, Bo Zhang, Zhilong Peng, Shaohua Chendoi:10.1016/j.mechmat.2024.105238防腐涂层起泡行为的弯曲-屈曲耦合模型Anti-corrosion coatings are widely applied in marine engineering and marine equipment. Understanding their blistering failure mechanisms is vital for optimizing coating designs and extending their service life. This paper develops a bending-buckling coupled model and employs the Rayleigh-Ritz method to investigate the axisymmetric circular blister of coatings with initial deflections, with a special focus on the situation where the transverse load is opposite to the deflection. By incorporating the chemo-mechanical coupling, an analytical solution of the critical buckling load in terms of diffusion strain is well achieved, concisely explaining the impacts of transverse loads, initial deflections, and aspect ratios on the critical buckling load. The influence of these parameters on the post-buckling behavior of the coating is further discussed and the contour of the coating blister can be presented. The results should have theoretical guidance significance for predicting and analyzing the service behavior of anti-corrosion coatings.防腐涂料广泛应用于船舶工程和船舶设备中。了解其起泡失效机制对于优化涂层设计和延长其使用寿命至关重要。本文建立了弯曲-屈曲耦合模型，采用瑞利-里兹方法研究了具有初始挠度的涂层的轴对称圆泡，特别关注了横向载荷与挠度相反的情况。通过结合化学-力学耦合，得到了扩散应变下临界屈曲载荷的解析解，简明地解释了横向载荷、初始挠度和长径比对临界屈曲载荷的影响。进一步讨论了这些参数对涂层后屈曲行为的影响，并给出了涂层起泡的轮廓。研究结果对预测和分析防腐涂层的使用行为具有理论指导意义。International Journal of PlasticityStudy of orientation-dependent residual strains during tensile and cyclic deformation of an austenitic stainless steelNamit Pai, Indradev Samajdar, Anirban Patradoi:10.1016/j.ijplas.2024.104228奥氏体不锈钢拉伸和循环变形过程中取向相关残余应变的研究This work presents a combined experimental and crystal plasticity finite element modeling study on the development of bulk and local residual strains during tensile and cyclic deformation of an austenitic stainless steel. The (hkl)-specific bulk (residual) lattice strains are measured using X-ray Diffraction, while the local residual strains are measured using High Resolution Electron Back Scatter Diffraction. The residual strains are predicted using a dislocation density-based crystal plasticity model, with consideration for directional hardening due to backstress evolution. The work emphasizes on residual strain developments for four specific grain families: (111), (001), (101) and (311), specifically in terms of their correlation with the underlying microstructure, studied using crystallographic orientation, misorientation, dislocation density and backstress evolution. Large intragranular orientation gradients, dislocation densities and backstress are observed during tensile deformation for the texturally dominant (101) grain family, indicating that these grains have higher plastic deformation as compared to the (001) and (111) grain families. This also contributes to the observed relaxation in lattice strains for the (101) grain family, with the resulting load shed being primarily accommodated by the (001) grain family. In contrast, no such orientation gradients or lattice strain relaxations are observed in the cyclically deformed material. The measured local residual strains, which are also qualitatively predicted by the crystal plasticity simulations, highlight the additional effect of spatial heterogeneity and neighboring grains on the development of residual strains. Finally, statistical analysis of the simulated residual strains reveals that the hierarchy in the development of lattice strains is in the following order for the different grain families: (001) > (311) > (111) > (101) for tensile deformation, and (001) > (311) > (111) ∼ (101) for cyclic deformation. The dominant factors contributing to the observed hierarchy are the elastic stiffness and the grain rotations (or lack thereof) for the different grain families during tensile and cyclic deformation.本研究通过实验与晶体塑性有限元建模相结合的方式，对奥氏体不锈钢在拉伸和循环变形过程中整体和局部残余应变的发展进行了研究。利用 X 射线衍射测量了（hkl）特定的体（残余）晶格应变，同时采用高分辨率电子背散射衍射测量局部残余应变。基于位错密度的晶体塑性模型预测了残余应变，同时考虑了由于反应力演变导致的各向异性硬化。本研究重点关注四个特定晶粒族（111）、（001）、（101）和（311）的残余应变发展，特别是它们与微观结构的关联，通过晶体学取向、取向差、位错密度和反应力演变进行研究。在拉伸变形过程中，对于纹理占主导地位的（101）晶粒族，观察到较大的晶内取向梯度、位错密度和反应力，表明这些晶粒的塑性变形程度高于（001）和（111）晶粒族。这也导致了（101）晶粒族晶格应变的明显松弛，而由此卸载的载荷主要由（001）晶粒族承担。相比之下，在循环变形的材料中未观察到这种取向梯度或晶格应变的松弛。所测得的局部残余应变也与晶体塑性模拟的定性预测相符，这突出了空间异质性和相邻晶粒对残余应变发展的影响。最后，对模拟残余应变的统计分析表明，在不同晶粒族中，拉伸变形时晶格应变发展的层次顺序为：（001）＞（311）＞（111）＞（101），循环变形时为：（001）＞（311）＞（111）≈（101）。导致观察到的这种层次结构的主要因素是不同晶粒族在拉伸和循环变形过程中的弹性刚度和晶粒旋转（或缺乏旋转）。Interfacial Dislocation Networks in Nickel-based Superalloys: the Hidden Link between Moiré Patterns and Sample SizesBin Dong, Haifei Zhan, Yongnan Chen, He Zhang, Yihan Nie, Yuantong Gu, Chaofeng Lüdoi:10.1016/j.ijplas.2024.104239 镍基高温合金中的界面位错网络：莫尔条纹和样品尺寸之间的隐藏联系Nickel-based single crystal superalloys exhibit exceptional yield strength and creep resistance owing to their distinctive two-phase microstructure. This in silico study reported the hidden relationship between the moiré patterns and sample sizes, which govern the formation of interfacial dislocation networks (IDNs). The moiré superlattice arises from lattice misfit, and its compatibility with the γ′ phase size determines the integrity of IDNs, resulting in size-dependent dislocation patterns. Smaller models (size < 25 nm) display discrete dislocation networks due to high residual stress, while larger ones (size > 25 nm) maintain uniformly distributed perfect dislocation networks. These initial IDNs contribute to pseudo-elastic behavior and influence the dislocation activities. Specifically, smaller models experience intensified dislocation pile-up, resulting in higher plastic strength and lower ductility. This study provides insights into γ′ phase size effects on moiré patterns and mechanical behaviour across the elastic to plastic regimes in nickel-aluminium superalloys, offering valuable guidance for their modeling and experimental design.镍基单晶高温合金由于其独特的两相组织而表现出优异的屈服强度和抗蠕变性能。这一计算机研究报告了控制界面位错网络（IDNs）形成的莫尔模式和样品大小之间的隐藏关系。moir<s:1>超晶格产生于晶格失配，其与γ′相尺寸的相容性决定了IDNs的完整性，从而导致与尺寸相关的位错模式。较小的模型（尺寸< 25 nm）由于高残余应力而显示离散的位错网络，而较大的模型（尺寸为> 25 nm）则保持均匀分布的完美位错网络。这些初始idn有助于伪弹性行为并影响位错活动。具体而言，较小模型的位错堆积加剧，导致塑性强度升高，塑性降低。本研究提供了γ′相尺寸对镍铝高温合金中弹性到塑性状态的波纹模式和力学行为的影响，为其建模和实验设计提供了有价值的指导。Thin-Walled StructuresFatigue behavior of CFRP-strengthened inclined welded steel plates with initial cracksLili Hu, Xinyu Ding, Lingzhen Li, Man-Tai Chen, Yaolin Zhangdoi:10.1016/j.tws.2024.112903具有初始裂纹的cfrp加固倾斜焊接钢板疲劳行为Fatigue behavior of welded steel structures under multi-axial stress is complicated. In this study, fatigue tests were conducted on inclined welded steel plates with initial cracks without and with strengthening using bonded carbon fiber reinforced polymer (CFRP) sheets. The butt-welds in the steel plates were prepared with different inclination angles (i.e., 30°, 45°, 60°, 90°) to the loading direction. In these welded steel plates, initial cracks were artificially induced to either the acute and obtuse angle sides of the weld toes. During fatigue loading, cracks were of mixed-mode I/II type and soon developed to propagate perpendicularly to the loading direction. It was observed that cracks at the acute angle side (L type) developed though both the welds and the base steel plates, while those at the obtuse angle side (R type) propagated only though the base steel plates. The specimen with a smaller initial weld angle yielded a lower fatigue life. Fatigue life of L-type specimen was longer than that of R-type specimen. Bonding CFRP sheets could effectively prolong the fatigue lives of the specimens to 1.32 to 6.01 times, compared with those without strengthening. This strengthening effect is more pronounced for L-type specimens with a larger initial weld angle. Finally, ABAQUS and FRANC3D were combined to analyze the fatigue crack propagation considering residual stress, CFRP strengthening, and external load, and the stress intensity at the crack tip was obtained, which align well with the findings from experimental results.焊接钢结构在多轴应力作用下的疲劳行为比较复杂。在本研究中，对带有初始裂纹的倾斜焊接钢板进行了疲劳试验，试验采用碳纤维增强聚合物（CFRP）薄板进行了加固。钢板对接焊缝与加载方向的倾角分别为30°、45°、60°、90°。在这些焊接钢板中，最初的裂纹是人为地在焊接脚趾的锐角和钝角边引起的。在疲劳加载过程中，裂纹呈I/II型混合模式，并迅速发展成垂直于加载方向扩展。结果表明，锐角边（L型）裂纹同时穿过焊缝和底钢板，而钝角边（R型）裂纹仅穿过底钢板。初始焊接角越小，试样的疲劳寿命越低。l型试样的疲劳寿命比r型试样长。粘结CFRP片材可有效延长试件的疲劳寿命，是未加固试件的1.32 ~ 6.01倍。对于初始焊缝角较大的l型试样，这种强化效果更为明显。最后，结合ABAQUS和FRANC3D对考虑残余应力、CFRP强化和外载荷的疲劳裂纹扩展进行了分析，得到了裂纹尖端的应力强度，与实验结果吻合较好。Metal flow and rib growth model in multi-DOF envelope forming process of component with thin wall and high web ribsYaxiong Hu, Xinghui Han, Lin Hua, Wuhao Zhuangdoi:10.1016/j.tws.2024.112906薄壁高腹板构件多自由度包络成形过程中的金属流动与肋生长模型To excavate plastic forming potential for fabricating complex component with thin wall and high web ribs, a new multi-DOF envelope forming technique is developed in this study. Owing to multi-DOF loading of envelope die, the multi-directional metal flow and rib growth are complex and difficult to be predicted. Hence, the aim of this study is to develop the metal flow and rib growth model in multi-DOF envelope forming of component with thin wall and high web ribs. The multi-directional metal flow velocities of contact zone between envelope die and billet are firstly derived. Then, the time-varying radial stresses of contact zone are derived, and correspondingly the time-varying radial neutral surface is obtained. Based on the above calculated metal flow velocities and neutral radius, the volume distribution ratio of metal flow along radial and tangential direction is calculated, and correspondingly the model, which can simultaneously predict time-varying metal flow and rib growth at different locations, is established. The effect mechanisms of process parameters on rib growth are also revealed. It indicates that the height of inner transverse rib and longitudinal rib gradually increases, while the height of outer longitudinal rib gradually decreases with the increase of feeding amount per cycle or the decrease of inclination angle of envelope die. Finally, experiments on multi-DOF envelope forming of component with thin wall and high web ribs are carried out, which verifies the effectiveness of developed metal flow and rib growth model. This study not only develops new multi-DOF envelope forming process to realize plastic forming of complex components with thin wall and high web ribs, but also lays the foundation for predicting complex metal flow and rib growth of complex components under complex multi-DOF loading path of dies.为了挖掘薄壁高腹板复杂构件的塑性成形潜力，提出了一种新的多自由度包络成形技术。由于包络模的多自由度加载，使得金属的多向流动和棱纹生长过程复杂且难以预测。因此，本研究的目的是建立薄壁高腹板构件多自由度包络成形过程中的金属流动和肋生长模型。首先推导了包络模与坯料接触区金属的多向流动速度。然后，导出了接触区径向应力的时变，得到了相应的时变径向中性面。基于上述计算的金属流动速度和中性半径，计算了金属沿径向和切向流动的体积分布比，建立了能够同时预测不同位置时变金属流动和肋生长的模型。揭示了工艺参数对肋生长的影响机理。结果表明：随着每周期进给量的增加或包封模倾角的减小，内横筋和纵筋高度逐渐增大，外纵筋高度逐渐减小；最后，对薄壁高腹板肋构件进行了多自由度包络成形实验，验证了所建立的金属流动和肋生长模型的有效性。本研究不仅开发了新的多自由度包络成形工艺，实现了薄壁高腹板筋复杂零件的塑性成形，而且为复杂模具多自由度加载路径下复杂零件复杂金属流动和筋生长预测奠定了基础。High-cycle fatigue-constrained isogeometric topology optimizationJinyu Gu, Jianghong Yang, Yingjun Wangdoi:10.1016/j.tws.2025.112907 高周疲劳约束等几何拓扑优化This paper focuses on the study of structural high-cycle fatigue problems commonly encountered in engineering and presents a fatigue-constrained isogeometric topology optimization (FCITO) method. First, the isogeometric analysis (IGA) framework for high-cycle fatigue problems is outlined. On this basis, a mathematical model for the FCITO method is established using the solid isotropic material with penalization (SIMP) method. The model aims to minimize compliance while considering volume and the Soderberg fatigue criterion constraints. Additionally, a modified P-norm function is employed to manage the numerous fatigue constraints, while the relaxation method is applied to address singularity issues. Moreover, the complete sensitivity equations for the objective function, volume constraint function, and fatigue constraint function are also provided. Finally, the effectiveness and capability of the presented FCITO method are demonstrated through several 2D and 3D examples.针对工程中常见的结构高周疲劳问题，提出了一种疲劳约束等几何拓扑优化方法。首先，概述了高周疲劳问题的等几何分析框架。在此基础上，采用固体各向同性材料惩罚法（SIMP）建立了FCITO方法的数学模型。该模型的目标是在考虑体积和Soderberg疲劳准则约束的同时最小化顺应性。此外，采用改进的p -范数函数来管理众多的疲劳约束，同时采用松弛法来解决奇异性问题。并给出了目标函数、体积约束函数和疲劳约束函数的完整灵敏度方程。最后，通过二维和三维算例验证了所提FCITO方法的有效性和性能。Statistical analysis of dimensional deviations and geometrical imperfections of pultruded GFRP open-section profilesJoão Alfredo de Lazzari, André Dias Martins, João R. Correia, Luís Lages Martins, Álvaro Silva Ribeiro, Alexandre Pinheiro, Nuno Silvestredoi:10.1016/j.tws.2024.112902拉挤GFRP开截面型材尺寸偏差和几何缺陷的统计分析This study presents a statistical analysis of the geometrical variability measured in glass-fibre reinforced polymer (GFRP) open-section profiles from the process-induced deformations of pultrusion. This study offers insights into the variability of geometric parameters, critical for reliability assessments and for establishing partial factors for design. Prior research has often provided limited data on geometric measurements, with some studies employing questionable measurement methodologies. Leveraging accurate measurement technology, specifically a 3D coordinate measurement machine (CMM), the authors analysed twenty-one pultruded-GFRP (pGFRP) specimens, each measuring 1.5 m in length. These specimens represented seven distinct open cross-section geometries, spanning four typological shapes: I-, W-, C-, and L-sections. The methodology employed in this analysis involved the evaluation of two groups of variables: dimensional deviation and geometrical imperfection. The measured data is compared against manufacturing tolerances outlined in the current standards, including EN 13706-2, ASTM D3917, and GB/T 31539. The statistical analysis includes correlation matrix analysis, box plots, mode shape assessment, probability distribution function fitting, and goodness-of-fit evaluation. It is shown that Lognormal and Normal distributions effectively capture most of the variability observed in geometrical variables within pGFRP open-section profiles. Moreover, this study underscores discrepancies between existing manufacturing standards and our findings, pointing out to a need for their revision. Furthermore, it emphasizes the importance of establishing standardized procedures for quantifying geometric imperfections in pGFRP composites to enhance computational simulations and design procedures.本研究对玻璃纤维增强聚合物（GFRP）开截面型材在拉挤变形过程中测量的几何变异性进行了统计分析。这项研究提供了对几何参数可变性的见解，这对于可靠性评估和建立设计的部分因素至关重要。先前的研究通常提供有限的几何测量数据，一些研究采用可疑的测量方法。利用精确的测量技术，特别是三维坐标测量机（CMM），作者分析了21个拉伸gfrp （pGFRP）样品，每个样品的长度为1.5米。这些标本代表了七种不同的开放截面几何形状，跨越四种类型形状：I型，W型，C型和l型。在这个分析中采用的方法涉及两组变量的评估：尺寸偏差和几何缺陷。测量数据与现行标准中概述的制造公差进行比较，包括EN 13706-2， ASTM D3917和GB/T 31539。统计分析包括相关矩阵分析、箱形图分析、模态振型评估、概率分布函数拟合和拟合优度评估。结果表明，对数正态分布和正态分布有效地捕获了pGFRP开截面剖面中几何变量中观察到的大部分变异性。此外，这项研究强调了现有制造标准与我们的发现之间的差异，指出需要对其进行修订。此外，它强调了建立量化pGFRP复合材料几何缺陷的标准化程序的重要性，以增强计算模拟和设计程序。Experimental and numerical study of high-strength materials on slender steel-reinforced CFST columns in fireDavid Medall, Carmen Ibáñez, Ana Espinós, Manuel L. Romerodoi:10.1016/j.tws.2024.112904高强材料对钢管混凝土细长钢柱火灾作用的试验与数值研究Innovative composite sections are gaining popularity for their cost-effectiveness and reduced environmental impact. Several innovative sections have appeared to enhance the behaviour of traditional composite columns, such as steel-reinforced concrete-filled steel tubular (SR-CFST) columns, where an open steel profile is embedded within a CFST section. These sections exhibit enhanced structural capacity and fire performance compared to regular CFST. Despite these benefits, experimental data on the fire behaviour of SR-CFST columns, especially with high-strength materials, is still limited. In this work an experimental thermo-mechanical testing program on the fire behaviour of slender SR-CFST columns with high-strength materials is presented to extend the available database. Four SR-CFST columns were tested, with circular and square geometries, which combined the use of high-strength steel (700 MPa yield strength) and high-strength concrete (90 MPa compressive strength). Afterwards, the results from these experiments were used to develop and validate a numerical model for slender SR-CFST columns. With the use of this model, an extensive parametric analysis was conducted to study the influence of high-strength materials over the fire performance of slender SR-CFST columns. It was found that employing high-strength materials significantly improved the fire behaviour of SR-CFST slender columns as compared to SR-CFST slender columns with normal strength materials.创新的复合材料截面因其成本效益和减少对环境的影响而越来越受欢迎。一些创新的截面已经出现，以提高传统复合柱的性能，如钢增强钢管混凝土（SR-CFST）柱，其中一个开放的钢型材嵌入在CFST截面内。与常规CFST相比，这些截面具有增强的结构能力和防火性能。尽管有这些好处，关于SR-CFST柱，特别是高强度材料的火灾行为的实验数据仍然有限。在这项工作中，提出了一个关于高强度材料的细长SR-CFST柱的燃烧性能的实验热力学测试程序，以扩展现有的数据库。测试了四根SR-CFST柱，具有圆形和方形几何形状，结合使用高强度钢（700 MPa屈服强度）和高强度混凝土（90 MPa抗压强度）。然后，利用这些实验结果开发并验证了细长SR-CFST柱的数值模型。利用该模型，进行了广泛的参数分析，研究了高强材料对SR-CFST细长柱防火性能的影响。研究发现，与普通强度材料的SR-CFST细长柱相比，采用高强度材料显著改善了SR-CFST细长柱的防火性能。Elastic local buckling behaviour of ultra-long wind turbine blades with flexible core supportsShenglin Dai, Yuhang Wang, Xuhong Zhou, Xiaoming Zhangdoi:10.1016/j.tws.2024.112905柔性核心支撑的超长风力机叶片弹性局部屈曲行为Ultra-long wind turbine blades, exceeding 100 meters, are characterized by their thin-walled cylindrically curved shells sandwiched by flexible core supports; buckling analysis is, therefore, crucial in the cross-sectional designing. Conventional analytical solutions, which are based on models of compressive curved shells with simple or fixed supports, fail to account for the constraints imposed by flexible core supports. As a result, the buckling stability is under- or over-estimated, leading to either material waste or buckling occurrence. To address this challenge, this paper presents a study of the entire sandwich structure. Except for the existing modified Batdorf's parameter Z, which accounts for the curvature of curved shells, this study introduces a new dimensionless parameter β, which represents the ratio of the core web to the curved shell thickness, after eliminating the core web height h, which has a negligible impact on buckling loads. Although the elastic local buckling stress of the curved shell increased with the increase in both β and Z, but for the most common range of Z used in blades (8 ≤ Z ≤ 37), a range of β between 0.75 and 1.25 is recommended to balance buckling performance and material usage. This paper, then, identified a new suite of buckling deformation equations and developed an analytical equation based on the principle of minimum total potential energy to calculate the buckling loads of curved shells with flexible core supports by modifying that of simply supported, with the difference between analytical and validated numerical results being mainly in 10%.超过100米的超长风力涡轮机叶片，其特点是薄壁圆柱形弯曲壳体夹有柔性核心支撑；因此，屈曲分析在截面设计中是至关重要的。传统的解析解基于具有简单或固定支撑的压缩弯曲壳模型，无法考虑柔性核心支撑施加的约束。结果，屈曲稳定性被低估或高估，导致材料浪费或屈曲发生。为了解决这一挑战，本文提出了整个三明治结构的研究。除了现有的修正Batdorf参数Z（表示弯曲壳的曲率）外，本研究引入了一个新的无量纲参数β，该参数在消除对屈曲载荷影响较小的核心腹板高度h后，表示核心腹板与弯曲壳厚度的比值。虽然弯曲壳的弹性局部屈曲应力随β和Z的增加而增加，但对于叶片中最常用的Z范围（8≤Z≤37），建议在0.75 ~ 1.25之间的β范围内平衡屈曲性能和材料使用。在此基础上，建立了一套新的屈曲变形方程，并通过对简支弯曲壳屈曲载荷的修正，建立了基于最小总势能原理的解析方程，解析结果与验证数值结果的差异主要在10%以内。来源：复合材料力学仿真Composites FEM
