International Journal of Solids and Structures最新文献_第2页

Influence of block arrangement on mechanical performance in topological interlocking assemblies: A study of the versatile block 块体排列对拓扑互锁组件机械性能的影响：对多功能块的研究

IF 3.4 3区工程技术 Q1 MECHANICS

International Journal of Solids and Structures

Pub Date : 2024-10-20 DOI: 10.1016/j.ijsolstr.2024.113102

Topological interlocking assemblies (TIA) are arrangements of blocks kinematically constrained by a fixed frame, such that all rigid body motions of each block are prevented by the neighbouring blocks and the frame. In the literature, several blocks are introduced that can be arranged into interlocking assemblies, however only few of them can be arranged in non-unique ways. This study investigates a particularly versatile interlocking block called the Versatile Block: this block can be arranged in three different doubly periodic ways given by wallpaper symmetries. We investigate the hypothesis that the arrangement of copies of the same block influences the mechanical response of a TIA. We examine the interlocking mechanism and the correlation between arrangement and overall structural performance in planar TIA consisting of the Versatile Block. Furthermore, we analyse load transfer mechanisms within the assemblies and from the assemblies onto the frame. For fast apriori evaluation of the load transfer onto the frame we introduce a combinatorial model called Interlocking Flows. To investigate our assemblies from a mechanical point of view we conduct several finite element studies. These reveal a strong influence of arrangement on the structural behaviour, for instance, an impact on both the point and amount of maximum deflection under a given load, thereby confirming our hypothesis. We also evaluate the accuracy of the proposed Interlocking Flow model by a comparison with the finite element simulations.

拓扑互锁组件（TIA）是指在运动学上受固定框架约束的块体排列，这样每个块体的所有刚体运动都会受到相邻块体和框架的阻止。文献中介绍了几种可以排列成互锁组件的积木块，但只有少数积木块可以以非唯一的方式进行排列。本研究调查了一种被称为 "多功能积木 "的多功能互锁积木：这种积木可以通过壁纸对称性以三种不同的双周期方式排列。我们研究的假设是，相同积木块副本的排列方式会影响 TIA 的机械响应。我们研究了由多功能块组成的平面 TIA 的互锁机制以及排列方式与整体结构性能之间的相关性。此外，我们还分析了组件内部以及从组件到框架的荷载传递机制。为了快速先验地评估荷载传递到框架上的情况，我们引入了一个名为 "互锁流 "的组合模型。为了从机械角度研究我们的组件，我们进行了多项有限元研究。研究结果表明，排列方式对结构行为有很大影响，例如，对给定载荷下的最大挠度点和最大挠度量都有影响，从而证实了我们的假设。我们还通过与有限元模拟进行比较，评估了所提出的互锁流模型的准确性。

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引用次数: 0

A multi-scale constitutive model for AlSi10Mg alloy fabricated via laser powder bed fusion 通过激光粉末床熔融技术制造的 AlSi10Mg 合金的多尺度构成模型

IF 3.4 3区工程技术 Q1 MECHANICS

International Journal of Solids and Structures

Pub Date : 2024-10-19 DOI: 10.1016/j.ijsolstr.2024.113111

Additively Manufactured (AM) aluminum alloys find extensive applications in various fields due to their favorable properties. Numerical simulations play a crucial role in reducing experimental costs and enhancing reliability. Developing a reliable constitutive numerical model requires careful consideration of the hierarchical microstructure inherent in AM aluminum alloys. In response, a multiscale constitutive model has been formulated for the AlSi10Mg alloy, fabricated through laser powder bed fusion. This model incorporates crystal plasticity theory and micromechanics-based homogenization methods to establish representative volume elements at different length scales. These scales include the grain scale, polycrystalline scale, and macro scale, thus facilitating a seamless transition between them. The model is calibrated using macroscopic and average phase stress–strain relationships, demonstrating its capability to predict lattice strain in each phase. Additionally, this model incorporates a quantitative analysis of the effects of two-phase structure, melt pool structure, and porosity by adjusting microstructure parameters. The developed model is embedded into a user-defined material subroutine, providing an efficient approach to investigate microstructure-property relationships in AM alloys.

快速成型（AM）铝合金因其良好的性能而在各个领域得到广泛应用。数值模拟在降低实验成本和提高可靠性方面发挥着至关重要的作用。要开发可靠的结构数值模型，就必须仔细考虑 AM 铝合金固有的分层微观结构。为此，我们为通过激光粉末床融合制造的 AlSi10Mg 合金制定了一个多尺度构成模型。该模型结合了晶体塑性理论和基于微观力学的均质化方法，以建立不同长度尺度的代表性体积元素。这些尺度包括晶粒尺度、多晶尺度和宏观尺度，从而促进了它们之间的无缝过渡。该模型使用宏观和平均相应力应变关系进行校准，证明了其预测各相晶格应变的能力。此外，该模型还通过调整微观结构参数，对两相结构、熔池结构和孔隙率的影响进行了定量分析。开发的模型被嵌入到用户定义的材料子程序中，为研究 AM 合金的微观结构-性能关系提供了一种有效的方法。

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引用次数: 0

Three-dimensional buckling analysis of stiffened plates with complex geometries using energy element method 利用能量元素法对具有复杂几何形状的加劲板进行三维屈曲分析

IF 3.4 3区工程技术 Q1 MECHANICS

International Journal of Solids and Structures

Pub Date : 2024-10-18 DOI: 10.1016/j.ijsolstr.2024.113105

A novel numerical method, energy element method (EEM), is proposed for the three-dimensional (3D) buckling analysis of stiffened plates with complex geometries. The problem is formulated in a cuboidal domain, and any complex geometric stiffened plate is modeled by assigning cutouts within the cuboidal domain. The stiffened plate is considered as an energy body and is discretized using Gauss points with variable stiffness properties to simulate its energy distribution. Incorporating the extended interval integration, Gauss quadrature, variable stiffness properties, and Chebyshev polynomials, the strain energy of stiffened plates with complex geometries can be numerically simulated by putting the stiffness and thickness of Gauss points in the cutouts to zero in the cuboidal domain. Using the principle of minimum potential energy and Ritz solution procedure, the deformation and buckling behaviors of stiffened plates with complex geometries can be captured. As a result of the new formulations in EEM, new standard energy functionals and solving procedures have been developed. In addition, Gauss points are generated within the energy elements accounting for the geometric boundaries of the stiffened plate, which are characterized by level set functions. EEM is employed to investigate complex-shaped stiffened plates with straight or curvilinear stiffeners, and the results are compared to those obtained using FEM or mesh-free method. The precision, generalization, and stability of EEM are demonstrated.

针对具有复杂几何形状的加劲板的三维（3D）屈曲分析，提出了一种新的数值方法--能量元素法（EEM）。问题在一个立方体域中提出，通过在立方体域中分配切口来模拟任何复杂几何加劲板。加劲板被视为一个能量体，使用具有可变刚度属性的高斯点进行离散化，以模拟其能量分布。结合扩展区间积分、高斯四则运算、可变刚度特性和切比雪夫多项式，通过在长方体域内将切口中高斯点的刚度和厚度置零，可对具有复杂几何形状的加劲板的应变能进行数值模拟。利用最小势能原理和 Ritz 求解程序，可以捕捉到具有复杂几何形状的加劲板的变形和屈曲行为。在 EEM 中采用新公式后，还开发了新的标准能量函数和求解程序。此外，还在能量元素内生成了高斯点，这些高斯点反映了加劲板的几何边界，并以水平集函数为特征。EEM 用于研究带有直线或曲线加强筋的复杂形状加强板，并将结果与使用有限元或无网格方法获得的结果进行比较。证明了 EEM 的精确性、通用性和稳定性。

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引用次数: 0

Hydro-mechanical modeling of cohesive crack propagation of concrete lining in high internal pressure tunnels 高内压隧道混凝土衬砌内聚裂缝扩展的水力机械建模

IF 3.4 3区工程技术 Q1 MECHANICS

International Journal of Solids and Structures

Pub Date : 2024-10-16 DOI: 10.1016/j.ijsolstr.2024.113108

High pressure tunnels with concrete lining have been extensively utilized in project practice. However, due to the characteristic of concrete being susceptible to cracking under tension, the lining inevitably develops cracks under high internal water pressure, posing a serious threat to the operation of tunnels. This study aims at developing a hydro-mechanical numerical model of cohesive crack propagation of concrete lining in high internal pressure tunnels. In this regard, the determination of cohesive element parameters is elucidated, the contact simulation within the software ABAQUS is improved to accurately characterize the interface between lining and surrounding rock, and the numerical calculation process in ABAQUS is realized using indirect coupled method. The simulation results align well with the physical model test and engineering monitoring data, demonstrating that the proposed method can accurately simulate the hydraulic interactions of high pressure tunnel. Additionally, a comparison with calculation models employing tie constraints to simulate the lining-surrounding rock interface is conducted. Finally, comparison with traditional continuum method reveals that while both methods exhibit consistent overall trends. It is recommended to choose the proposed method when describing the discontinuous propagation process of cracks, which cannot be simulated by the continuum analysis method.

采用混凝土衬砌的高压隧道在工程实践中得到了广泛应用。然而，由于混凝土受拉易开裂的特性，衬砌在高内水压作用下不可避免地会产生裂缝，对隧道运营构成严重威胁。本研究旨在开发高内压隧道混凝土衬砌内聚裂缝扩展的水力学数值模型。为此，阐明了内聚元素参数的确定，改进了 ABAQUS 软件中的接触模拟，以准确表征衬砌与围岩之间的界面，并采用间接耦合法实现了 ABAQUS 中的数值计算过程。模拟结果与物理模型试验和工程监测数据非常吻合，表明所提出的方法能够准确模拟高压隧道的水力相互作用。此外，还与采用拉杆约束模拟衬砌-围岩界面的计算模型进行了比较。最后，通过与传统连续介质法的比较发现，两种方法的总体趋势一致。建议在描述连续分析方法无法模拟的裂缝不连续扩展过程时，选择建议的方法。

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引用次数: 0

An optimal penalty method for the joint stiffening in beam models of additively manufactured lattice structures 用于叠加制造晶格结构梁模型连接刚度的优化惩罚方法

IF 3.4 3区工程技术 Q1 MECHANICS

International Journal of Solids and Structures

Pub Date : 2024-10-16 DOI: 10.1016/j.ijsolstr.2024.113107

Additive manufacturing is revolutionizing structural design, with lattice structures becoming increasingly prominent due to their superior mechanical properties. However, simulating these structures quickly and accurately using the finite element method (FEM) remains challenging. Recent research has highlighted beam element simulation within FEM as a more efficient alternative to traditional solid FE simulations, achieving similar accuracy with reduced computational resources. However, a significant challenge is managing the lack of rigidity at nodes and the prevalence of low aspect ratio beams. While various methodologies have been proposed to address these issues, there is still a gap in the comprehensive evaluation of their limitations. An optimal node penalization methodology is required to expand the limited range of accurately represented lattice behavior. A preliminary study investigates lattice geometries through comparative analysis of solid and beam FE simulations. Built on this, we developed a methodology suitable to linear, dynamics and nonlinear beam FE simulations, contributing to enhanced computational speed and accuracy. Several lattice structures were printed using material jetting and quasi-static compressive tests were conducted to validate the methodology’s accuracy. The numerical results reveal a good accuracy between the proposed beam FE methodology and the experimental data, offering a better alternative to conventional FEM for energy absorption in terms of computing time.

增材制造正在彻底改变结构设计，晶格结构因其卓越的机械性能而日益突出。然而，使用有限元法（FEM）快速、准确地模拟这些结构仍然具有挑战性。最近的研究表明，有限元法中的梁元素模拟是传统实体有限元模拟的一种更有效的替代方法，它能以更少的计算资源实现类似的精度。然而，一个重大的挑战是如何处理节点刚性不足和低纵横比梁的普遍存在。虽然已经提出了各种方法来解决这些问题，但在全面评估这些方法的局限性方面仍存在差距。需要一种最佳节点惩罚方法来扩大精确表示晶格行为的有限范围。一项初步研究通过对实体和梁的 FE 仿真进行比较分析，对晶格几何进行了研究。在此基础上，我们开发了一种适用于线性、动力学和非线性梁 FE 仿真的方法，有助于提高计算速度和精度。我们使用材料喷射打印了几种晶格结构，并进行了准静态压缩试验，以验证该方法的准确性。数值结果表明，所提出的梁有限元方法与实验数据之间具有良好的准确性，在计算时间方面，可以更好地替代传统的能量吸收有限元方法。

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引用次数: 0

Finite element analysis of crack propagation, crack-gap-filling, and recovery behavior of mechanical properties in oxidation-induced self-healing ceramics 氧化诱导自修复陶瓷中裂纹扩展、裂隙填充和机械性能恢复行为的有限元分析

IF 3.4 3区工程技术 Q1 MECHANICS

International Journal of Solids and Structures

Pub Date : 2024-10-11 DOI: 10.1016/j.ijsolstr.2024.113104

The oxidation-induced self-healing of cracks is an attractive function for the application of ceramics in high-temperature structural components requiring high reliability. To further optimize materials or components for practical applications, the development of numerical simulation techniques is of importance. In this study, we examined crack growth, crack-gap-filling by oxide, and re-cracking behaviors in chevron-notched specimens under various load and temperature conditions by adopting a finite element analysis (FEA) approach incorporating a damage-healing constitutive model based on fracture mechanics and oxidation kinetics. Furthermore, by implementing the mechanical properties and oxidation kinetic parameters of reported self-healing ceramics composites into the FEA, we examined the effects of the composition and composite structure on the cracking and healing behaviors. Crack-gap-filling simulations suggested that the damage variables gradually decreased from the crack tip, and the minimum healing time was determined by the time required for the complete filling of the element at the crack mouth with the largest crack opening width. Furthermore, the recovery of the stiffness and strength could be successfully reproduced after complete healing with a reasonable healing temperature and time. The proposed FEA approach could also contribute to estimating the minimum healing time required at various temperatures to heal a given damage for various composites.

氧化引起的裂纹自愈合是陶瓷在要求高可靠性的高温结构部件中应用的一项极具吸引力的功能。为了进一步优化材料或部件的实际应用，数值模拟技术的发展具有重要意义。在本研究中，我们采用有限元分析（FEA）方法，结合基于断裂力学和氧化动力学的损伤愈合构成模型，研究了在不同载荷和温度条件下，楔形缺口试样的裂纹生长、氧化物填充裂纹间隙和再开裂行为。此外，通过将已报道的自愈合陶瓷复合材料的机械性能和氧化动力学参数应用到有限元分析中，我们研究了成分和复合材料结构对开裂和愈合行为的影响。裂缝间隙填充模拟表明，损伤变量从裂缝尖端逐渐减小，最小愈合时间由裂缝开口宽度最大的裂缝口元素完全填充所需的时间决定。此外，在合理的愈合温度和时间下，完全愈合后的刚度和强度恢复也能成功再现。所提出的有限元分析方法还有助于估算各种复合材料在不同温度下愈合特定损伤所需的最短愈合时间。

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引用次数: 0

Three-dimensional elastic–plastic lattice-spring model based on sapphire crystal structure and its application to impact characterisation studies 基于蓝宝石晶体结构的三维弹塑性晶格弹簧模型及其在冲击特性研究中的应用

IF 3.4 3区工程技术 Q1 MECHANICS

International Journal of Solids and Structures

Pub Date : 2024-10-10 DOI: 10.1016/j.ijsolstr.2024.113097

A thirteen-node octahedral three-dimensional lattice-spring model based on the sapphire crystal structure is established by applying the parameter mapping theory, and the finite element stiffness matrix is mapped into the linear spring stiffness coefficients of the lattice-spring model according to the parameter mapping method, so that the selection of the spring stiffness coefficients has a strict mathematical derivation. The elastic–plastic potential function that unifies the elastic–plastic characteristics of the material and the fracture energy is established. The lattice-spring model is tested by three algorithms, including longitudinal wave velocity, three-dimensional crack extension path under dynamic indentation, and impact compression deformation and lattice size sensitivity test, and the test results show that the established three-dimensional lattice-spring model has a high computational accuracy. The correctness of the calculation of the lattice-spring model is verified by comparing the calculation of the evolution process of spherical impact damage on the edge of sapphire under different crystal directions with the experiment.

应用参数映射理论建立了基于蓝宝石晶体结构的十三节点八面体三维晶格弹簧模型，并根据参数映射方法将有限元刚度矩阵映射为晶格弹簧模型的线性弹簧刚度系数，从而使弹簧刚度系数的选择具有严格的数学推导。建立了统一材料弹塑性特征和断裂能的弹塑性势函数。通过纵波速度、动态压痕下三维裂纹扩展路径、冲击压缩变形与晶格尺寸敏感性试验等三种算法对晶格弹簧模型进行了测试，测试结果表明所建立的三维晶格弹簧模型具有较高的计算精度。通过比较不同晶向下蓝宝石边缘球形冲击损伤演变过程的计算结果与实验结果，验证了晶格弹簧模型计算的正确性。

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引用次数: 0

Elastic wave propagation in periodic stress-driven nonlocal Timoshenko beams 周期应力驱动非局部季莫申科梁中的弹性波传播

IF 3.4 3区工程技术 Q1 MECHANICS

International Journal of Solids and Structures

Pub Date : 2024-10-10 DOI: 10.1016/j.ijsolstr.2024.113103

Nonlocal theories are well established to model statics and dynamics of small-size structures. Recent studies investigated elastic wave propagation in nonlocal beams and attention focused on periodic nonlocal beams, either endowed with resonators or resting on supports, for relevant applications at small scale. In this context, this work proposes a stress-driven nonlocal Timoshenko beam formulation and develops an original and comprehensive analytical/computational framework for wave propagation analysis in bare and periodic beams.

The framework addresses infinite and finite beams. First, exact analytical expressions are derived for the dispersion curves of the bare beam, which provide full insight into the effects of nonlocality. Second, an exact Plane Wave Expansion method is devised for periodic beams, either equipped with mass-spring resonators or resting on elastic supports; both

ω (q)

and

q (ω)

dispersion curves are derived in this work, where

ω

is the frequency and

q

is the wave number. Third, an approximate homogenization approach is formulated to estimate opening frequencies and sizes of band gaps induced by mass-spring resonators. Finally, a two-field finite element method is proposed to calculate the transmittance of finite periodic beams.

Numerical applications investigate the dispersion diagram of bare and periodic beams for different internal lengths of the stress-driven nonlocal model. Remarkably, results for finite periodic beams validate the predictions from wave propagation analysis of corresponding infinite ones. Moreover, parametric analyses show the capability of the stress-driven nonlocal model in capturing typical small-size effects.

非局部理论在模拟小尺寸结构的静力学和动力学方面已得到广泛应用。最近的研究调查了非局部梁中的弹性波传播，并将注意力集中在周期性非局部梁上，这些梁要么带有谐振器，要么位于支撑物上，可用于小尺度的相关应用。在此背景下，本研究提出了应力驱动的非局部季莫申科梁公式，并为裸梁和周期梁中的波传播分析开发了一个原创性的综合分析/计算框架。首先，推导出裸梁频散曲线的精确分析表达式，从而全面了解非局部性的影响。其次，针对配备质量弹簧谐振器或位于弹性支撑上的周期梁，设计了精确的平面波展开方法；在这项工作中，ω(q) 和 q(ω) 扩散曲线都被推导出来，其中 ω 是频率，q 是波数。第三，提出了一种近似均质化方法来估算质量弹簧谐振器诱导的开口频率和带隙大小。最后，提出了一种双场有限元方法来计算有限周期梁的透射率。数值应用研究了应力驱动非局部模型不同内部长度的裸梁和周期梁的色散图。值得注意的是，有限周期梁的结果验证了相应无限周期梁的波传播分析预测。此外，参数分析表明应力驱动非局部模型能够捕捉典型的小尺寸效应。

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引用次数: 0

Dynamic digital image correlation method for rolling convective contact 滚动对流接触的动态数字图像相关方法

IF 3.4 3区工程技术 Q1 MECHANICS

International Journal of Solids and Structures

Pub Date : 2024-10-09 DOI: 10.1016/j.ijsolstr.2024.113096

Digital image correlation (DIC) is an increasingly popular and effective non-contact method for measuring full-field displacements and strains of deformable bodies under load. Current DIC methods applied to bodies undergoing large displacements and rotations require a large measurement area for both the reference (i.e., undeformed) image and the deformed images. This can limit the resulting resolution of the displacement and strain fields. To address this issue, we propose a two-stage dynamic DIC method capable of measuring displacements and strains under material convection with high resolution. During the first stage, the reference image is assembled from smaller, high-resolution images of the undeformed object obtained using a spatially-fixed or moving frame. Following capture, each sub-image is rigidly translated and rotated into its appropriate place, thereby producing a full, high-resolution image of the reference body. In stage two, images of the loaded and deformed body, again obtained using a small camera frame with high resolution, are aligned with matching regions of the undeformed composite image using BRISK feature detection before performing DIC. We demonstrate the method on a contact problem whereby an elastomeric roller travels along a rigid surface. In doing so, we obtain fine-resolution measurements of the state of strain of the region of the roller sidewall in contact with the substrate, even as new material convects through the region of interest. We present these measurements as a series of images and videos capturing strain evolution as the roller transitions from static loads to a fully dynamic steady-state, documenting the effectiveness of the method.

数字图像相关（DIC）是一种日益流行和有效的非接触式方法，用于测量负载下可变形体的全场位移和应变。目前应用于大位移和大旋转体的 DIC 方法需要对参考（即未变形）图像和变形图像进行大面积测量。这会限制位移和应变场的分辨率。为了解决这个问题，我们提出了一种两阶段动态 DIC 方法，能够以高分辨率测量材料对流下的位移和应变。在第一阶段，参考图像由未变形物体的较小、高分辨率图像组合而成，这些图像通过空间固定或移动框架获得。捕捉后，每个子图像都会被刚性平移和旋转到适当的位置，从而生成参考体的完整高分辨率图像。在第二阶段，再次使用高分辨率的小型相机帧获取加载和变形体的图像，在执行 DIC 之前，使用 BRISK 特征检测将其与未变形复合图像的匹配区域对齐。我们在弹性辊子沿刚性表面移动的接触问题上演示了该方法。在此过程中，我们获得了辊筒侧壁与基体接触区域应变状态的精细分辨率测量值，甚至在新材料通过相关区域对流时也是如此。我们将这些测量结果以一系列图像和视频的形式呈现，捕捉滚筒从静态负载过渡到完全动态稳态时的应变演变，记录下该方法的有效性。

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引用次数: 0

A force-density framework for flexible multi-body dynamic analysis of clustered tensegrity structures 用于集群张弦结构柔性多体动态分析的力密度框架

IF 3.4 3区工程技术 Q1 MECHANICS

International Journal of Solids and Structures

Pub Date : 2024-10-09 DOI: 10.1016/j.ijsolstr.2024.113098

This paper develops a versatile and effective force-density framework for the flexible multi-body dynamic analysis of clustered tensegrity structures. In this framework, the force density is selected as the basic variable instead of force, and the clustered tensegrity structure is mathematically described in a vector and matrix form, encompassing topology, geometry, material, and force properties. A non-negative variable is defined as an indicator of the member stress state, and a complementary function is constructed to address the discontinuity issues that arise from the unidirectional axial stiffness of cables. Dynamic formulas are established within this force-density framework, with nodal coordinates selected as generalized parameters and formulations constructed in a matrix form. A complementary framework is established as an alternative for solving the dynamic equations, transforming the isolated steps of Newton’s iteration and cable state judgment (slack or tension) into a unified one, bringing more potential for improving solving efficiency. Numerical simulations are carried out to validate the approach, demonstrating that it effectively reveals the dynamic oscillation, tension changes, and cable slack behavior of clustered tensegrity structures during shape control. Comparative studies highlight the advantage of computational efficiency. The method proposed in this paper provides a robust mathematical model for studying clustered tensegrity structures, particularly regarding the shape control of deployable, active, and intelligent structures, aiding in understanding dynamic oscillation, tension changes, and cable slack behavior during their deformation. The methods can also be applied to cable net structures and other prestressed pin-jointed systems.

本文开发了一种多功能且有效的力密度框架，用于对集束张弦结构进行灵活的多体动力学分析。在这一框架中，力密度被选为基本变量而不是力，聚类张拉整体结构以矢量和矩阵的形式进行数学描述，包括拓扑、几何、材料和力属性。一个非负变量被定义为构件应力状态的指示器，并构建了一个补充函数，以解决电缆单向轴向刚度引起的不连续性问题。在此力密度框架内建立动态公式，选择节点坐标作为通用参数，并以矩阵形式构建公式。作为求解动态方程的替代方法，建立了一个补充框架，将牛顿迭代和电缆状态判断（松弛或拉伸）的孤立步骤转化为统一步骤，为提高求解效率带来了更多潜力。为了验证该方法，我们进行了数值模拟，结果表明该方法能有效揭示集群张弦结构在形状控制过程中的动态振荡、张力变化和拉索松弛行为。对比研究凸显了计算效率的优势。本文提出的方法为研究簇状张弦结构，特别是可部署、主动和智能结构的形状控制提供了一个稳健的数学模型，有助于理解其变形过程中的动态振荡、张力变化和缆索松弛行为。这些方法还可应用于索网结构和其他预应力销钉连接系统。

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引用次数: 0