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Nonlocal effects on curved double-walled carbon nanotubes based on nonlocal theory
IF 2.2 3区 工程技术 Q2 MECHANICS Pub Date : 2025-01-29 DOI: 10.1007/s00419-025-02762-2
Ayşegül Tepe

Curved double-walled carbon nanotubes (CDWCNTs) are crucial components in nanoelectronics, mechanical sensors, and composite materials due to their unique geometry and structural properties. Electron microscopy images have revealed that carbon nanotubes are rarely perfectly straight, often exhibiting curvature or waviness along their length due to inherent geometrical imperfections. The accurate mechanical modeling of these structures is essential, particularly to capture size-dependent effects that classical elasticity theories fail to account for. In this study, a novel analytical framework was introduced for combining the initial value method with the approximate transfer matrix approach to analyze the mechanical behavior of CDWCNTs under anti-plane loading within the framework of nonlocal elasticity theory. The proposed methodology provides an effective and computationally efficient alternative to traditional analytical approaches. By analyzing displacements, rotations, bending moments, and shear forces, substantial deviations were revealed between classical and nonlocal elasticity solutions, particularly as the dimensionless nonlocal parameter (R/gamma ) decreased. The results show that nonlocal effects become dominant at smaller size parameters, especially in displacements, rotations, and bending moments, while shear forces remain unaffected. These findings emphasize the critical role of nonlocal effects in accurately predicting nanoscale mechanical responses and offer valuable insights for modeling advanced nanostructures in emerging technologies, such as microelectromechanical systems and nanotechnology. Convergence studies have confirmed the accuracy and stability of the proposed approach, thereby establishing this as a robust tool for modeling nanoscale structures.

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引用次数: 0
Nonlinear analysis of buckling and post-buckling behavior of porous FGM sandwich plates using a high-order continuity finite element approach
IF 2.2 3区 工程技术 Q2 MECHANICS Pub Date : 2025-01-27 DOI: 10.1007/s00419-025-02759-x
Hamza Chaabani, Abdessamed Baaddi, Lhoucine Boutahar, Khalid El Bikri

This study proposes an innovative numerical approach combining the finite element method and high-order continuation algorithm (FE-HCA) to analyze the nonlinear buckling and post-buckling behavior of porous FGM sandwich plates, evaluating the impact of porosity distribution and boundary loading types on their response. The approach is based on a Taylor series expansion of the unknowns in the problem, which transforms the nonlinear equations into a sequence of linear problems solved using the finite element method. The continuation technique is then employed to search for solution curves branch by branch, inverting a single tangent stiffness matrix per branch and providing an adaptive step size that adjusts according to the local nonlinearity of the solution branch. The mathematical formulation of the problem, based on high-order shear deformation theory (HSDT), introduces parabolic shear deformations, thus eliminating the need for shear correction factors. However, the applicability of HSDT is primarily limited to moderately thick plates, as it does not fully capture three-dimensional stress effects in very thick structures. The results show that the FE-HCA algorithm significantly reduces computation time, as demonstrated by a numerical example in the results section, where the number of tangent matrix inversions decreases from 4086 to only 12. A detailed parametric study highlights the influence of key parameters, such as porosity distribution, layer thickness, and loading types, on the buckling behavior. Compared to traditional iterative methods, the FE-HCA approach is faster and more efficient, offering significant gains in accuracy and computational cost, making it a powerful tool for analyzing FGM structures.

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引用次数: 0
Elastic–plastic bending analysis of beams with tension–compression asymmetry: bimodular effect and strength differential effect
IF 2.2 3区 工程技术 Q2 MECHANICS Pub Date : 2025-01-23 DOI: 10.1007/s00419-025-02758-y
Xiao-Ting He, Zhi-Peng Chen, Jun-Yi Sun

The tension–compression asymmetry is a basic mechanical property of materials themselves, which results in differences in elastic constant, yield strength, creep and fatigue. Among them, bimodular elastic effect and strength differential (SD) effect in plastic yielding will influence the whole elastic–plastic response. Existing studies have focused either on bimodular elastic effect of structures or on SD effect of materials, and few of them have combined the two effects. In this study, we theoretically analyze, for the first time, the elastic–plastic bending behavior of beams with the bimodular and SD effects, including loading and unloading process. The comparisons with our numerical simulation results and others’ experimental results validate the analytical solution obtained. The results indicate that during loading, the ratio of plastic limit bending moment to elastic limit bending moment is greater than known 3/2 and during unloading, the bending moment required by reverse yielding is greater than twice of elastic limit bending moment. The modulus ratio and yield strength ratio play an important role in elastic–plastic analysis and their relative magnitude determines whether the tensile edge yields first or the compressive edge. These results may help design optimal structural components in engineering.

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引用次数: 0
Forced vibration of an axially moving beam with nonhomogeneous boundary 非均匀边界轴向运动梁的受迫振动
IF 2.2 3区 工程技术 Q2 MECHANICS Pub Date : 2025-01-22 DOI: 10.1007/s00419-025-02760-4
Liang Jintao, Wang Ze, Li Xingli, Li Chongbo

Nonlinear vibration of axially moving systems has been a hot research topic. In the present paper, the influence of nonhomogeneous boundaries caused by wheel curvature on the dynamics of axially moving beams is explored. The equilibrium deformation of axially moving beams with nonhomogeneous boundaries is solved by using the iterative scheme developed by the differential quadrature method (DQM). Moreover, the forced vibration response of the system is evaluated by using the multi-scale method. The stability of the solutions for given parameters was determined. The results of the multi-scale method are verified by using the Galerkin truncation method (GTM). Numerical examples disclose that nonhomogeneous boundary conditions exhibit specific phenomena, namely an increase in the amplitude of the steady-state response, a decrease in the nonlinear characteristics, and an upward shift of the instability boundary. The discovery of this phenomenon is of great significance for the analysis of the dynamic response of axially moving beams under nonhomogeneous boundary conditions caused by wheel curvature. It is helpful for structural optimization and performance improvement in corresponding engineering fields.

轴向运动系统的非线性振动一直是一个研究热点。本文探讨了车轮曲率引起的非均匀边界对轴向运动梁动力学的影响。采用微分正交法(DQM)提出的迭代格式求解具有非均匀边界的轴向运动梁的平衡变形。此外,采用多尺度法对系统的强迫振动响应进行了评估。确定了给定参数下解的稳定性。采用伽辽金截断法(GTM)对多尺度方法的结果进行了验证。数值算例表明,非均匀边界条件表现出稳态响应幅度增大、非线性特征减小、不稳定边界向上移动等特殊现象。这一现象的发现对于分析车轮曲率引起的非均匀边界条件下轴向运动梁的动力响应具有重要意义。对相应工程领域的结构优化和性能改进具有一定的指导意义。
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引用次数: 0
A numerical study of the normal loading–unloading contact behaviors considering yield plateau and strain hardening 考虑屈服平台和应变硬化的正常加卸载接触行为的数值研究
IF 2.2 3区 工程技术 Q2 MECHANICS Pub Date : 2025-01-21 DOI: 10.1007/s00419-025-02761-3
Juncheng Luo, Jianhua Liu, Huanxiong Xia, Xiaohui Ao, Jian Zhang, Xuerui Zhang, Hui Zhang, Xin Liu

Loading–unloading is a ubiquitous phenomenon in engineering applications and an enduring topic in contact mechanics. Yield plateau and strain hardening are essential for material behaviors, but they have not been well considered in contact mechanics. This work developed a three-phase constitutive model to accurately describe the elastoplastic contact behaviors considering both yield plateau and strain hardening, merging the elastic-perfectly plastic and power-law hardening behaviors. The significance of the yield plateau and strain hardening was emphasized, and new empirical formulations of dimensionless contact load, area, and residual interference were presented, expanding the present knowledge of the elastoplastic contact problem.

加载-卸载是工程应用中普遍存在的现象,也是接触力学中一个经久不衰的课题。屈服平台和应变硬化是材料行为的必要条件,但在接触力学中尚未得到很好的考虑。本文建立了一个考虑屈服平台和应变硬化的三相本构模型,以准确描述弹塑性接触行为,融合了弹塑性和幂律硬化行为。强调了屈服平台和应变硬化的重要性,提出了新的无因次接触载荷、面积和残余干涉的经验公式,扩展了弹塑性接触问题的现有知识。
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引用次数: 0
Spectral realization of the method of matched sections for thin-plate vibration 薄板振动匹配截面法的频谱实现
IF 2.2 3区 工程技术 Q2 MECHANICS Pub Date : 2025-01-20 DOI: 10.1007/s00419-024-02755-7
Igor Orynyak, Anton Tsybulnyk, Kirill Danylenko

The paper further develops the method of matched sections as a new universal numerical technique. Like the finite element method, FEM, it supposes that: a) the domain is represented as a mesh of simple elements; b) algebraic relations between the main parameters are established from the governing differential equations; c) relationships from all elements are assembled into one global matrix. The relations between the main parameters are established similarly to those for the corresponding 1D task, so any 2D problem is considered a combination of two 1D problems—one is x-dependent, and the other is y-dependent. In all technical aspects, this paper resembles our previous one, which was devoted to the static analysis of plate bending. It operates by the same governing parameters, the same structure of the dependencies between them as well as the organization of the calculation scheme. The only difference consists in connection equations (analogy of element interpolation functions), which establish the relationship between inlet parameters (about the left and lower sides of the element) and outlet parameters (the left and upper sides). They are derived as the frequency-dependent ones (frequency is explicitly used in them) and in the liming case of very long (narrow) plates coincide with the known beam frequency-dependent solution. Several practical examples demonstrate the efficiency of the proposed method.

本文进一步发展了匹配截面法这一新的通用数值方法。与有限元法(FEM)一样,它假设:a)将域表示为简单单元的网格;B)由控制微分方程建立了主要参数之间的代数关系;C)所有元素的关系被组装成一个全局矩阵。主要参数之间的关系与相应的一维任务之间的关系类似,因此任何二维问题都可以认为是两个一维问题的组合,一个是x相关的,另一个是y相关的。在所有的技术方面,这篇论文类似于我们之前的一篇,这篇论文致力于板弯曲的静力分析。它通过相同的控制参数,它们之间的依赖关系的相同结构以及计算方案的组织来操作。唯一的区别在于连接方程(单元插值函数的类比),它建立了入口参数(关于单元的左下两侧)和出口参数(左上两侧)之间的关系。它们推导为频率相关的(其中明确使用频率),并且在很长(窄)板的限定情况下与已知的光束频率相关的解决方案相吻合。实例验证了该方法的有效性。
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引用次数: 0
Null-lagrangians in the micro-inertia contribution of the reduced relaxed micromorphic model. Theoretical and computational insights with applications 简化松弛微形态模型微惯量贡献中的零拉格朗日量。具有应用的理论和计算见解
IF 2.2 3区 工程技术 Q2 MECHANICS Pub Date : 2025-01-20 DOI: 10.1007/s00419-024-02709-z
Félix Erel-Demore, Jendrik Voss, Patrizio Neff, Angela Madeo

This paper identifies a null-Lagrangian in the reduced relaxed micromorphic model. We show that the introduction of a micro-inertia depending on the skew-symmetric part of (nabla dot{u}) with the macroscopic displacement field u does not enrich the dispersion relations of the reduced relaxed micromorphic model. Reciprocally, we show that one can switch from the full micro-inertia (with both sym(nabla dot{u}) and skew(nabla dot{u}) terms) to the reduced micro-inertia (only sym(nabla dot{u})) without any additional fitting. This is related to the fact that the introduction of such a skew-symmetric term is equivalent to a null-Lagrangian that leaves the bulk response unchanged while modifying the Neumann boundary conditions at the boundaries. Thus, the introduction of the skew-symmetric part of the micro-inertia, while redundant for wave dispersion, may potentially be used to improve the response of finite-size mechanical metamaterials at the homogenized macroscale due to boundary effects.

本文确定了简化松弛微态模型中的一个零拉格朗日量。我们证明了引入依赖于(nabla dot{u})的偏对称部分和宏观位移场u的微惯量并不能丰富简化松弛微形态模型的色散关系。反过来,我们表明可以从完整的微惯量(包含sym (nabla dot{u})和skew (nabla dot{u})项)切换到减少的微惯量(仅包含sym (nabla dot{u})项),而无需任何额外的拟合。这与这样一个事实有关,即引入这样一个偏对称项相当于零拉格朗日量,它在修改边界处的诺伊曼边界条件时保持体响应不变。因此,引入微惯性的偏对称部分,虽然对波色散是多余的,但可能被用来改善有限尺寸机械超材料在均匀化宏观尺度上由于边界效应的响应。
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引用次数: 0
Multi-scale Mohr–Coulomb strength criterion considering particle characteristic for soil 考虑土颗粒特性的多尺度莫尔-库仑强度准则
IF 2.2 3区 工程技术 Q2 MECHANICS Pub Date : 2025-01-20 DOI: 10.1007/s00419-024-02750-y
Deluan Feng, Lirui Zhou, Shihua Liang

Soil is a multi-scale granular material and has dramatic particulate and structural characteristics. Soil particles are divided into matrix and reinforcing particles to establish a multi-scale soil cell model according to the mechanical effect generated by the interaction between soil particles at various scales and the physical mechanism at different structural levels of soil. A multi-scale Mohr–Coulomb strength criterion (MCSC) that accounts for the particle size of soil is proposed by using the soil cell model. A series of soil cell samples are prepared to conduct consolidated and undrained tri-axial compression test to determine the model parameters. The yield locus of the multi-scale MCSC is drawn on the deviatoric plan based on the theoretical analysis and test results. Results show that the yield locus of the multi-scale MCSC is also hexagonal and expands with the decrease in the size of the reinforcing particle and the increase in the volume fraction of these particles. In this regard, the multi-scale MCSC can relate the microscopic physical details of soil to its macroscopic shear strength.

土壤是一种多尺度的颗粒状物质,具有显著的颗粒性和结构性特征。根据不同尺度土壤颗粒相互作用产生的力学效应和土壤不同结构层次的物理机制,将土壤颗粒分为基质颗粒和增强颗粒,建立多尺度土壤细胞模型。利用土细胞模型,提出了考虑土粒径的多尺度莫尔-库仑强度准则。制备了一系列土胞样,进行固结不排水三轴压缩试验,确定模型参数。在理论分析和试验结果的基础上,绘制了多尺度MCSC屈服轨迹的偏差图。结果表明:多尺度MCSC的屈服轨迹也是六边形的,并随着增强颗粒尺寸的减小和体积分数的增加而扩大;因此,多尺度MCSC可以将土的微观物理细节与其宏观抗剪强度联系起来。
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引用次数: 0
Dynamic strength of lined tunnel in hard rock medium under cylindrical unloading waves with visco-elastic interface effect 考虑粘弹性界面效应的圆柱卸载波作用下硬岩介质衬砌隧道动强度研究
IF 2.2 3区 工程技术 Q2 MECHANICS Pub Date : 2025-01-13 DOI: 10.1007/s00419-024-02752-w
Xue-Qian Fang, Xin-Yu Liu, Ya-Wen Xiong

In deep rock medium excavation, the unloading waves due to the blasting excavation can bring great damage to the neighboring structures. In this paper, the visco-elastic interface model is introduced to study the dynamic strength around an existing lined tunnel subjected to blasting and unloading waves. Three unloading paths because of tunnel blasting excavation are considered, and the dynamic interface stresses of existing lined tunnel resulting from these unloading paths are derived. To describe the wave fields around the existing tunnel and in the tunnel lining, the wave function expansion method is used, and the elastic and viscosity coefficients of interface is used to describe the interfacial characters. The analytical solutions of displacement and stress fields in the rock mass are obtained. An approximate numerical integration method is introduced to calculate the displacements and stresses around the existing tunnel. In numerical examples, the circumferential stress around the existing tunnel under different interface parameters, unloading paths and geometrical and physical parameters of tunnels is analyzed. Comparison with the existing numerical results validates this model.

在深部岩体开挖中,爆破开挖产生的卸荷波会对邻近结构体造成较大的破坏。本文引入粘弹性界面模型,研究既有衬砌隧道在爆破和卸荷波作用下的动强度。考虑了隧道爆破开挖引起的三种卸荷路径,推导了这些卸荷路径对既有衬砌隧道动界面应力的影响。采用波函数展开法描述既有隧道周围和隧道衬砌内的波场,用界面弹性系数和黏度系数描述界面特征。得到了岩体内位移场和应力场的解析解。采用近似数值积分法计算既有隧道周围的位移和应力。通过数值算例,分析了不同界面参数、卸荷路径和隧道几何物理参数下既有隧道的周向应力。与已有数值结果的对比验证了该模型的正确性。
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引用次数: 0
Assembly damage assessment of composite plates using uncertainty quantification and statistical analysis 用不确定度量化和统计分析评价复合材料板的装配损伤
IF 2.2 3区 工程技术 Q2 MECHANICS Pub Date : 2025-01-13 DOI: 10.1007/s00419-024-02753-9
Xin Tong, Jianfeng Yu, Shengqiang Cui, Dong Xue, Jie Zhang, Yuan Li

During the assembly process, deformation occurs in composite thin-walled parts, leading to damage at the hole connections of their single-longitudinal splice (SLS) joints. To predict assembly damage in the design process, it is usually necessary to combine uncertainty analysis with finite element analysis (FEA) methods. However, this field has limited progress due to the large size of the analyzed objects relative to their span and the large number of constraints that increase computational costs and complexity. In this study, we employed a linear elastic method to analyze the assembly process of thin-walled components. We achieved the uncertainty propagation (UP) and uncertainty quantification (UQ) of profile deviation random fields by using sub-modeling techniques, and obtained the stress distribution around the connection holes. The validity of the method was confirmed through a comparison with a full-process FEA of a three-hole SLS model. By integrating our method with the Hashin damage criterion, we proposed a statistical analysis approach for predicting assembly failure in SLS joints. The results demonstrated that considering only the profile deviation of the composite panel wall had a significant impact on material damage.

复合材料薄壁件在装配过程中会发生变形,导致其单纵向拼接(SLS)接头的孔连接处出现损伤。为了预测设计过程中的装配损伤,通常需要将不确定性分析与有限元分析方法相结合。然而,由于分析对象相对于其跨度的大尺寸以及增加计算成本和复杂性的大量约束,该领域的进展有限。本文采用线弹性方法对薄壁零件的装配过程进行了分析。利用子建模技术实现了剖面偏差随机场的不确定性传播(UP)和不确定性量化(UQ),得到了连接孔周围的应力分布。通过与三孔SLS模型的全过程有限元分析对比,验证了该方法的有效性。将该方法与Hashin损伤准则相结合,提出了一种预测SLS接头装配失效的统计分析方法。结果表明,仅考虑复合板壁廓形偏差对材料损伤有显著影响。
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引用次数: 0
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