Engineering Analysis with Boundary Elements最新文献_第6页

A hybrid radial basis function-finite difference method for modelling two-dimensional thermo-elasto-plasticity, Part 3: Application to thermo-mechanical modelling of continuous casting of steel billets 二维热弹塑性建模的径向基函数-有限差分混合方法，第3部分：在连铸钢坯热力学建模中的应用

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2025-12-31 DOI: 10.1016/j.enganabound.2025.106619

Gašper Vuga, Boštjan Mavrič, Tadej Dobravec, Božidar Šarler

This paper, Part 3 of a series, extends the previously developed strong-form hybrid radial basis function-finite difference (RBF-FD) method to model the thermomechanics of continuous casting (CC) of steel. Part 1 introduced the method for non-linear thermomechanics, and Part 2 applied it to the cooling of steel bars on a cooling bed. Here, a one-way coupled thermo-mechanical slice model is developed, where the temperature field provides thermal loading for the mechanical analysis. The previously introduced 2.5D formulation is adapted to include strand straightening. A visco-plastic material model, validated in our recent work, is used to describe material behaviour close to the mushy-zone temperatures. The analysis focuses on the solidified part of the strand, while the space discretisation remains constant and liquid-zone results are disregarded. Two hot-tearing criteria—temperature-based and stress-based are implemented and compared with experimental data, showing that the stress-based approach produces more realistic predictions. The influence of electromagnetic stirring, steel grade composition, and casting speed on hot-tearing susceptibility is explored. This study represents the first strong-form RBF-FD solution of CC thermomechanics, demonstrating that the hybrid RBF-FD can efficiently handle complex non-linear thermo-mechanical behaviour and allows for further process optimisation and defect mitigation in industrial CC.

本文是该系列的第3部分，扩展了先前开发的强形式混合径向基函数-有限差分（RBF-FD）方法来模拟钢的连铸（CC）的热力学。第一部分介绍了非线性热力学方法，第二部分将其应用于冷床上钢筋的冷却。本文建立了单向耦合热-机械切片模型，其中温度场为力学分析提供热载荷。先前介绍的2.5D配方适用于包括钢绞线矫直。在我们最近的工作中验证的粘塑性材料模型用于描述接近糊状区温度的材料行为。分析的重点是钢绞线的凝固部分，而空间离散保持不变，并忽略液区结果。实现了基于温度和基于应力的热撕裂判据，并与实验数据进行了比较，结果表明基于应力的方法预测结果更加真实。探讨了电磁搅拌、钢种成分、浇注速度对热撕裂敏感性的影响。这项研究代表了CC热力学的第一个强形式RBF-FD解决方案，证明了混合RBF-FD可以有效地处理复杂的非线性热力学行为，并允许进一步优化工业CC的过程和缺陷缓解。

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引用次数: 0

Numerical study of hole-cutting effect using annular shaped charges in underwater explosions 水下爆炸环形聚能药孔切割效应的数值研究

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2025-12-31 DOI: 10.1016/j.enganabound.2025.106624

Yu Tian , Fu-Ren Ming , Hao Chen , Xiang-Li Fang , Ping-Ping Wang

The metal jet formed by a conventional shaped charge has a high penetration depth but a narrow damage range. To expand the damage range of the metal jet, an annular shaped charge can be employed. In this paper, the underwater explosions of annular shaped charges are simulated by a graphic processing unit accelerated axisymmetric Riemann-SPH method, and the accuracy is verified by experiments. The hole-cutting effect using an annular shaped charge in an underwater explosion is analyzed, and the characteristics of the annular shaped charge are compared with a spherical segment shaped charge. Furthermore, the effects of the liner thickness on the annular jet are explored. It is revealed that the damage mode inflicted on the plate by an explosive formed projectile (EFP) is impact penetration, whereas that by an annular jet is cutting. The plate’s breach size caused by the annular jet reaches 1.79 times the charge radius and 3.15 times that of EFP. Our findings also reveal that there is an optimal dimensionless maximum liner thickness

λ

(

λ = T

/

R_{z}

) to maximize the breach size

d_{p}

, which is 0.12 for a charge mass of 60kg. This paper can provide support for the optimization design of the shaped charge.

传统聚能形成的金属射流侵彻深度高，但损伤范围窄。为了扩大金属射流的破坏范围，可以采用环形聚能装药。本文采用图形处理单元加速轴对称Riemann-SPH方法对水下环形装药爆炸进行了模拟，并通过实验验证了模拟结果的准确性。分析了水下爆炸中环形聚能药的割孔效果，并将环形聚能药与球段聚能药的特性进行了比较。此外，还探讨了衬板厚度对环形射流的影响。结果表明，爆炸成形弹丸（EFP）对板的损伤模式为冲击侵彻，而环形射流对板的损伤模式为切割。环形射流引起的板裂尺寸达到装药半径的1.79倍，EFP的3.15倍。我们的研究结果还表明，存在一个最佳无因次最大衬里厚度λ (λ=T/Rz)来最大化裂口尺寸dp，当装药质量为60kg时，裂口尺寸dp为0.12。本文可为聚能药的优化设计提供依据。

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引用次数: 0

An RBF–FD method for pricing under the Bates model: Handling stochastic volatility and jump processes 贝茨模型下的RBF-FD定价方法：处理随机波动和跳跃过程

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2025-12-30 DOI: 10.1016/j.enganabound.2025.106622

Yicheng Liu , Yilin Li , Tao Liu

This work introduces a meshless computational methodology for the valuation of European-style options under the Bates stochastic volatility jump-diffusion framework. The governing dynamics are described by a two-dimensional partial integro-differential equation (PIDE) that incorporates both mixed derivative operators and a nonlocal integral component. The numerical strategy is constructed within the Radial Basis Function-Finite Difference (RBF–FD) paradigm, employing a modified multiquadric kernel that facilitates the analytical determination of localized differentiation weights. Spatial discretization is achieved through the method of lines, where the integral operator is approximated by means of quadrature rules combined with accurate interpolation techniques. Numerical experiments reveal that the proposed solver delivers superior accuracy while lowering computational cost in comparison with classical schemes.

本文介绍了在贝茨随机波动跳-扩散框架下欧式期权估值的无网格计算方法。控制动力学由包含混合导数算子和非局部积分分量的二维偏积分微分方程（PIDE）描述。数值策略是在径向基函数-有限差分（RBF-FD）范式内构建的，采用改进的多重二次核，便于解析确定局部微分权值。空间离散化是通过线的方法实现的，其中积分算子是通过正交规则结合精确的插值技术来逼近的。数值实验表明，与经典格式相比，该算法具有更高的精度和更低的计算成本。

引用次数: 0

A time-domain method of auxiliary sources for efficient analysis of transient electromagnetic scattering by moderately conductive cylinders 中等导电性圆柱瞬变电磁散射有效分析的辅助源时域方法

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2025-12-29 DOI: 10.1016/j.enganabound.2025.106605

Minas Kouroublakis , Nikolaos L. Tsitsas , Yehuda Leviatan

This paper presents a time-domain implementation of the Method of Auxiliary Sources (MAS) combined with the Standard Impedance Boundary Condition (SIBC) for electromagnetic scattering problems involving cylindrical scatterers with finite but moderate conductivity. The proposed approach focuses on solving the two-dimensional problem using a first-order SIBC, which is valid when the conductivity is sufficiently higher than the maximum spectral frequency times the dielectric permittivity of the scatterer. This regime includes moderately conductive materials — such as carbon-based composites, conductive polymers, and doped dielectrics — that are increasingly used in real-world radio-frequency applications, including wearable electronics, electromagnetic interference shielding, and biomedical sensors. Under the above validity conditions, the interaction between the incident wave and the scatterer is dominated by surface effects, allowing for an efficient and accurate modeling strategy without the need to compute internal fields. The theoretical formulation of the time-domain MAS-SIBC method is developed, followed by extensive numerical testing on various geometries whose cross section is a closed curve. Such geometries include circular, elliptical, super-circular, rounded-triangular, and inverted-elliptical scatterers. A planar geometry is also tested. All results are validated against analytical solutions and commercial frequency-domain solvers, demonstrating the accuracy and practical potential of the proposed method. The findings suggest that time-domain MAS-SIBC offers a promising and computationally efficient approach for modeling scattering from materials even with moderate conductivity.

本文提出了一种结合标准阻抗边界条件（SIBC）的辅助源法（MAS）的时域实现方法，用于求解电导率有限但中等的圆柱形散射体的电磁散射问题。该方法着重于利用一阶SIBC求解二维问题，当电导率足够高于散射体的最大频谱频率乘以介电常数时，该方法有效。该体系包括中等导电性材料，如碳基复合材料、导电聚合物和掺杂电介质，这些材料越来越多地用于现实世界的射频应用，包括可穿戴电子产品、电磁干扰屏蔽和生物医学传感器。在上述有效条件下，入射波与散射体之间的相互作用主要由表面效应主导，因此无需计算内部场即可实现高效准确的建模策略。建立了时域MAS-SIBC方法的理论公式，并对各种截面为封闭曲线的几何形状进行了大量的数值试验。这些几何形状包括圆形、椭圆形、超圆形、圆三角形和倒椭圆形散射体。一个平面几何也进行了测试。所有结果都与解析解和商用频域解进行了验证，证明了所提出方法的准确性和实用潜力。研究结果表明，时域MAS-SIBC为中等导电性材料的散射建模提供了一种有前途的、计算效率高的方法。

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引用次数: 0

A stochastic dynamic analysis method for plate structures based on meshless method and new point estimate method: A case study of high-speed railway box girder bridges 基于无网格法和新的点估计法的板结构随机动力分析方法——以高速铁路箱梁桥为例

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2025-12-27 DOI: 10.1016/j.enganabound.2025.106616

Zhanjun Shao , Zefeng Liu , Xuan Peng , Yufei Chen , Delei Yang , Linxin Peng , Ping Xiang

In previous studies of train–track–bridge coupled systems (TTBCS), box girder bridges were often simplified as one-dimensional Euler beam models, which limited the investigation of the effects of material uncertainties in the top plate, webs, and bottom plate on dynamic responses. To address this limitation, this study introduces a multi-plate box girder bridge model and proposes a stochastic dynamic computation framework combining the meshless method and new point estimate method (NPEM). Two-dimensional random field modeling is applied to the material parameters of each plate, and Karhunen–Loève (KL) expansion is employed to transform these fields into random variables. Subsequently, NPEM is utilized to compute the statistical characteristics of the dynamic responses of the TTBCS. By comparing the effects of different random fields on the dynamic responses, the sensitivity of the responses to various material parameters is quantitatively analyzed. The results indicate that the vertical displacement of the bridge is most sensitive to the thickness uncertainty of the bottom plate, followed by the Young’s modulus. The lateral displacement is most sensitive to the thickness uncertainty of the traffic-side web, followed by the Young’s modulus. The density random field exerts the greatest influence on the bridge natural frequency. In the absence of seismic effects, uncertainties in the substructure have minimal influence on vehicle accelerations.

在以往的列车-轨道-桥梁耦合系统（TTBCS）研究中，箱梁桥通常被简化为一维欧拉梁模型，这限制了对顶板、腹板和底板材料不确定性对动力响应影响的研究。针对这一局限性，本文引入多板箱梁桥模型，提出了一种结合无网格法和新点估计法（NPEM）的随机动力计算框架。对每块板的材料参数进行二维随机场建模，利用karhunen - lo (KL)展开将这些场转化为随机变量。随后，利用NPEM计算TTBCS动态响应的统计特征。通过比较不同随机场对动态响应的影响，定量分析了响应对不同材料参数的敏感性。结果表明：桥梁的竖向位移对底板厚度的不确定性最敏感，其次是杨氏模量；横向位移对车辆侧腹板厚度的不确定性最敏感，其次是杨氏模量。密度随机场对桥梁固有频率的影响最大。在没有地震影响的情况下，子结构的不确定性对车辆加速度的影响最小。

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引用次数: 0

CHFV model: Chinese herbal formula verification model CHFV模型：中草药配方验证模型

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2025-12-27 DOI: 10.1016/j.enganabound.2025.106620

Wenhua Zheng , Jianqiang Du , Yanchen Zhu , Yang Yuan , Zhikai Zhang , Shaokun Lan

The rapid advancement of artificial intelligence (AI) has greatly accelerated the development of AI-driven solutions in the medical field. However, research on the application of AI in Chinese Medicine has lagged behind this trend. A critical area in Chinese Medicine is the verification of Chinese herbal formulas, which plays an essential role in pharmacy and in the development of automated formula dispensing systems. At present, there is a significant lack of studies exploring the use of AI for Chinese Herbal Formula Verification (CHFV). To address this gap, we conducted a comprehensive analysis of the challenges associated with CHFV and proposed an innovative CHFV model designed to improve the verification process of Chinese herbal formulas. To mitigate the problems of class imbalance and poor label quality in Chinese herbal medicine datasets, we introduced a personalized focusing mechanism (FM) grounded in both spatial simulations and real experiments. Furthermore, to overcome the challenges posed by limited inter-class variance and substantial intra-class variance in Chinese herbal medicine features, we developed a prior knowledge matrix and confidence reconstruction algorithms, which significantly enhanced the performance of our CHFV model. The source code and data are publicly available at https://github.com/Wenhua-Zheng/CHFV.

人工智能（AI）的快速发展极大地加速了AI驱动解决方案在医疗领域的发展。然而，人工智能在中医领域的应用研究却滞后于这一趋势。中药的一个关键领域是中药配方的验证，这在药学和自动配方配药系统的发展中起着至关重要的作用。目前，人工智能在中药配方验证（CHFV）中的应用研究明显缺乏。为了解决这一差距，我们对CHFV相关的挑战进行了全面分析，并提出了一个创新的CHFV模型，旨在改进中草药配方的验证过程。为了缓解中草药数据集的类别不平衡和标签质量差的问题，我们引入了一种基于空间模拟和真实实验的个性化聚焦机制（FM）。此外，为了克服中草药特征类间方差有限和类内方差较大带来的挑战，我们开发了先验知识矩阵和置信度重构算法，显著提高了CHFV模型的性能。源代码和数据可在https://github.com/Wenhua-Zheng/CHFV上公开获得。

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引用次数: 0

A velocity reconstruction algorithm for immersed smoothed point interpolation method in fluid-structure interaction problems 流固耦合问题中浸入式光滑点插值法的速度重建算法

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2025-12-26 DOI: 10.1016/j.enganabound.2025.106614

Peng Wang , Guiyong Zhang , Da Hui , Jinxin Wu

The Immersed Smoothed Point Interpolation Method (IS-PIM) is an effective technique for simulating fluid-structure interaction (FSI) problems involving structural motions and deformations. As a boundary non-conforming method, IS-PIM introduces a fictitious fluid domain to form a continuous fluid field, thereby circumventing computationally expensive mesh reconstruction. However, its reliance on non-coincident fluid and solid nodes at the interface leads to an inherent spatially non-matching node problem, which degrades the accuracy of FSI velocity boundary conditions and induces spurious numerical oscillations.

To address this fundamental issue, this study proposes a novel velocity reconstruction algorithm (VRA). The proposed VRA strategically reconstructs the near-boundary fluid velocity field by extrapolating from the kinematically consistent fictitious fluid velocity inside the solid domain and a set of intersection points of the fluid mesh with the solid boundary. These reconstructed velocities are then imposed as boundary conditions, leading to a better satisfaction of the no-slip and no-penetration conditions at the fluid-structure interface. The proposed VRA is implemented within the IS-PIM framework and validated through several numerical benchmarks. Comparative analyses demonstrate that the proposed VRA significantly enhances the accuracy of FSI velocity boundary conditions during structural motions and deformations. This improvement consequently suppresses spurious fluid flux across the solid boundary and refines the pressure solution, thereby enabling a more accurate evaluation of the FSI forces. Furthermore, the algorithm maintains high computational efficiency, introducing minimal overhead compared to the essential interpolation of the original IS-PIM.

浸入式平滑点插值法（is - pim）是模拟结构运动和变形等流固耦合问题的有效方法。IS-PIM作为一种边界非一致性方法，引入了一个虚拟的流体域来形成一个连续的流体场，从而避免了计算代价高昂的网格重建。然而，它依赖于界面处的非重合流体和固体节点，导致固有的空间不匹配节点问题，这降低了FSI速度边界条件的精度，并引起了虚假的数值振荡。为了解决这一基本问题，本研究提出了一种新的速度重建算法（VRA）。该方法利用实体域内运动一致的虚拟流体速度和流体网格与实体边界的一组交点进行外推，有策略地重构了近边界流体速度场。然后将这些重建的速度作为边界条件施加，从而更好地满足流固界面处的无滑移和无侵穿条件。提出的VRA在is - pim框架内实现，并通过几个数值基准进行了验证。对比分析表明，该方法显著提高了结构运动和变形过程中FSI速度边界条件的精度。因此，这种改进抑制了穿过固体边界的虚假流体通量，并改进了压力解，从而能够更准确地评估FSI力。此外，该算法保持了较高的计算效率，与原始IS-PIM的基本插值相比，引入了最小的开销。

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引用次数: 0

An automatic trimming method for arbitrary non-matching surface meshes 一种任意不匹配曲面网格的自动切边方法

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2025-12-24 DOI: 10.1016/j.enganabound.2025.106607

Chong Zhang , Jianming Zhang , Rongxiong Xiao

In computer-aided engineering (CAE), coupled non-matching meshes are indispensable for disposing scenarios such as mesh deformations arising from nonlinear problems, domain decomposition to mitigate meshing complexity and computational scale, and gluing of non-matching interfaces across multiphysics simulations. However, the generation of high-precision conformal mesh remains challenging due to geometric and topological constraints. This paper proposes a systematic novelty automated trimming method (ATM) for non-matching surface meshes, which is independent of mesh shape (arbitrary polygons) and continuity (discontinuous or continuous). The proposed methodology extends the boundary representation (B-Rep) framework to interface trimming, constructing a topological structure of multiple “faces” to enable precise interface partitioning. The triangulation of the boundary mesh in the overlapping region of the interface is implemented according to the circumscribed circle criterion. A straightforward optimization scheme is subsequently applied to triangular cells to generate high-quality interface meshes. Compared to existing algorithms, ATM fully utilizes interface topology information, enforces geometric constraints during boundary recovery via Delaunay triangulation, and employs cell vertex relocation strategy to ensure trimmed mesh quality. Numerical examples demonstrate that ATM achieves automated, efficient, and robust trimming of arbitrary non-matching interfaces.

在计算机辅助工程（CAE）中，耦合非匹配网格对于处理由非线性问题引起的网格变形、减轻网格复杂性和计算规模的域分解以及跨多物理场模拟的非匹配接口的粘合等场景是必不可少的。然而，由于几何和拓扑的限制，高精度保形网格的生成仍然具有挑战性。提出了一种不依赖于网格形状（任意多边形）和连续性（不连续或连续）的非匹配曲面网格自动裁剪方法（ATM）。提出的方法将边界表示（B-Rep）框架扩展到接口裁剪，构建多个“面”的拓扑结构以实现精确的接口划分。根据外圆准则对界面重叠区域的边界网格进行三角剖分。随后，将一种简单的优化方案应用于三角形单元，以生成高质量的界面网格。与现有算法相比，ATM充分利用了界面拓扑信息，通过Delaunay三角剖分在边界恢复过程中施加几何约束，并采用单元顶点重定位策略保证裁剪后的网格质量。数值算例表明，该算法实现了对任意不匹配接口的自动、高效、鲁棒裁剪。

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引用次数: 0

Gradient-smoothing physics-informed neural networks for elastic solids 弹性固体的梯度平滑物理信息神经网络

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2025-12-24 DOI: 10.1016/j.enganabound.2025.106609

BingBing Wang , YanBin Li , Chunsheng Lu , MingHao Zhao , Zengtao Chen , Yue Mei , JianWei Zhang

The physics-informed neural networks (PINNs) have shown great potential in solving partial differential equations. However, their reliance on repeated automatic differentiation to evaluate derivatives in training the loss function often results in reduced accuracy and computational efficiency. In this paper, gradient smoothing-based PINNs (GS-PINNs) are proposed for elastic solids. In this method, the geometric model is discretized into a series of nodes with corresponding representative domains. Instead of standard derivatives, second-order smoothed displacement gradients, calculated using a gradient smoothing technique, are employed to evaluate the loss at training points, thereby avoiding repeated automatic differentiation. A series of numerical examples, ranging from one-dimensional to three-dimensional cases, demonstrate that GS-PINNs achieve superior accuracy and convergence compared with conventional PINNs, for both forward and inverse problems.

基于物理的神经网络在求解偏微分方程方面显示出巨大的潜力。然而，在训练损失函数时，它们依赖于重复的自动微分来评估导数，往往导致准确性和计算效率降低。本文提出了一种基于梯度平滑的弹性固体PINNs （GS-PINNs）。该方法将几何模型离散为具有相应代表域的一系列节点。用梯度平滑技术计算二阶平滑位移梯度来代替标准导数来评估训练点上的损失，从而避免了重复的自动微分。从一维到三维的一系列数值算例表明，与传统的PINNs相比，GS-PINNs在正解和逆解问题上都具有更好的精度和收敛性。

引用次数: 0

Piezoelectric and piezomagnetic effects on functionally graded triply periodic minimal surface smart sandwich nanoscale plates using Chebyshev shear deformation theory 应用切比雪夫剪切变形理论研究功能梯度三周期最小表面智能夹层纳米板的压电和压磁效应

IF 4.1 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements

Pub Date : 2025-12-24 DOI: 10.1016/j.enganabound.2025.106602

P. Phung-Van , P.T. Hung , M. Abdel Wahab , Chien H. Thai

This study investigates the nanoscale free vibration behavior of a novel smart sandwich nanoplate integrating a functionally graded triply periodic minimal surface (FG-TPMS) core combined with magneto-electro-elastic face sheets. Unlike conventional sandwich structures, this design leverages the mechanical efficiency of FG-TPMS architectures with coupled piezoelectric–piezomagnetic responses of magneto-electro-elastic materials to enhance vibrational performance compared to traditional sandwich composites. The governing equations are formulated using nonlocal strain gradient theory to accurately capture small-scale effects, while isogeometric analysis is employed to ensure high precision and continuity in numerical simulations. Additionally, the displacement approximation is constructed using a newly developed Chebyshev shear deformation theory, which provides improved representation of shear effects in nanoscale plates. The findings demonstrate that synergistic interaction between FG-TPMS topologies, magneto-electro-elastic face sheets and small-scale effects significantly influences natural frequencies. Moreover, this study shows that a larger length scale parameter increases stiffness and raises frequencies, while a higher nonlocal parameter lowers stiffness and reduces frequencies. And the magnetic field strengthens the nanoplate, whereas the electric voltage weakens it. These results offer valuable insights into the dynamic analysis of smart nanostructures with potential applications in aerospace, biomedical engineering and vibration control systems.

本文研究了一种由功能梯度三周期最小表面（FG-TPMS）核心与磁电弹性面片相结合的新型智能夹层纳米板的纳米级自由振动行为。与传统的夹层结构不同，该设计利用了FG-TPMS结构的机械效率和磁-电弹性材料的耦合压电-压电响应，与传统的夹层复合材料相比，增强了振动性能。采用非局部应变梯度理论建立控制方程以准确捕捉小尺度效应，同时采用等几何分析保证数值模拟的高精度和连续性。此外，利用新发展的切比雪夫剪切变形理论构建了位移近似，该理论提供了纳米尺度板剪切效应的改进表示。研究结果表明，FG-TPMS拓扑结构、磁电弹性面片和小尺度效应之间的协同作用显著影响了固有频率。此外，该研究表明，较大的长度尺度参数会增加刚度并提高频率，而较大的非局部参数会降低刚度并降低频率。磁场增强了纳米板，而电压削弱了它。这些结果为智能纳米结构的动态分析提供了有价值的见解，在航空航天、生物医学工程和振动控制系统中具有潜在的应用。

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引用次数: 0