International Journal of Engineering Science最新文献_第8页

Approaching and overcoming the limitations of the multiscale Capriccio method for simulating the mechanical behavior of amorphous materials 探讨并克服多尺度卡布里西奥法模拟非晶材料力学行为的局限性

IF 5.7 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal of Engineering Science

Pub Date : 2025-12-01 Epub Date: 2025-08-11 DOI: 10.1016/j.ijengsci.2025.104317

Lukas Laubert , Felix Weber , Fabrice Detrez , Sebastian Pfaller

The Capriccio method is a computational technique for coupling finite element (FE) and molecular dynamics (MD) domains to bridge their length scales and to provide boundary conditions typically employed in large-scale engineering applications. Earlier studies showed that strain inconsistencies between the coupled domains are caused by the coupling region’s (bridging domain, BD) resistance to spatial motion. Thus, this work examines influences of coupling parameters on strain convergence in Capriccio-coupled setups to study the mechanical behavior of solid amorphous materials. To this end, we employ a linear elastic 1D setup, imitating essential features of the Capriccio method, including force-transmitting anchor points (AP), which couple the domains via linear elastic springs. To assess the effect of more complex interactions in 3D models versus 1D results, we use an interdimensional mapping scheme, allowing qualitative and quantitative comparisons. For validation, we employ both an inelastic polystyrene MD model and a predominantly elastic silica glass MD model, each coupled to a corresponding FE material description. Our 1D results demonstrate that decreasing the conventionally high AP stiffness, along with other less significant measures, diminishes this motion resistance, revealing an optimal ratio between the material stiffness of the coupled domains and the cumulative AP stiffness. The 3D silica setup confirms that these measures ensure decent domain adherence and sufficiently low strain incompatibilities to study the mechanical behavior of elastic models. However, these measures turn out limited and may not ensure sufficient accuracy for studying the deformation and fracture behavior of Capriccio-coupled inelastic models. To overcome this, we employ a modified coupling approach, revising the Capriccio method’s AP concept by introducing a much lower so-called molecular statics stiffness during the FE calculation and a higher AP stiffness during only the MD calculation. Initial results on the 1D setup indicate that essential coupling limitations can be overcome, albeit with the risk of oscillatory strain amplifications depending on the BD’s design. This novel approach may enable a more accurate analysis of the mechanical behavior of coupled inelastic amorphous materials. We recommend evaluating its performance in 3D alongside additional methodological extensions. Overall, our results outline the current limitations of the Capriccio method and lay the groundwork for its targeted extension to study the mechanical behavior and, in particular, fracture phenomena in inelastic amorphous materials.

Capriccio方法是一种耦合有限元（FE）和分子动力学（MD）域的计算技术，以桥接它们的长度尺度，并提供大型工程应用中通常使用的边界条件。早期的研究表明，耦合域之间的应变不一致是由耦合区域（桥接域，BD）对空间运动的阻力引起的。因此，这项工作考察了耦合参数对卡布里西奥耦合装置中应变收敛的影响，以研究固体非晶材料的力学行为。为此，我们采用线性弹性一维设置，模仿Capriccio方法的基本特征，包括力传递锚点（AP），它通过线性弹性弹簧耦合域。为了评估3D模型中更复杂的相互作用与1D结果的影响，我们使用了一种多维映射方案，允许定性和定量比较。为了验证，我们采用了非弹性聚苯乙烯MD模型和主要弹性硅玻璃MD模型，每个模型都耦合到相应的FE材料描述。我们的一维结果表明，降低传统的高AP刚度，以及其他不太重要的措施，减少了这种运动阻力，揭示了耦合域的材料刚度和累积AP刚度之间的最佳比例。3D二氧化硅装置证实，这些措施确保了良好的区域粘附性和足够低的应变不相容性，以研究弹性模型的力学行为。然而，这些措施是有限的，可能不能保证足够的精度，以研究变形和断裂行为的capriccio -耦合非弹性模型。为了克服这个问题，我们采用了一种改进的耦合方法，修改了Capriccio方法的AP概念，在有限元计算中引入了一个更低的所谓分子静力刚度，而在MD计算中引入了一个更高的AP刚度。1D设置的初步结果表明，可以克服基本的耦合限制，尽管根据BD的设计存在振荡应变放大的风险。这种新方法可以更准确地分析耦合非弹性非晶态材料的力学行为。我们建议评估其在3D中的性能以及其他方法扩展。总的来说，我们的研究结果概述了当前Capriccio方法的局限性，并为其有针对性地扩展到研究非弹性非晶材料的力学行为，特别是断裂现象奠定了基础。

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引用次数: 0

Effect of wall models on hemodynamics in left coronary artery: A comparative numerical study 左冠状动脉壁模型对血流动力学影响的比较数值研究

IF 5.7 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal of Engineering Science

Pub Date : 2025-12-01 Epub Date: 2025-07-31 DOI: 10.1016/j.ijengsci.2025.104358

Asif Equbal, Paragmoni Kalita

Hemodynamic variables are vital for understanding the progression of cardiovascular diseases, but their accuracy depends on assumptions about arterial wall behaviour. Although the left anterior descending (LAD) branch of the left coronary artery (LCA) has been reported to be highly susceptible to atherosclerosis, there is a significant lack of studies comparing the effects of different wall models in this context. This study employs two-way fluid-structure interaction (FSI) simulations to investigate the impact of rigid, elastic, and hyperelastic wall models on the hemodynamics of a moderately stenosed LAD branch in an idealised LCA. The non-Newtonian properties of blood are captured using the Carreau viscosity model. Key hemodynamic parameters—primary velocity (

V_{p}

), streamwise vorticity, time-averaged wall shear stress (TAWSS), oscillatory shear index (OSI), relative residence time (RRT), and fractional flow reserve (FFR)—are evaluated across these models. Results show that the rigid model mostly exhibits higher

V_{p}

and TAWSS at the stenosis throat compared to the elastic and hyperelastic models. It overestimates the peak TAWSS by 6.22 % and 14.46 % relative to the elastic and hyperelastic models, respectively, suggesting a higher risk of plaque rupture in rigid walls. In terms of plaque progression, both the pre- and post-stenotic regions of the arterial wall show the most extensive affected areas in the hyperelastic model compared to the rigid and elastic models, indicated by severe negative

V_{p}

and critically low values of TAWSS, and critically high values of OSI and RRT. The FFR value is the highest for the hyperelastic model (0.95), followed by the elastic (0.94) and rigid models (0.91). These findings underscore the importance of incorporating arterial wall flexibility in hemodynamic studies to improve risk assessment and clinical accuracy.

血液动力学变量对于了解心血管疾病的进展至关重要，但其准确性取决于对动脉壁行为的假设。尽管有报道称左冠状动脉（LCA）的左前降支（LAD）极易发生动脉粥样硬化，但在这种情况下，比较不同壁模型的影响的研究明显缺乏。本研究采用双向流固相互作用（FSI）模拟来研究刚性、弹性和超弹性壁模型对理想LCA中中度狭窄LAD分支血流动力学的影响。血液的非牛顿特性是用卡罗黏度模型捕获的。主要的血流动力学参数——初级速度（Vp）、流向涡度、时间平均壁剪切应力（TAWSS）、振荡剪切指数（OSI）、相对停留时间（RRT）和分流储备（FFR）——通过这些模型进行了评估。结果表明：与弹性和超弹性模型相比，刚性模型在狭窄喉部表现出更高的Vp和TAWSS；相对于弹性模型和超弹性模型，TAWSS峰值分别高估了6.22%和14.46%，这表明刚性壁斑块破裂的风险更高。在斑块进展方面，与刚性和弹性模型相比，超弹性模型中动脉壁的狭窄前和狭窄后区域都显示出最广泛的受影响区域，表现为严重的负vpp和TAWSS的极低值，以及OSI和RRT的极高值。超弹性模型的FFR值最高（0.95），其次是弹性模型（0.94）和刚性模型（0.91）。这些发现强调了将动脉壁柔韧性纳入血流动力学研究以提高风险评估和临床准确性的重要性。

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引用次数: 0

Sound transmission through stiffened magnetoelectroelastic sandwich plates with negative Poisson’s ratio core 负泊松比磁芯加劲磁电弹性夹层板的声传输

IF 5.7 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal of Engineering Science

Pub Date : 2025-12-01 Epub Date: 2025-08-20 DOI: 10.1016/j.ijengsci.2025.104372

Y.S. Li , B.L. Liu , S. Li

This study investigates free vibration and sound transmission loss of stiffened magnetoelectroelastic (MEE) sandwich plates incorporating negative Poisson's ratio (NPR) cores. Firstly, a novel three-dimensional NPR structure is designed, and the effective material properties of the NPR structure are calibrated via an artificial neural network. Secondly, the equations of motion for stiffened MEE sandwich plates incorporating NPR cores mentioned above are derived using Hamilton's principle, yielding analytical solutions for free vibration under simply supported boundary conditions. Sound transmission loss (STL) under harmonic acoustic wave incidence is subsequently formulated. Finally, numerical case studies analyze the material properties of NPR cores and STL performance of stiffened MEE sandwich plates. This study elucidates the unique mechanical properties of intelligent NPR structures and establishes evaluation methodologies for multifield coupling effects on the acoustic insulation performance of such lightweight adaptive systems.

本文研究了带负泊松比（NPR）芯的加劲磁电弹性（MEE）夹层板的自由振动和传声损失。首先，设计了一种新型的三维NPR结构，并通过人工神经网络对NPR结构的有效材料性能进行了标定。其次，利用Hamilton原理推导了上述含NPR核的MEE夹层板的运动方程，得到了简支边界条件下自由振动的解析解。推导出谐波入射下的声传输损耗（STL）公式。最后，通过数值算例分析了核芯的材料性能和MEE加筋夹层板的STL性能。本研究阐明了智能NPR结构独特的力学性能，并建立了多场耦合对此类轻量化自适应系统隔声性能影响的评估方法。

引用次数: 0

Cosserat media in dynamics 动力学中的交叉介质

IF 5.7 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal of Engineering Science

Pub Date : 2025-12-01 Epub Date: 2025-08-20 DOI: 10.1016/j.ijengsci.2025.104368

Géry de Saxcé

Our aim is to develop a general approach for the dynamics of material bodies of dimension

d

represented by a matter manifold

N

of dimension

(d + 1)

embedded into the space–time

M

. It can be specialized for

d = 0

(pointwise object),

d = 1

(arch if it is a solid, flow in a pipe or jet if it is a fluid),

d = 2

(plate or shell if it is a solid, sheet of fluid),

d = 3

(bulky bodies). We call torsor a skew-symmetric bilinear map on the vector space of affine real functions on the affine tangent space to the space–time. We use the affine connections as originally developed by Élie Cartan, that is the connections associated to the affine group. We introduce a general principle of covariant divergence free torsor from which we deduce 10 balance equations. We show the relevance of this general principle by applying it for

d

from 1 to 4 in the context of the Galilean relativity.

我们的目标是为嵌入时空m中的维数（d+1）的物质流形N所表示的维数d的物质体的动力学开发一种通用方法。它可以专门用于d=0（点状物体），d=1（如果它是固体，则为拱形，如果它是流体，则为管道或射流），d=2（如果它是固体，则为板或壳），d=3（笨重的物体）。我们称其为仿射实数函数在仿射切空间到时空的向量空间上的偏对称双线性映射。我们使用最初由Élie Cartan提出的仿射连接，也就是与仿射基团相关的连接。引入协变散度自由扭量的一般原理，推导出10个平衡方程。我们通过在伽利略相对性的背景下应用d从1到4来证明这个一般原理的相关性。

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引用次数: 0

Effective field methods vs finite element models for microgeometries with ellipsoidal inclusions. Theory and application 椭球形夹杂微观几何的有效场方法与有限元模型。理论与应用

IF 5.7 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal of Engineering Science

Pub Date : 2025-12-01 Epub Date: 2025-09-11 DOI: 10.1016/j.ijengsci.2025.104373

E. Polyzos, L. Pyl

This study compares the predictions of analytical and numerical models employing ellipsoidal inclusions to determine the effective properties of composite materials. Three groups of factors influencing homogenization accuracy are investigated: the type of homogenization problem (elasticity, expansion, and conductivity), the material phase characteristics (isotropy, inclusion orientation, and inclusion aspect ratio), and the modeling methodologies, where effective field methods (EFMs) – including the Non-Interaction, the Mori–Tanaka and Maxwell methods – are evaluated against the pseudo grain decomposition method (PGDM) and numerical finite element (FE) models in a parametric study. The study considers ellipsoidal inclusions with aspect ratios ranging from 0.2 to 5 and orientation scattering from completely random to fully aligned. The results indicate that the type of homogenization problem does not significantly affect the prediction accuracy of EFMs and that the Mori–Tanaka and Maxwell methods show excellent agreement with FE models for all properties. The PGDM is shown to yield reliable results only for certain elastic properties (e.g.,

E_{11}

) for composites with inclusions of aspect ratios greater than 1. Therefore, it is concluded that the Mori–Tanaka and the Maxwell methods serve as the most suitable analytical alternatives to computationally intensive FE models.

本研究比较了采用椭球体夹杂物的解析模型和数值模型的预测结果，以确定复合材料的有效性能。研究了影响均质精度的三组因素：均质化问题的类型（弹性、膨胀和电导率）、材料相特性（各向同性、夹杂取向和夹杂长宽比）以及建模方法，其中有效的场方法(efm) -包括非相互作用、Mori-Tanaka和Maxwell方法-在参数化研究中对伪颗粒分解方法（PGDM）和数值有限元（FE）模型进行了评估。研究考虑椭球状包裹体，其纵横比为0.2 ~ 5，取向散射从完全随机到完全排列。结果表明，均匀化问题的类型对efm的预测精度没有显著影响，Mori-Tanaka和Maxwell方法在所有性质上都与有限元模型具有很好的一致性。对于长径比大于1的复合材料，PGDM仅对某些弹性性能（例如E11）产生可靠的结果。因此，Mori-Tanaka和Maxwell方法是计算密集型有限元模型的最合适的分析选择。

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引用次数: 0

On effect of anisotropy on anti-plane shear waves in elastic monoclinic half-space and plates 弹性单斜半空间和板中各向异性对反平面横波的影响

IF 5.7 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal of Engineering Science

Pub Date : 2025-12-01 Epub Date: 2025-09-30 DOI: 10.1016/j.ijengsci.2025.104392

Gennadi I. Mikhasev , Victor A. Eremeyev

Within the context of linear surface elasticity, we discuss the propagation of anti-plane surface waves, taking into account the anisotropy of the material. Here, we consider one of the most general crystal systems in the bulk, i.e. monoclinic symmetry. For the free surface, however, we consider rectangular symmetry. We derived the dispersion relations for three structures with surface energy: a half-space with a free surface; a layer of finite thickness; and a two-layered half-space. Surprisingly, these coincide with their isotropic counterparts, differing only in notation. Conversely, the anisotropy of the material in the bulk affects the displacement decay with depth. The pure exponential decay of displacements with the depth now transforms into decay with oscillations.

在线性表面弹性的背景下，考虑到材料的各向异性，我们讨论了反平面表面波的传播。在这里，我们考虑最普遍的晶体系统之一，即单斜对称。然而，对于自由曲面，我们考虑矩形对称。我们推导了三种具有表面能结构的色散关系：具有自由表面的半空间；层：有限厚度的一层；两层半空间。令人惊讶的是，它们与各向同性的对应物一致，只是在符号上有所不同。相反，块体中材料的各向异性影响位移随深度的衰减。位移随深度的纯粹指数衰减现在转变为振荡衰减。

引用次数: 0

Effect of periodic lamellar inclusions on interface integrity 周期性层状夹杂物对界面完整性的影响

IF 5.7 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal of Engineering Science

Pub Date : 2025-12-01 Epub Date: 2025-09-05 DOI: 10.1016/j.ijengsci.2025.104380

Chao Tang , Fei Su , Wen Zhao , Jingyu Zhang , Biao Wang , Lifeng Ma

The bond strength between dissimilar solids is highly sensitive to defects near or within the interface. Interfacial inclusions, which are ubiquitous in materials engineering, play a critical role in determining the local and global integrity of materials or structures. In this article, we propose a theoretical model for periodic rectangular lamellar inclusions at the interface of dissimilar solids. In view of the concept of line inclusion, the Kolosov–Muskhelishvili complex potentials for the homogeneous periodic inclusion problem are derived based on the Green’s function method within the framework of plane elasticity. The explicit analytical solution of the stress field of the inhomogeneous periodic rectangular lamellar inclusion problem with arbitrary eigenstrain distribution is derived with the aid of the equivalent eigenstrain principle. A new stress concentration factor (SCF) is consequently defined to assess the interface strength. The influence of the size and material of rectangular lamellar inclusions on the SCF is analyzed. The accuracy of the theoretical results is further verified by finite element simulations. The analytical formulae established in this study offer a straightforward yet effective approach for various inhomogeneous and homogeneous interfacial inclusion problems encountered in engineering practice.

不同固体之间的结合强度对界面附近或界面内的缺陷高度敏感。界面夹杂物在材料工程中无处不在，在决定材料或结构的局部和整体完整性方面起着至关重要的作用。本文提出了不同固体界面上周期性矩形片层夹杂物的理论模型。考虑到线包含的概念，在平面弹性的框架下，基于格林函数方法，导出了齐次周期包含问题的Kolosov-Muskhelishvili复势。利用等效本征应变原理，导出了具有任意本征应变分布的非均匀周期性矩形片层夹杂问题应力场的显式解析解。因此，定义了一个新的应力集中系数（SCF）来评估界面强度。分析了矩形层状夹杂物的尺寸和材料对SCF的影响。通过有限元仿真进一步验证了理论结果的准确性。本研究建立的解析公式为工程实践中遇到的各种非均匀和均匀界面夹杂问题提供了一个简单而有效的方法。

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引用次数: 0

Nonlinear dispersive waves in soft elastic laminates under finite magneto–deformations 有限磁变形下软弹性层合板的非线性色散波

IF 5.7 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal of Engineering Science

Pub Date : 2025-12-01 Epub Date: 2025-08-20 DOI: 10.1016/j.ijengsci.2025.104369

Harold Berjamin, Stephan Rudykh

Layered media can be used as acoustic filters, allowing only waves of certain frequencies to propagate. In soft magneto-active laminates, the shear wave band gaps (i.e., the frequency intervals for which shear waves cannot propagate) can be adjusted after fabrication by exploiting the magneto-elastic coupling. In the present study, the control of shear wave propagation in magneto-active stratified media is revisited by means of homogenisation theory, and extended to nonlinear waves of moderate amplitude. Building upon earlier works, the layers are modelled by means of a revised hard-magnetic material theory for which the total Cauchy stress is symmetric, and the incompressible elastic response is of generalised neo-Hookean type (encompassing Yeoh, Fung-Demiray, and Gent materials). Using asymptotic homogenisation, a nonlinear dispersive wave equation with cubic nonlinearity is derived, under certain simplifying assumptions. In passing, an effective strain energy function describing such laminates is obtained. The combined effects of nonlinearity and wave dispersion contribute to the formation of solitary waves, which are analysed using the homogenised wave equation and a modified Korteweg–de Vries (mKdV) approximation of the latter. The mKdV equation is compared to direct numerical simulations of the impact problem, and various consequences of these results are explored. In particular, we show that an upper bound for the speed of solitary waves can be adjusted by varying the applied magnetic field, or by modifying the properties of the microstructure.

层状介质可以用作声波过滤器，只允许某些频率的波传播。在软磁有源层合板中，可以利用磁弹性耦合在制作后调节剪切波带隙（即剪切波不能传播的频率间隔）。在本研究中，利用均匀化理论重新研究了磁活性层状介质中剪切波传播的控制，并将其推广到中等振幅的非线性波。在早期工作的基础上，通过修正的硬磁材料理论对这些层进行建模，其中总柯西应力是对称的，不可压缩弹性响应是广义的新hookean类型（包括Yeoh， Fung-Demiray和Gent材料）。在一定的简化假设下，利用渐近均匀化，导出了具有三次非线性的非线性色散波动方程。同时，得到了描述这种层合板的有效应变能函数。非线性和波色散的综合作用有助于孤波的形成，使用均匀波动方程和后者的改进Korteweg-de Vries （mKdV）近似来分析孤波。将mKdV方程与撞击问题的直接数值模拟进行了比较，并探讨了这些结果的各种后果。特别地，我们证明了孤波速度的上限可以通过改变外加磁场或通过改变微观结构的性质来调整。

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引用次数: 0

Experimental validation of Lamb wave dispersion curves using the Scaled Boundary Finite Element Method (SBFEM) 尺度边界有限元法（SBFEM）对Lamb波色散曲线的实验验证

IF 5.7 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal of Engineering Science

Pub Date : 2025-12-01 Epub Date: 2025-09-16 DOI: 10.1016/j.ijengsci.2025.104370

Carlos A. Galán Pinilla , Jorge Gosálbez , Darío Yesid Peña Ballesteros , Adan Y. León , Jabid Eduardo Quiroga

Dispersion curves are essential for characterizing Lamb wave propagation. A key challenge in estimating these curves is ensuring both computational efficiency and agreement with experimental results, particularly in complex, multilayered materials. This study focuses on bilayer structures, specifically metallic substrates with viscoelastic coatings, and employs the Scaled Boundary Finite Element Method (SBFEM) to generate dispersion curves. SBFEM discretizes the waveguide cross-section using high-order spectral finite elements and a Gauss–Lobatto–Legendre (GLL) node distribution, assigning a single spectral element per material layer. To validate the SBFEM curves, estimation is compared with experimental data obtained from metallic plates and bilayer structures consisting of viscoelastic coatings on steel substrates. The strong correlation between numerical predictions and experimental results highlights the effectiveness of SBFEM in accurately capturing Lamb wave behavior in bilayer waveguides with viscoelastic coatings while maintaining computational efficiency. These findings reinforce the method’s applicability for the analysis of wave propagation in complex, layered, and dissipative materials.

色散曲线是表征兰姆波传播的关键。估计这些曲线的一个关键挑战是确保计算效率和与实验结果的一致性，特别是在复杂的多层材料中。本研究针对双层结构，特别是粘弹性涂层的金属基底，采用缩放边界有限元法（SBFEM）生成色散曲线。SBFEM采用高阶光谱有限元和Gauss-Lobatto-Legendre （GLL）节点分布对波导截面进行离散化，为每层材料分配单个光谱单元。为了验证SBFEM曲线的有效性，将估计结果与金属板和由粘弹性涂层组成的钢基双层结构的实验数据进行了比较。数值预测与实验结果之间的强相关性表明了SBFEM在保持计算效率的同时准确捕获粘弹性涂层双层波导中兰姆波行为的有效性。这些发现加强了该方法在复杂、分层和耗散材料中波传播分析的适用性。

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引用次数: 0

Isogeometric boundary element analysis of nonlinear liquid sloshing in containers under pitching oscillation 俯仰振荡下容器内非线性液体晃动等几何边界元分析

IF 5.7 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal of Engineering Science

Pub Date : 2025-12-01 Epub Date: 2025-08-20 DOI: 10.1016/j.ijengsci.2025.104371

Quansheng Zang , Hao Hong , Jun Liu , Yanhui Zhong , Bei Zhang , Bin Li , Lei Gan

This paper proposes an isogeometric boundary element method (IGABEM) to solve the nonlinear liquid sloshing problem in a rectangular container subjected to oscillatory excitation. Based on the semi-Lagrange approach, a fixed global coordinate system and a local Cartesian coordinate system that moves synchronously with the container are defined. Starting from the Laplace equation, the boundary integral equations for the liquid sloshing problem are derived using Gauss’s divergence theorem and the integration by parts technique, while incorporating nonlinear kinematic and dynamic boundary conditions of the free surface. The corresponding boundary element solution system is then formulated. Non-Uniform Rational B-Splines (NURBS) are employed as shape functions to accurately describe the geometric boundaries and approximate the unknown physical fields. This method ultimately produces the discrete equations governing nonlinear liquid sloshing problem in an oscillating container. Compared with traditional polynomial interpolation shape functions, NURBS provide improved continuity both within elements and across element interfaces as well as local support. These properties make them particularly suitable for satisfying the continuity requirements of the liquid surface. For time integration, a second-order Runge–Kutta algorithm is employed for time-stepping to solve the IGABEM system equations, compute variable gradients at each time step, and update the computational grid in real-time. A series of numerical examples are presented, the results are compared with analytical solutions, experimental data, and alternative numerical methods for free and forced liquid sloshing, free surface fluctuations and internal pressures. These comparisons validate the accuracy and robustness of the proposed method. The numerical examples further investigate the effects of external excitation frequency, excitation amplitude, rotation center position, and bottom obstacle height on liquid sloshing responses in the rectangular container. The results indicate that changes in excitation frequency, vertical eccentricity of the rotation center, and obstacle height significantly influence the liquid sloshing behavior.

本文提出了一种求解振动激励下矩形容器内非线性液体晃动问题的等几何边界元法（IGABEM）。基于半拉格朗日方法，定义了一个固定的全局坐标系和一个与容器同步运动的局部笛卡尔坐标系。从拉普拉斯方程出发，利用高斯散度定理和分部积分法，结合自由曲面的非线性运动和动力边界条件，导出了液体晃动问题的边界积分方程。然后建立相应的边界元解体系。采用非均匀有理b样条（NURBS）作为形状函数，精确描述几何边界，逼近未知的物理场。该方法最终得到了振动容器中非线性液体晃动问题的离散方程。与传统的多项式插值形状函数相比，NURBS提供了更好的单元内和跨单元接口的连续性以及局部支持。这些特性使它们特别适合满足液体表面的连续性要求。对于时间积分，采用二阶龙格-库塔算法进行时间步进，求解IGABEM系统方程，在每个时间步长计算变量梯度，实时更新计算网格。给出了一系列的数值算例，并将结果与解析解、实验数据和可选的数值方法进行了比较，分析了自由和强制液体晃动、自由表面波动和内压。这些比较验证了所提方法的准确性和鲁棒性。数值算例进一步研究了外部激励频率、激励幅值、旋转中心位置和底部障碍物高度对矩形容器内液体晃动响应的影响。结果表明，激振频率、旋转中心垂直偏心率和障碍物高度的变化对液体晃动行为有显著影响。

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引用次数: 0