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Peridynamics simulation of failure behavior of engineering cementitious composites (ECC) under impact loading 工程水泥基复合材料(ECC)在冲击载荷下的破坏行为的周动力学模拟
IF 2.7 3区 材料科学 Q2 ENGINEERING, MECHANICAL Pub Date : 2024-04-12 DOI: 10.1007/s10999-024-09712-w
Zhanqi Cheng, Xing Ren, Jiyu Tang, Xiangxi Jia, Chengcong Gao

Engineering cementitious composites (ECC) are widely used in concrete structures for resisting impact loads. This paper establishes a peridynamics (PD)-based model for impact crack propagation in ECC, incorporating a failure criterion considering the strain rate effect, to investigate the damage behavior of ECC under impact loading. Firstly, an improved prototype microelastic brittle material (PMB) model considering the strain softening stage is used to model the cementitious matrix of ECC, and the fibers are modeled as one-dimensional rod to establish a PD fully-discrete model of ECC. At the same time, an interface exponential friction attenuation model is introduced. Then, the effectiveness of the model and the PD impact contact algorithm incorporating the strain rate effect was validated through simulations of the four-point bending test on ECC rectangular plates and the drop hammer impact test on plain concrete beams. Finally, the effects of pre-cracks-to-span distance, fiber content, fiber aspect ratio, different strain rate, and impact velocity on the crack propagation and structural deflection of ECC beams under impact loading are investigated.

工程水泥基复合材料(ECC)被广泛应用于混凝土结构中以抵抗冲击荷载。本文建立了基于周动力学(PD)的工程水泥基复合材料冲击裂纹扩展模型,并结合考虑应变速率效应的失效准则,研究工程水泥基复合材料在冲击荷载作用下的破坏行为。首先,使用考虑应变软化阶段的改进型微弹性脆性材料(PMB)模型对 ECC 的水泥基体进行建模,并将纤维建模为一维杆,从而建立了 ECC 的 PD 全离散模型。同时,引入了界面指数摩擦衰减模型。然后,通过模拟 ECC 矩形板的四点弯曲试验和素混凝土梁的落锤冲击试验,验证了模型和包含应变率效应的 PD 冲击接触算法的有效性。最后,研究了预裂缝跨距、纤维含量、纤维长宽比、不同应变率和冲击速度对冲击荷载下 ECC 梁的裂缝扩展和结构挠度的影响。
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引用次数: 0
Material extrusion additive manufacturing of novel lightweight collinear stayed polymer lattices 新型轻质平行滞留聚合物晶格的材料挤出增材制造
IF 2.7 3区 材料科学 Q2 ENGINEERING, MECHANICAL Pub Date : 2024-03-30 DOI: 10.1007/s10999-024-09709-5
Yating Ou, Anton Köllner, Antonia Gwendolyn Dönitz, Tim Erik Richter, Christina Völlmecke

A novel type of lightweight and high-performance, collinear polymer lattices is presented in which the concept of stayed slender columns is exploited with the aid of material extrusion additive manufacturing (MEX). The stays, preventing lower order buckling, are additively manufactured using the printing strategy bridging. Through conducting experimental test series on representative elements and two-dimensional lattices, it is demonstrated that the 3D printed stayed column lattices exhibit significantly improved compressive strength in comparison with conventional collinear lattices. The potential of introducing deliberate geometric imperfections to affect the structural behaviour is furthermore outlined in the current work.

本文介绍了一种新型的轻质、高性能共线聚合物晶格,借助材料挤出增材制造(MEX)技术,利用了细长支柱的概念。采用打印桥接策略,以快速成型的方式制造出可防止低阶屈曲的支撑杆。通过对代表性元素和二维晶格进行系列实验测试,证明与传统的共线晶格相比,三维打印的支撑柱晶格的抗压强度显著提高。目前的研究还进一步概述了故意引入几何缺陷影响结构行为的可能性。
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引用次数: 0
FEM-supported machine learning for residual stress and cutting force analysis in micro end milling of aluminum alloys 用于铝合金微端铣削过程中残余应力和切削力分析的有限元支持机器学习
IF 2.7 3区 材料科学 Q2 ENGINEERING, MECHANICAL Pub Date : 2024-03-30 DOI: 10.1007/s10999-024-09713-9
M. K. Sharma, Hamzah Ali Alkhazaleh, Shavan Askar, Noor Hanoon Haroon, Saman M. Almufti, Mohammad Rustom Al Nasar

This study delves into a Bayesian machine learning (ML) framework designed to comprehensively characterize cutting force and residual stress in the micro end milling process across a diverse range of aluminum alloys. The foundation of this investigation rested on acquiring dependable training data through finite element method simulations, encompassing material properties and processing parameters as inputs, while the output targets included residual stress in both the transverse and cutting directions, as well as cutting force divided into feed force and thrust force. The outcomes were remarkable, unveiling high predictive accuracy for both residual stress and cutting force, with a slight advantage in residual stress prediction. Moreover, the study revealed the significant influence of output target values on the weight functions of input parameters, highlighting distinct dependencies between each output target and the corresponding input features. This investigation elucidated that predicting residual stress and cutting force in micro end milling represents a multifaceted process contingent upon the interplay of material properties and processing parameters. The intricate nature of this process underscores the Bayesian ML model’s potential as a robust and highly accurate approach, adept at effectively encapsulating these complex objectives.

本研究深入探讨了贝叶斯机器学习(ML)框架,旨在全面描述各种铝合金微端铣削过程中的切削力和残余应力。这项研究的基础是通过有限元法模拟获取可靠的训练数据,将材料属性和加工参数作为输入,而输出目标包括横向和切削方向的残余应力,以及分为进给力和推力的切削力。结果非常显著,残余应力和切削力的预测精度都很高,其中残余应力的预测略胜一筹。此外,研究还揭示了输出目标值对输入参数权重函数的重要影响,突出了每个输出目标与相应输入特征之间的明显依赖关系。这项研究表明,预测微型端铣加工中的残余应力和切削力是一个多方面的过程,取决于材料特性和加工参数的相互作用。这一过程的复杂性凸显了贝叶斯 ML 模型作为一种稳健、高精度方法的潜力,它能够有效地概括这些复杂的目标。
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引用次数: 0
Data-driven analysis of spinodoid topologies: anisotropy, inverse design, and elasticity tensor distribution 以数据为导向的刺状拓扑分析:各向异性、反向设计和弹性张量分布
IF 2.7 3区 材料科学 Q2 ENGINEERING, MECHANICAL Pub Date : 2024-03-15 DOI: 10.1007/s10999-024-09711-x
Farshid Golnary, Mohsen Asghari

Spinodoid topologies are bicontinuous porous microstructures inspired by the natural spinodal decomposition process. They offer a vast design space and are capable of representing anisotropic topologies, which makes them suitable for use in biomedical applications. This work focuses on some fundamental aspects in spinodoid microstructures. As the first, the extent of anisotropy is computed by a universal index and its correlation with spinodoid design parameters, including relative density and the three cone angles, is investigated. In order to do this, the k-means clustering method is utilized to group the topologies based on their level of anisotropy. Within each cluster, the relationship between the statistical features of the design parameters and the extent of anisotropy is analyzed in detail. As one of the findings, it is revealed that topologies created by larger cone angles will lie in low anisotropy category. Although the sensitivity analysis indicates that all the cone angles are equally important in determining the elasticity tensor elements, our findings demonstrate that there are some discrepancies in the probability density function of cone angles in topologies with high anisotropy. In addition, the results show that lower relative densities tend to lead to higher anisotropy in the structures regardless of cone angle values. In the second stage of this work, a data-driven framework for inverse design is proposed. This approach involves generating high-quality samples and utilizing an efficient data-driven framework capable of handling unequal queries. It can identify multiple spinodoid candidates for a desired elasticity tensor, rather than just one. This approach has great advantages, especially in manufacturing, where different topologies may have varying manufacturing costs. This provides designers with more choices to select from. In the final stage, we estimated the statistical distribution of the elasticity tensor components for the generated spinodoid topologies. By measuring the Mahalanobis distance between a query and the estimated distribution, one can determine whether the query belongs to the property space of spinodoid topologies or not. This approach allows for assessing the similarity or dissimilarity of a query to the distribution of the generated spinodoid topologies.

旋转体拓扑结构是一种双连续多孔微结构,其灵感来自于自然旋转体分解过程。它们提供了广阔的设计空间,能够表现各向异性的拓扑结构,因此适用于生物医学应用。这项工作的重点是旋转体微结构的一些基本方面。首先,通过一个通用指数计算各向异性的程度,并研究其与尖晶石设计参数(包括相对密度和三个锥角)的相关性。为此,利用 K 均值聚类法根据各向异性程度对拓扑结构进行分组。在每个聚类中,详细分析了设计参数的统计特征与各向异性程度之间的关系。其中一项研究结果表明,锥角较大的拓扑结构属于低各向异性类别。尽管灵敏度分析表明,所有锥角在确定弹性张量元素方面同等重要,但我们的研究结果表明,在高各向异性拓扑中,锥角的概率密度函数存在一些差异。此外,结果表明,无论锥角值如何,相对密度越低,结构的各向异性越大。在这项工作的第二阶段,提出了一个数据驱动的逆向设计框架。这种方法涉及生成高质量样本,并利用能够处理不平等查询的高效数据驱动框架。它可以为所需的弹性张量识别多个旋进样条候选,而不仅仅是一个。这种方法具有很大的优势,尤其是在制造领域,不同的拓扑结构可能会产生不同的制造成本。这为设计者提供了更多选择。在最后阶段,我们估算了所生成的旋片拓扑结构的弹性张量成分的统计分布。通过测量查询与估计分布之间的马哈拉诺比斯距离,我们可以确定查询是否属于椎体拓扑的属性空间。通过这种方法,可以评估查询与生成的刺状拓扑分布之间的相似性或不相似性。
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引用次数: 0
Inversion performance and multi-objective optimization of multi-component conical energy absorber with a spherical cap 带球形帽的多成分锥形吸能器的反转性能和多目标优化
IF 2.7 3区 材料科学 Q2 ENGINEERING, MECHANICAL Pub Date : 2024-03-13 DOI: 10.1007/s10999-023-09694-1
Sajad Azarakhsh, Mohammad Javad Rezvani, Adel Maghsoudpour, Ali Jahan

This paper presents the quasi-static free inversion behavior of a new conical tube absorber. The absorber is composed of a multi-component conical tube with a spherical end cap and varying lengths and diameters. When this structure undergoes an axial load, each tube component freely inverts inside the next component like a telescope. Finite element (FE) models were made using ABAQUS explicit code to simulate the deformation and energy absorption of multi-component conical tubes. To verify the accuracy of the FE models, they were validated with experimental tests. As a general framework for a design optimization study, structural parameters such as wall thickness, cap radius, and edge length of the absorber affect the initial peak load and specific energy absorption. To achieve the optimal design for the multi-component conical tube, mathematical models were developed using the response surface method, and the multi-objective optimization procedure was applied to find the optimal values for the design variables. The results of the multi-objective optimization demonstrated improvements in both objective functions compared to existing designs. Specifically, by increasing the cap radius and decreasing the edge length, the initial peak load was reduced, while increasing the wall thickness the specific energy absorption was enhanced.

本文介绍了一种新型锥形管吸收器的准静态自由反转行为。该吸收器由带有球形端盖、长度和直径各异的多组分锥形管组成。当该结构承受轴向载荷时,每个管部件都会像望远镜一样在下一个部件内部自由倒转。我们使用 ABAQUS 显式代码制作了有限元(FE)模型,以模拟多组件锥形管的变形和能量吸收。为了验证有限元模型的准确性,还通过实验测试对其进行了验证。作为设计优化研究的一般框架,吸收器的壁厚、盖半径和边长等结构参数会影响初始峰值载荷和比能量吸收。为实现多组件锥形管的优化设计,使用响应面法建立了数学模型,并应用多目标优化程序找到了设计变量的最佳值。多目标优化的结果表明,与现有设计相比,两个目标函数都有所改进。具体来说,通过增大盖帽半径和减小边缘长度,降低了初始峰值载荷,而增大壁厚则增强了比能量吸收。
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引用次数: 0
Optimization of vibration analysis for functionally graded graphene platelets (FGGP) reinforced twisted cantilever thin shallow shell blades subjected to axial loading 对承受轴向载荷的功能分级石墨烯平板(FGGP)增强扭曲悬臂薄浅壳叶片的振动分析进行优化
IF 2.7 3区 材料科学 Q2 ENGINEERING, MECHANICAL Pub Date : 2024-03-09 DOI: 10.1007/s10999-023-09706-0
X. J. Gu, Q. S. Bi, W. Zhang, Y. F. Zhang, X. J. Han

Vibration characteristics for rotating thin shallow shell blades reinforced with functionally graded graphene platelets (FGGP) under the axial force are conducted. The blade is modeled as four twisted cantilever thin shallow shells, each with a unique shape cylindrical shallow shell panel with a straight or curved boundary as the cantilever side, spherical shallow shell panel and hyperbolic parabolic shallow shell panel. The Halpin–Tsai model, the first-order shear deformation theory and the Rayleigh–Ritz method are used to calculate the frequencies and mode shapes of the blade. The results are validated by comparing them with previous literature and ANSYS. An analysis is conducted on a range of parameters, encompassing graphene properties, rotational velocity, torsional angle, curvature radius, aspect ratio and axial forces, in order to assess their influence on the vibrational properties of the blade. The vibration behaviors of a rotating cylindrical shallow shell panel with a straight cantilever edge are found to be distinctive. The findings indicate that the blade’s stiffness is significantly higher when reinforced with FGGP-X compared to FGGP-U distribution, with FGGP-O distribution exhibiting the lowest stiffness. Furthermore, the study implies that a total layer count exceeding ten has a negligible impact on the degree of graphene distribution. Finally, the study concludes that the curvature and graphene distribution pattern significantly influence the vibration characteristics of the blade.

摘要 研究了用功能分级石墨烯平板(FGGP)增强的旋转薄浅壳叶片在轴向力作用下的振动特性。叶片被建模为四个扭曲的悬臂薄浅壳,每个浅壳都有一个独特形状的圆柱形浅壳面板,悬臂侧的边界为直线或曲线;球形浅壳面板和双曲抛物线形浅壳面板。采用 Halpin-Tsai 模型、一阶剪切变形理论和 Rayleigh-Ritz 方法计算叶片的频率和模态振型。通过与以前的文献和 ANSYS 进行比较,验证了计算结果。对一系列参数进行了分析,包括石墨烯特性、旋转速度、扭转角、曲率半径、长宽比和轴向力,以评估它们对叶片振动特性的影响。研究发现,带有直悬臂边缘的旋转圆柱形浅壳面板的振动行为与众不同。研究结果表明,与 FGGP-U 分布相比,使用 FGGP-X 分布加固的叶片刚度明显更高,而 FGGP-O 分布的刚度最低。此外,研究还表明,总层数超过 10 层对石墨烯分布程度的影响微乎其微。最后,研究得出结论,曲率和石墨烯分布模式对叶片的振动特性有重大影响。
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引用次数: 0
Large deformation analysis of the magneto-responsive beam and its applications in flexible grippers and robots 磁响应梁的大变形分析及其在柔性抓手和机器人中的应用
IF 2.7 3区 材料科学 Q2 ENGINEERING, MECHANICAL Pub Date : 2024-02-23 DOI: 10.1007/s10999-024-09708-6
Shiyang Liu, Gongqi Cao, Yuchen Jin, Jianlin Liu

Due to their superior biocompatibility, flexibility and control strategy compared to the traditional robots, soft robots have been widely used in a wide spectrum of engineering areas, such as biomedical, exploration, aerospace, intelligent devices and other fields. However, the existing soft robot structures mainly focus on employing homogeneous materials, which greatly limits the design flexibilities of soft robots, and correspondingly, the existing theories are usually invalid for calculating heterogeneous large deformation beam models. Therefore, we developed a novel simulation method and an advanced theoretical calculation method for representing the large deformation of both the homogeneous and heterogeneous beams made of magneto-responsive materials prepared by mixing silicon rubber with NdFeB particles. We found the experimental and numerical results agree very well, showing that the heterogeneous beam can demonstrate a better driving performance than the homogeneous beam. Optimal parameters are afterwards obtained based on the developed simulation and theorical methods. Next, we generalize the optimized heterogeneous structure to engineer the flexible gripper and the soft robot. The grasping forces of the gripper are calculated based on the variational model of large deformation beams, which are consistent with the simulation and experimental values. Moreover, the motion mechanism of magnetic soft robot has been revealed through comprehensive force analysis and formulaic rigid body motion analysis. These findings have strengthened our understandings on the deformation of slender structures and the locomotion of magnetic soft robot, which are promising to guide the design and analysis of innovative devices and robots.

与传统机器人相比,软机器人具有更优越的生物相容性、灵活性和控制策略,已被广泛应用于生物医学、勘探、航空航天、智能设备等多个工程领域。然而,现有的软机器人结构主要集中于采用同质材料,这极大地限制了软机器人的设计灵活性,相应地,现有理论通常也无法计算异质大变形梁模型。因此,我们开发了一种新颖的模拟方法和先进的理论计算方法,用于表示由硅橡胶与钕铁硼颗粒混合制备的磁响应材料制成的同质和异质梁的大变形。我们发现实验结果和数值结果非常吻合,表明异质梁比同质梁具有更好的驱动性能。随后,根据所开发的模拟和理论方法,我们获得了最佳参数。接下来,我们将优化后的异质结构推广到柔性抓手和软体机器人的设计中。根据大变形梁的变分模型计算了抓手的抓取力,结果与模拟和实验值一致。此外,通过综合受力分析和公式化刚体运动分析,揭示了磁性软机器人的运动机理。这些发现加深了我们对细长结构变形和磁软机器人运动的理解,有望指导创新装置和机器人的设计与分析。
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引用次数: 0
A mode-matching analysis of flexible shells and waveguides with partitioning and muffler conditions 具有分区和消声条件的柔性壳和波导的模式匹配分析
IF 2.7 3区 材料科学 Q2 ENGINEERING, MECHANICAL Pub Date : 2024-02-16 DOI: 10.1007/s10999-024-09710-y
Rab Nawaz, Aqsa Yaseen, Hani Alahmadi, Burhan Tiryakioglu

This article explores the waveguide phenomenon that possesses trifurcated rigid inlet/outlet and muffler conditions. Additionally, this waveguide is linked to a finite, thin, and flexible shell with the aid of partitioning discs located at the interfaces. The inside of the discs is coated with sound absorbent material, which can be fibrous or perforated, depending on the impedance conditions of the surface. To demonstrate the use of absorbent material at the interfaces, impedance formulation is used. The mode matching procedure is then utilized to find solution, it relies on the orthogonality conditions accompanying the material characteristics of the bounding surface and within the fluid. The study includes modeling the utilization of absorbent material at interfaces, and numerical experiments to analyze the acoustic attenuation. The analysis focuses on a specific configuration with duct region radii and a half length of the chamber at a frequency of 700 Hz. The results demonstrate that the absorption of power and transmission loss versus frequency vary through the fibrous coating and the edge conditions, and changing the clamped ends to pin-jointed ends optimizes the dispersion powers and the loss due to transmission. The study yields useful information to the acoustic dispersion via flexural expansion chamber, highlighting the importance of material properties, edge conditions, and configuration settings in the acoustic attenuation. The mode matching method and numerical experiments presented in this study can be useful for designing acoustic devices with flexible shells, providing a better understanding of the underlying physics and optimizing their performance.

本文探讨了具有三叉刚性入口/出口和消声器条件的波导现象。此外,借助位于接口处的分隔圆盘,该波导与有限、薄而灵活的外壳相连。圆盘内部涂有吸音材料,根据表面阻抗条件的不同,吸音材料可以是纤维状的,也可以是穿孔的。为了演示在界面上使用吸声材料,我们使用了阻抗配方。然后利用模式匹配程序找到解决方案,它依赖于边界表面和流体内部材料特性的正交条件。研究包括对界面吸声材料的使用进行建模,以及对声学衰减进行分析的数值实验。分析的重点是频率为 700 Hz 时管道区域半径和腔体半长的特定配置。结果表明,吸收功率和传输损耗随频率的变化随纤维涂层和边缘条件的变化而变化,将夹紧端改为针接端可优化扩散功率和传输损耗。这项研究为通过挠性膨胀腔进行声学扩散提供了有用的信息,突出了材料特性、边缘条件和配置设置在声学衰减中的重要性。本研究提出的模式匹配方法和数值实验可用于设计具有挠性外壳的声学装置,从而更好地理解其基本物理原理并优化其性能。
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引用次数: 0
DNN assisted optimization of composite cylinder subjected to axial compression using customized differential evolution algorithm 使用定制的微分进化算法对承受轴向压缩的复合材料圆柱体进行 DNN 辅助优化
IF 2.7 3区 材料科学 Q2 ENGINEERING, MECHANICAL Pub Date : 2024-02-12 DOI: 10.1007/s10999-023-09705-1
Manash Kumar Bhadra, G. Vinod, Atul Jain

Composite materials offer the unique advantage of allowing customization of their properties based on their load. However, the optimization of composite laminate properties can often be challenging, often leading to quasi-isotropic designs or the use of industry guidelines. This paper presents a novel method for optimizing of a composite cylinder under axial compression. It introduces an innovative approach by merging a tailored differential evolution algorithm with a deep neural network. The key modification is in the method of constraint implementation. The initial population and trial vectors are constrained to balanced laminates using a while loop, effectively shrinking the design space and reducing computational requirements. The advantage of the customization is reflected in the faster convergence of the optimization as well as a much more accurate deep neural network model. It also enabled the differential evolution to escape the local maxima. Using the deep neural network to evaluate candidate solutions, further reduces the computational costs. The technique is validated using linear buckling analysis and applied to design an inter-tank truss structure. The optimization resulted in a drop in the mass of the truss structure from 5.28 to 4.87 kg. The study establishes a general optimization method applicable to various composite cylinders, including short and long, thin and thick cylinders, and honeycomb core sandwiched composite structures.

摘要 复合材料具有独特的优势,可以根据载荷定制其特性。然而,复合材料层压板性能的优化往往具有挑战性,往往导致准各向同性设计或使用行业准则。本文提出了一种优化轴向压缩复合材料圆柱体的新方法。它通过将量身定制的微分进化算法与深度神经网络相结合,引入了一种创新方法。修改的关键在于约束的实现方法。使用while循环将初始群体和试验向量约束为平衡层,从而有效地缩小了设计空间并降低了计算要求。定制的优势体现在优化收敛速度更快,深度神经网络模型也更加精确。它还使微分进化摆脱了局部最大值。使用深度神经网络评估候选解决方案,进一步降低了计算成本。该技术通过线性屈曲分析进行了验证,并应用于油箱间桁架结构的设计。通过优化,桁架结构的质量从 5.28 千克降至 4.87 千克。该研究建立了一种通用优化方法,适用于各种复合材料圆柱体,包括短圆柱体、长圆柱体、薄圆柱体、厚圆柱体和蜂窝芯夹层复合材料结构。
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引用次数: 0
Nonlocal nonlinear analysis of functionally graded piezoelectric porous nanoplates 功能分级压电多孔纳米板的非局部非线性分析
IF 2.7 3区 材料科学 Q2 ENGINEERING, MECHANICAL Pub Date : 2024-01-29 DOI: 10.1007/s10999-023-09701-5
P. Phung-Van, Lieu B. Nguyen, P. T. Hung, H. Nguyen-Xuan, Chien H. Thai

This study presents a novel and efficient approach for analyzing the nonlinear behavior of nanoscale plates composed of functionally graded (FG) piezoelectric porous materials. Our approach, which focuses on small-scale structures, demonstrates remarkable efficiency and represents the first of its kind. A generalized model for FG piezoelectric nanoplates with porosities satisfies assumptions of the nonlocal Eringen’s theory based on von Kármán strains. The porous distributions are modeled with even and uneven functions. According to Maxwell’s equations, an electric field is approximated by trigonometric and linear functions. A weak form of the piezoelectric nanoplate with porosity is derived via the principle of extended virtual displacement. Isogeometric approach, which provides accurate results, is easy to implement. The influence of porosity coefficient, small-scale parameter, power law exponent, external electrical voltage and geometric parameter on the nonlinear displacement of the piezoelectric porous nanoplate are examined. These results can provide benchmark solutions for the future numerical investigations of electroelastic nanoplates.

本研究提出了一种新颖高效的方法,用于分析由功能梯度(FG)压电多孔材料组成的纳米级板的非线性行为。我们的方法侧重于小尺度结构,具有显著的效率,在同类方法中尚属首创。具有多孔性的 FG 压电纳米板的广义模型满足基于 von Kármán 应变的非局部 Eringen 理论的假设。多孔分布用均匀和不均匀函数建模。根据麦克斯韦方程,电场用三角函数和线性函数近似。通过扩展虚拟位移原理推导出带有多孔性的压电纳米板的弱形式。等几何方法不仅能提供精确的结果,而且易于实现。研究了多孔系数、小尺度参数、幂律指数、外部电压和几何参数对压电多孔纳米板非线性位移的影响。这些结果可为未来的电弹性纳米板数值研究提供基准解。
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引用次数: 0
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