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Synergistic influence of MWCNTs/RGO on low-velocity impact response and mechanical properties of carbon fiber/epoxy composite MWCNTs/RGO对碳纤维/环氧复合材料低速冲击响应和力学性能的协同影响
Q2 NANOSCIENCE & NANOTECHNOLOGY Pub Date : 2023-05-30 DOI: 10.1177/23977914231176865
Mohammad Amin Bahrami, Saeed Feli
Nanoparticles can be used to enhance and improve the mechanical properties and low-velocity impact response of carbon fiber-reinforced polymer (CFRP) composites both simultaneously and individually. Also, the synergistic influence of two nanoparticles can be improved the mechanical properties and low-velocity impact response of CFRP composites. In this paper, the effects of reduced graphene oxide (RGO) and multi-walled carbon nanotubes (MWCNTs) on the mechanical properties, low-velocity impact response and damage area of epoxy/fiber carbon composites are investigated both simultaneously and individually. Composite specimens are fabricated with 0.4 weight percentages (wt.%) of RGO, 0.06 wt.% of MWCNTs individually, and a combination of RGO and MWCNTs with 0.6 and 0.06 wt.%, respectively. For comparison of the results, the neat epoxy specimens are fabricated and also tested. Direct homogenization technique is applied for preparation of nanocomposite mixture and then each layer of carbon fiber reinforced nanocomposite is fabricated using a hand lay-up process. Tensile modulus, tensile strength, variations of load, displacement, velocity, and absorbed energy of specimens versus time are obtained. For specimens with MWCNTs/RGO tensile modulus and tensile strength increased by about 21.30% and 17.12%, respectively, and the load peak increased by 15.15% at 1 J, 13.35% at 2 J, 39.62% at 3 J, and 39.62% at 3 J. It is concluded that the synergistic influence of MWCNTs and RGO on the results is more significant and has a higher effect on the impact responses. After the impact tests, Optical microscopy and SEM method are used to analyze fracture surfaces.
纳米颗粒可以同时或单独增强和改善碳纤维增强聚合物(CFRP)复合材料的力学性能和低速冲击响应。此外,两种纳米粒子的协同作用可以改善CFRP复合材料的力学性能和低速冲击响应。本文分别研究了还原氧化石墨烯(RGO)和多壁碳纳米管(MWCNTs)对环氧/纤维碳复合材料的力学性能、低速冲击响应和损伤面积的影响。复合材料样品分别以0.4重量百分比(wt.%)的RGO和0.06 wt.%的MWCNTs,以及分别以0.6和0.06 wt.%的RGO和MWCNTs的组合制备。为了比较结果,制作了纯环氧树脂试件并进行了试验。采用直接均质技术制备纳米复合材料,然后采用手工叠层法制备每一层碳纤维增强纳米复合材料。拉伸模量,拉伸强度,载荷变化,位移,速度,和吸收能量随时间的试样。添加MWCNTs/RGO的试件抗拉模量和抗拉强度分别提高了约21.30%和17.12%,在1 J、2 J、3 J和3 J时,载荷峰值分别提高了15.15%、13.35%、39.62%和39.62%。可见,MWCNTs和RGO对结果的协同影响更为显著,对冲击响应的影响更高。冲击试验结束后,采用光学显微镜和扫描电镜对断口进行分析。
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引用次数: 0
Medical imaging and nano-engineering advances with artificial intelligence 医学成像和纳米工程随着人工智能的发展而进步
IF 6 Q2 NANOSCIENCE & NANOTECHNOLOGY Pub Date : 2023-04-03 DOI: 10.1177/23977914231161443
Khalid Al Utaibi, Usama Ahmad, S. M. Sait, Sohail Iqbal
Medical imaging is a broad field of research and artificial intelligence used to explore such images is termed as AI-Imaging. AI-imaging is further divided into sub-branches including the computational, theoretical and practical experiments in wet and dry labs. The current research focuses on the background of medical imaging, recent advances in the field of medical imaging for oncology, challenges and possible solutions. During this research, some computational and programing tools are outlined. The process of image segmentation is important as it can help to explore the medical images in more detail. During this research, the steps involved in image segmentation are outlined and the numerical experiments are performed on a set of breast cancer medical images. It is concluded during this research that the achievements in this domain are always credited by the smart programing & computational tools and computer vision. The current research also outlines the step-wise protocols of deep learning, designed for different types of medical imaging such as X-rays, CT-scan and MRI are documented to provide a comprehensive understanding, that can help in bridging the two domains of medicine and computer vision, in a reliable and fruitful manner.
医学成像是一个广泛的研究领域,用于探索此类图像的人工智能被称为ai成像。人工智能成像进一步分为计算实验、理论实验和干湿实验三个分支。目前的研究重点是医学成像的背景,肿瘤医学成像领域的最新进展,挑战和可能的解决方案。在本研究中,概述了一些计算和编程工具。图像分割过程非常重要,因为它可以帮助我们更详细地探索医学图像。在本研究中,概述了图像分割的步骤,并对一组乳腺癌医学图像进行了数值实验。研究表明,智能编程与计算工具和计算机视觉技术是该领域取得成就的主要原因。目前的研究还概述了深度学习的逐步协议,为不同类型的医学成像(如x射线,ct扫描和MRI)设计,以提供全面的理解,有助于以可靠和富有成效的方式连接医学和计算机视觉的两个领域。
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引用次数: 0
Nanofluid containing motile gyrotactic microorganisms squeezed between parallel disks 包含在平行圆盘之间挤压的可移动的陀螺微生物的纳米流体
IF 6 Q2 NANOSCIENCE & NANOTECHNOLOGY Pub Date : 2023-03-16 DOI: 10.1177/23977914231161448
Jada Prathap Kumar, J. Umavathi, A. S. Dhone
Advanced nano and microtechnologies for nano/micro-electronic devices have made substantial advances in the past few years. These technologies are rapidly incorporating advanced fluid media such as nanofluids and biological microorganisms. Inspired by bio-nanofluid applications in medicine, biological systems and biotechnology in the present study, mathematical model is evolved for unsteady bio convective conducting nanofluid along with gyrotactic micro-organisms squeezed between parallel disks. The lower disk and upper disks are solids. The temperature field is improved by the methods of haphazard motion of nanoparticles and thermophoresis parameters. The nano-bio transfer model is written as a series of non-linear partial differential equations that are reduced into a set of ordinary differential equations using suitable transforms. The dimensionless problem is then numerically solved by RK-4th order scheme utilizing MATLAB bvp4c solver’s package to investigate the impact of the squeezing parameter, Hartman number, Brownian motion and thermophoresis parameter on motile microorganism velocity, temperature, nanoparticle concentration, and density. The friction factor, Nusselt number, Sherwood number and microorganism number distributions on Hartman number, thermophoresis and Brownian motion factors are also computed. The Brownian motion and the thermophoresis factors of nanoparticles cause an increment in temperature profiles for both suction and injection. The concentration and motile microorganism are both amplified for the Brownian parameter in the case of injection, whereas they are declined for suction and the opposite trend is observed for the thermophoresis parameter. The motile microorganism is deflated for both suction and injection with thermophoresis parameter. Suction and injection adversely affect the transfer properties at the disks. The resistive magnetic body force prevails in the core zone, resulting in a decrease in velocity. The heat generation in squeeze films with motile microorganisms can be successfully removed with magnetic nanoparticles which require a longer serviceability of the lubrication system, bio-medical systems and need for less maintenance and a longer lifespan approach. The finding is pertinent to novel bio-microsystems that combine nanofluid and the bioconvection phenomenon. The percentage increase in heat, mass, and microorganism transport rates is calculated.
用于纳米/微电子器件的先进纳米和微技术在过去几年中取得了实质性进展。这些技术正在迅速融合先进的流体介质,如纳米流体和生物微生物。受生物纳米流体在医学、生物系统和生物技术等领域应用的启发,建立了非定常生物对流纳米流体的数学模型。下盘和上盘均为固体。利用纳米颗粒的随机运动和热泳参数改善了温度场。纳米生物转移模型被写为一系列非线性偏微分方程,这些偏微分方程通过适当的变换被简化为一组常微分方程。利用MATLAB bvp4c求解器软件包,采用rk -4阶格式对无量纲问题进行数值求解,研究挤压参数、哈特曼数、布朗运动和热泳参数对运动微生物速度、温度、纳米颗粒浓度和密度的影响。计算了摩擦系数、努塞尔数、舍伍德数和微生物数量在哈特曼数、热电泳和布朗运动因子上的分布。纳米粒子的布朗运动和热泳动因子导致吸入和注射时温度分布的增加。在布朗参数下,注射时浓度和活动微生物均增大,而在吸力下浓度和活动微生物均减小,热泳参数则相反。利用热泳参数对活动微生物进行吸、注气。吸入和喷射对磁盘的传递特性有不利影响。磁阻体力在核心区盛行,导致速度下降。磁性纳米颗粒可以成功地去除带有活动微生物的挤压膜中产生的热量,这需要润滑系统和生物医疗系统的更长的使用寿命,并且需要更少的维护和更长的使用寿命。这一发现与结合纳米流体和生物对流现象的新型生物微系统有关。计算热量、质量和微生物输送率的百分比增加。
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引用次数: 0
Velocity and thermal slips impact on boundary layer flow of micropolar nanofluid over a vertical nonlinear stretched Riga sheet 速度和热滑移对垂直非线性拉伸Riga片上微极纳米流体边界层流动的影响
IF 6 Q2 NANOSCIENCE & NANOTECHNOLOGY Pub Date : 2023-03-13 DOI: 10.1177/23977914231156685
N. Abbas, W. Shatanawi, K. Rehman, Taqi A. M. Shatnawi
In the present analysis, heat and mass transfer of micropolar nanofluid flow over vertical nonlinear Riga stretching sheet is considered. Effects of velocity slip, thermal slip, Joule heating, thermal radiations, variable thermal conductivity, and heat generation are examined. Thermophoresis and Brownian motion effects are highlighted in current study. The mathematical model is developed under flow assumptions, the partial differential equations are formed by implementing the boundary layer approximations. The partial differential equations are further reduced in form of ordinary differential equations by means of suitable transformations. The ordinary differential equations are solved through numerical procedure. The effects physical parameters presented through tables and graphs for the both case of suction/injection. Velocity function declined due to higher values of micropolar parameter. The velocity function declined due to increasing the values of velocity slip. The concentration function declined due to larger values of Brownian motion. The positive values of velocity slip increases the Sherwood number and Nusselt number. The Nusselt number and Sherwood number declined for higher values of thermal slip [Formula: see text]. The values of Sherwood number and Nusselt number declined for higher values of Eckert number [Formula: see text].
在本分析中,考虑了微极纳米流体在垂直非线性里加拉伸片上的传热传质。速度滑移,热滑移,焦耳加热,热辐射,可变导热系数和热产生的影响进行了检查。热泳动效应和布朗运动效应是目前研究的热点。在流动假设下建立了数学模型,通过边界层近似建立了偏微分方程。通过适当的变换,将偏微分方程进一步化为常微分方程。用数值方法求解了常微分方程。通过表格和图表给出了两种吸注情况下物理参数的影响。微极参数越高,速度函数越小。速度函数随着速度差值的增大而减小。布朗运动值越大,浓度函数越小。速度滑移的正值增加了Sherwood数和Nusselt数。热滑移值越高,努塞尔数和舍伍德数越小[公式:见文]。Eckert数越高,Sherwood数和Nusselt数越低[公式:见文]。
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引用次数: 14
Buckling analysis of thick cylindrical shells using micropolar theory 用微极理论分析厚圆柱壳的屈曲
IF 6 Q2 NANOSCIENCE & NANOTECHNOLOGY Pub Date : 2023-03-11 DOI: 10.1177/23977914231157908
Parham Behzadi, M. Salehi
Modeling complex materials with internal structure such as porous solids is challenging as in some cases the classical theory cannot provide precise responses. By considering the scale effects through additional kinematic descriptors and six constants for isotropic materials, the micropolar theory can accurately model complex materials like bone. This paper studies the buckling of a thick cylindrical shell using classical and non-classical theories. The cylinder’s material is considered bone and isotropic, and the critical load value for different geometries and boundary conditions has been obtained. Finally, the size-effect and importance of micropolar theory in micro dimensions are investigated. The micropolar equations are solved by a numerical solution using the 3D finite element method. The results show that decreasing the macroscopic length increases the stiffness of the cylinder more than that predicted by classical theory; In addition, by increasing the thickness of the cylinder and the importance of shear stresses, the micropolar theory predicts a more critical load than the classical one, and the result differences become more significant between micropolar and classical theories. Also, the characteristic length of the micropolar is investigated. The results show that the change of the critical load increased by moving toward the micro dimensions.
模拟具有内部结构的复杂材料(如多孔固体)具有挑战性,因为在某些情况下经典理论无法提供精确的响应。通过对各向同性材料附加运动学描述符和6个常数考虑尺度效应,微极理论可以准确地模拟骨等复杂材料。本文采用经典和非经典理论研究了厚圆柱壳的屈曲问题。考虑柱体材料为骨结构和各向同性,得到了不同几何形状和边界条件下的临界载荷值。最后,探讨了微极性理论在微观尺度上的尺寸效应和重要性。采用三维有限元法对微极方程进行了数值求解。结果表明:减小宏观长度对圆柱刚度的影响大于经典理论预测;此外,随着圆柱体厚度的增加和剪切应力的重要性,微极理论预测的临界载荷比经典理论预测的更大,并且微极理论与经典理论的结果差异更显著。此外,还研究了微极性的特征长度。结果表明,临界载荷的变化随着向微尺度的移动而增大。
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引用次数: 0
Heat transfer analysis on Engine oil-based hybrid nanofluid past an exponentially stretching permeable surface with Cu/Al2O3 additives 含Cu/Al2O3添加剂的发动机油基混合纳米流体通过指数拉伸可渗透表面的传热分析
IF 6 Q2 NANOSCIENCE & NANOTECHNOLOGY Pub Date : 2023-03-01 DOI: 10.1177/23977914221093846
P. K. Pattnaik, Satyaranjan Mishra, S. Baag
The flow characteristic of the two-dimensional conducting hybrid nanofluid past an exponentially stretching permeable surface is analyzed. Flow through variable thicker surface for the free convective flow associated with transverse magnetic field in the flow phenomenon that enriches the study. The specialty of the model is the use of effective conductivity property considering the Mintsa model and the effective viscosity with the help of the Gharesim model for the enhancement of heat transport properties. Depending upon the recent applications related to industrial products, engineering as well as bio-medical science nanofluids are used as the best coolant. A comparative study is carried out for the transformed governing equations using both approximate analytical, that is, “Variational Iteration Method” (VIM), “Homotopy Perturbation Method” (HPM), and numerical techniques such as the in-build MATLAB command bvp5c. The simulated result in connection to the behavior of the physical parameters is deployed through graphs. The current outcomes validate the earlier established results in particular cases showing the conformity and the convergence of the methodology adopted. However, the observation shows that, shear rate retards with the significant enhancement in the particle concentration of the metal nanoparticles as well as the suction further the heat transfer rate enhanced. The fluid velocity profile boosts up for the increasing thermal buoyancy parameter whereas the reverse impact is rendered in the fluid temperature.
分析了二维导电杂化纳米流体通过指数拉伸可渗透表面的流动特性。流动中通过变厚表面的自由对流流动与横向磁场相关联,丰富了流动现象的研究。该模型的特点是考虑Mintsa模型的有效导电性和garesim模型的有效粘度来增强传热性能。根据最近与工业产品,工程以及生物医学科学相关的应用,纳米流体被用作最佳冷却剂。利用近似解析法,即“变分迭代法”(VIM)、“同伦摄动法”(HPM)和MATLAB内置命令bvp5c等数值技术,对变换后的控制方程进行了比较研究。模拟结果与物理参数的行为有关,通过图形进行部署。目前的结果在特定情况下验证了早先确定的结果,显示了所采用方法的一致性和收敛性。然而,观察表明,剪切速率随着金属纳米颗粒浓度的显著提高而减慢,吸力的增加进一步增强了传热速率。随着热浮力参数的增大,流体速度剖面增大,而流体温度则相反。
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引用次数: 2
Experimental analysis and optimization of process parameters using response surface methodology of surface nanocomposites fabricated by friction stir processing 基于响应面法的搅拌摩擦表面纳米复合材料工艺参数实验分析与优化
IF 6 Q2 NANOSCIENCE & NANOTECHNOLOGY Pub Date : 2023-02-04 DOI: 10.1177/23977914231151485
Ravi Butola, Kapil Dev Pandey, Q. Murtaza, R. S. Walia, M. Tyagi, K. Srinivas, A. Chaudhary
In the present research work, microhardness and ultimate tensile strength of the aluminum based metal surface nanocomposites is studied using response surface methodology. Aluminum alloy 5083 is used as a matrix material, boron carbide nanoparticles as a reinforcement and surface nanocomposites are fabricated using Friction stir processing (FSP). Central composite design (CCD) matrix is used to prepare a design of experiment with three process parameters/factors that is, Tool rotational speed, Tool traverse speed, and Number of passes, having three level each. The nanocomposite fabricated according to design of experiment are analyzed using Response surface methodology (RSM). The developed mathematical model well fitted experimental values and equations are stated by the model to predict the microhardness and ultimate tensile strength of the surface nanocomposites. The predicted value by the model and actual tested values are in close agreement. The developed model predicted that the optimum nanocomposites is to be fabricated at 1300 rpm tool rotational speed with a tool traverse speed of 30 mm/min and no of passes should be three times, in order to achieve enhance ultimate tensile strength and microhardness.
本文采用响应面法研究了铝基金属表面纳米复合材料的显微硬度和极限抗拉强度。以5083铝合金为基体材料,碳化硼纳米颗粒为增强材料,采用搅拌摩擦工艺(FSP)制备表面纳米复合材料。采用中心复合设计(CCD)矩阵编制有刀具转速、刀具横移速度和经过次数三个工艺参数/因素的实验设计,每个工艺参数/因素有三个层次。采用响应面法对实验设计制备的纳米复合材料进行了分析。所建立的数学模型与实验值和方程拟合良好,可用于预测表面纳米复合材料的显微硬度和极限拉伸强度。模型预测值与实测值吻合较好。该模型预测,在刀具转速为1300转/分、刀具横移速度为30 mm/min、不经过3道次的条件下制备纳米复合材料,可提高材料的极限拉伸强度和显微硬度。
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引用次数: 0
Buoyancy-driven flow of magnetohydrodynamic hybrid nanofluids in an open cavity with permeable horizontal walls 磁流体动力混合纳米流体在具有可渗透水平壁的开腔中的浮力驱动流动
IF 6 Q2 NANOSCIENCE & NANOTECHNOLOGY Pub Date : 2023-02-03 DOI: 10.1177/23977914231151481
Nepal Chandra Roy, S. Monira, Rama Subba Reddy Gorla
The buoyancy-driven flow of hybrid nanofluids in an open cavity is examined in the presence of a magnetic field with an angle to the horizontal axis. The right end of the cavity is open, and the left wall is supposed to be heated. Moreover, the horizontal walls are deemed to be permeable and maintained at ambient temperature. The successive over-relaxation (SOR) technique is applied with the finite-difference method to solve the dimensionless equations. A comparison is executed with formerly published results which provide a good agreement. The grid refinement test has also been carried out to increase the accuracy. Flow and temperature profiles are investigated for the Rayleigh number ( Ra = 104, 105, 106), Reynolds number (Re = 5, 8, 10, 20, 100), Hartmann number ( Ha = 0, 5, 10), concentration of nanoparticles ( φ1 or φ2 = 0.0, 0.05, 0.1), angle of inclination of the magnetic field ( γ = 0°, 30°, 45°), aspect ratio ( A = 1, 2, 3, 4), and suction/blow parameter ( S = −1, 0, 1). Results have been elucidated based on streamlines, isotherms, local Nusselt number ( Nu), and average Nusselt number ( Nuavg). It is noted that the changes in the variables significantly affect streamlines and isotherms. The heat transfer for Cu-Fe3O4/water hybrid nanofluid is higher about 9.98% compared to Fe3O4/water nanofluid and 26.41% compared to water. Furthermore, all other parameters noticeably augment both Nu and Nuavg.
在与水平轴有一定角度的磁场存在的情况下,研究了由浮力驱动的混合纳米流体在开放腔中的流动。腔的右端是开放的,左壁应该是加热的。此外,水平墙被认为是可渗透的,并在环境温度下保持。将逐次超松弛(SOR)技术与有限差分法应用于求解无量纲方程。与以前发表的结果进行了比较,结果很吻合。为了提高精度,还进行了网格细化试验。流和温度资料研究了瑞利数的(Ra = 104、105、106),雷诺数(Re = 5、8、10、20、100),哈特曼数(公顷= 0、5、10),纳米粒子的浓度(φ1或φ2 = 0.0,0.05,0.1),磁场倾角(γ= 0°、30°、45°),纵横比(= 1,2,3,4),和吸/吹参数(S =−1 0 1)。结果阐明基于流线,等温线,局部努塞尔特数(ν)和平均努塞尔特数(Nuavg)。值得注意的是,变量的变化显著影响流线和等温线。Cu-Fe3O4/water混合纳米流体的换热性能比Fe3O4/water纳米流体高9.98%,比water纳米流体高26.41%。此外,所有其他参数都明显增加了Nu和Nuavg。
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引用次数: 0
Progressive use of nanocomposite hydrogels materials for regeneration of damaged cartilage and their tribological mechanical properties 纳米复合水凝胶材料在损伤软骨再生中的应用及其摩擦学力学性能
IF 6 Q2 NANOSCIENCE & NANOTECHNOLOGY Pub Date : 2023-02-01 DOI: 10.1177/23977914231151487
P. Sagar, G. Kumar, A. Handa
Osteoarthritis (OA) is a non-inflammatory deteriorating debilitating state that bring about remarkable health and economic issues globally. Break down/deterioration of the articular cartilage (AC) is one of the pathologic characteristics of osteoarthritis (OA). Nanocomposite hydrogels (NCH) materials are evolving as a potential class of scaffolds for organ regeneration and tissue engineering. In recent years, innovative hydrogels specifically loaded with nanoparticles have been developed and synthesized with the goal of changing conventional cartilage treatments. The detailed development of a tailored nanocomposite hydrogels (NCH) material utilized for tissue engineering is presented in this review study. Also, the mechanical characteristics, particularly the tribological behavior, of these produced NCH have been highlighted. Large amounts of research and data on the hydrogel substance utilized in cartilage healing are summarized in the current review study. When determining future research gaps in the area of hydrogels for cartilage regeneration, such information will provide researchers an advantage to further develop NCH.
骨关节炎(OA)是一种非炎症性恶化的衰弱状态,在全球范围内带来了显著的健康和经济问题。关节软骨(AC)的破坏/恶化是骨关节炎(OA)的病理特征之一。纳米复合水凝胶(NCH)材料是一种潜在的器官再生和组织工程支架材料。近年来,专门装载纳米颗粒的创新水凝胶已被开发和合成,目的是改变传统的软骨治疗方法。本文介绍了用于组织工程的定制纳米复合水凝胶(NCH)材料的详细开发。此外,这些生产的NCH的机械特性,特别是摩擦学性能也得到了强调。本文综述了大量关于水凝胶物质在软骨愈合中的应用的研究和数据。在确定未来软骨再生水凝胶领域的研究空白时,这些信息将为研究人员进一步开发NCH提供优势。
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引用次数: 0
Vibration of nonlocal strain gradient functionally graded nonlinear nanobeams using a novel locally adaptive strong quadrature element method 基于局部自适应强正交元法的非局部应变梯度功能梯度非线性纳米梁振动研究
IF 6 Q2 NANOSCIENCE & NANOTECHNOLOGY Pub Date : 2022-11-21 DOI: 10.1177/23977914221129426
M. Trabelssi, S. El-Borgi
The primary objective of this paper is to propose a novel method to derive Differential Quadrature Method matrices with several degrees of freedom at the boundaries that can be used to build Strong Quadrature Elements to solve fourth and higher-order equations of motion. The proposed method, referred to as Locally adaptive Strong Quadrature Element Method, is applied to higher-order equations of motion for nonlinear graded Timoshenko and Euler-Bernoulli nanobeams formulated using the Second Strain Gradient Theory or the Nonlocal Strain Gradient Theory. To limit the formulation complexity, the proposed approach is based on the regular formulation of the differential quadrature method combined with custom-built transfer matrices. Moreover, it does not require a different formulation for fourth and sixth-order equations and can be extended beyond sixth-order equations. Validation was carried out using examples from the literature as well as data obtained using the classical Locally adaptive Quadrature Element Method. Both linear and nonlinear frequencies were evaluated for a large number of configurations and boundary conditions. The proposed approach resulted in good accuracy and a convergence speed comparable to the conventional Locally adaptive Quadrature Element Method.
本文的主要目的是提出一种新的方法来导出在边界处具有多个自由度的微分正交方法矩阵,这些矩阵可用于构建强正交单元来求解四阶和高阶运动方程。该方法被称为局部自适应强正交单元法,应用于用第二应变梯度理论或非局部应变梯度理论表述的非线性梯度Timoshenko和Euler-Bernoulli纳米梁的高阶运动方程。为了限制公式的复杂性,本文提出的方法是基于微分正交法的正则公式,并结合定制的传递矩阵。此外,对于四阶和六阶方程不需要不同的公式,并且可以推广到六阶方程之外。利用文献中的算例和经典的局部自适应正交元法得到的数据进行了验证。对大量的结构和边界条件进行了线性和非线性频率的计算。与传统的局部自适应正交元法相比,该方法具有较高的精度和收敛速度。
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引用次数: 0
期刊
Proceedings of the Institution of Mechanical Engineers Part N-Journal of Nanomaterials Nanoengineering and Nanosystems
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