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Rapidly convergent mixed fem for geometrically nonlinear analysis of laminated composite beams integrating 3d strain effects 考虑三维应变效应的层合组合梁几何非线性快速收敛混合有限元分析
IF 3.6 3区 材料科学 Q2 ENGINEERING, MECHANICAL Pub Date : 2026-02-24 DOI: 10.1007/s10999-026-09878-5
Umit N. Aribas, Merve Ermis, Elif Koc, Mehmet H. Omurtag

This study presents a mixed finite element (MFE) formulation designed to efficiently determine the geometrically nonlinear behavior of laminated composite beams, ensuring rapid convergence and reduced computational cost. This is achieved by incorporating all 3D strain components into the constitutive equations while satisfying the beam theory stress-free surface conditions. Von Kármán nonlinear strains are derived from a displacement field including three displacements and three rotations per node. The governing equations, obtained from the first variation of the Hellinger–Reissner functional, are linearized via an incremental formulation and solved iteratively using the Newton–Raphson algorithm. The proposed MFE is based on Timoshenko beam theory and enhanced by the integration of the cross-sectional warping deformations over a displacement-based FE formulation. The two-noded MFE involves twelve degrees of freedom per node and achieves rapid convergence with substantially reduced computational cost. Its performance is assessed through comparison with advanced beam formulations featuring refined kinematics, as well as 3D solid element simulations for asymmetric [0°/90°] cross-ply laminated beams. It provides satisfactory convergent results via very few degrees of freedom compared to the 20-node brick finite elements and 4-node shell finite elements of ANSYS. Parametric studies discuss the influence of cross-ply lamination, material anisotropy, and geometric design on the ratio of geometrically nonlinear to linear displacements, highlighting the significance of design-induced nonlinearities in high-performance structural applications.

本研究提出了一种混合有限元(MFE)公式,旨在有效地确定层合组合梁的几何非线性行为,确保快速收敛并降低计算成本。这是通过将所有三维应变分量纳入本构方程而实现的,同时满足梁理论无应力表面条件。Von Kármán非线性应变由包含三个位移和每个节点三个旋转的位移场导出。从Hellinger-Reissner泛函的第一个变化得到的控制方程通过增量公式线性化,并使用Newton-Raphson算法迭代求解。提出的MFE基于Timoshenko梁理论,并通过在基于位移的有限元公式上集成截面翘曲变形来增强。双节点MFE每个节点包含12个自由度,可以快速收敛,大大降低了计算成本。通过与具有精细运动学的先进梁配方的比较,以及非对称[0°/90°]交叉层合梁的3D实体单元模拟,评估了其性能。与ANSYS的20节点砖有限元和4节点壳有限元相比,该方法在很小的自由度下获得了令人满意的收敛结果。参数化研究讨论了交叉层合、材料各向异性和几何设计对几何非线性与线性位移之比的影响,强调了设计引起的非线性在高性能结构应用中的重要性。
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引用次数: 0
Interaction between inclusions and prismatic dislocation loops in Bi-containing free-cutting steel under nanoindentation: a molecular dynamics study 纳米压痕下含铋易切削钢中夹杂物与棱柱位错环的相互作用:分子动力学研究
IF 3.6 3区 材料科学 Q2 ENGINEERING, MECHANICAL Pub Date : 2026-02-24 DOI: 10.1007/s10999-026-09882-9
Lujia Yu, Fazhan Wang, Xiaopeng Li, Haochen Wang, Haizhou Zhang, Xinyang Zhao, Yumeng Cai

To clarify the micromechanical performance of Bi-containing free-cutting steels, molecular dynamics simulation was employed to investigate the nucleation process and slip mechanism of prismatic dislocation loops (PDLs) within the FeNiCr alloy matrix under nanoindentation conditions. Meanwhile, special emphasis was placed on studying the interaction between Bi inclusions of varying sizes and PDLs. The simulation results show that Bi inclusions influence the dislocation loop movement significantly through the interface between Bi inclusions and the FeNiCr alloy matrix. It is found that the dislocation loop will slide gradually from below the parallelogram indenter to the inclusion interface. Small-sized inclusions will slow down the slip velocity, while large-sized inclusions will lead to the absorption or severe distortion of dislocation loops, and simultaneously induce plastic deformation of Bi inclusions. This process is beneficial to eliminating dislocation accumulation and slowing down the initiation of fatigue cracks caused by dislocation loops generated during machining. These atomic-scale discoveries elucidate the mechanism by which inclusions coordinate local plastic deformation through unique interactions with crystal defects, thereby providing key theoretical insights for the design of high-performance Bi-containing free-cutting steels.

为了阐明含铋易切削钢的微观力学性能,采用分子动力学模拟研究了纳米压痕条件下FeNiCr合金基体中棱柱位错环(PDLs)的成核过程和滑移机制。同时,重点研究了不同尺寸Bi包裹体与pdl之间的相互作用。结果表明,Bi夹杂物通过与FeNiCr合金基体的界面对位错环的运动有显著影响。发现位错环从平行四边形压头下方逐渐向夹杂物界面滑动。较小的夹杂物会减缓滑移速度,而较大的夹杂物会导致位错环的吸收或严重变形,同时引起Bi夹杂物的塑性变形。这有利于消除位错积累,减缓加工过程中产生的位错环引起的疲劳裂纹的萌生。这些原子尺度的发现阐明了夹杂物通过与晶体缺陷的独特相互作用协调局部塑性变形的机制,从而为高性能含铋易切削钢的设计提供了关键的理论见解。
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引用次数: 0
Structure, chemical composition and mechanical properties of MIG-CMT-Cladded Inconel 625/16Mo3 bimetallic layers mig - cmt包覆Inconel 625/16Mo3双金属层的组织、化学成分和力学性能
IF 3.6 3区 材料科学 Q2 ENGINEERING, MECHANICAL Pub Date : 2026-02-24 DOI: 10.1007/s10999-026-09883-8
Daniel Chrast, Stepan Kolomy, Martin Slany, Marek Doubrava, Lukas Rehorek, Jan Zouhar

The demand for materials capable of reliable service at elevated temperatures is steadily increasing. Therefore, this research presents the manufacturing process of MIG-CMT linear Inconel 625 cladding onto the 16Mo3 base material to create high efficiency and corrosion resistant bimetallic material. Microstructure of the bimetallic material was examined by SEM, which revealed NbC, TiC, and MoC carbides within the structure and dendrites that were directionally solidified and aligned parallel to the thermal gradient. Dislocation in microstructure was examined by TEM analysis. The grain size and orientation were examined by EBSD analysis, which found that the grain size in heat affected zone was on average about 10 µm. Furthermore, the chemical analysis unveiled that the chemical composition of Fe decreased from the average value of 3.5–1.2% after overlapping with the second Inconel 625 layer. Micro-CT analysis showed that the bimetallic material exhibited minimum internal defects due to the appropriate welding parameters. Microhardness testing revealed that the highest value of hardness was measured between welded layers 398 HV0.1. The base 16Mo3 material exhibited a average hardness of 210 HV0.1. It was concluded that bimetallic material consisted of Inconel 625 and 16Mo3 steel offers a robust solution for industrial environments requiring high strength, corrosion resistance, and thermal stability such as the incinerating kettle.

对能够在高温下可靠工作的材料的需求正在稳步增加。因此,本研究提出了在16Mo3基材上进行米格- cmt线性Inconel 625包层的制造工艺,以制造高效耐腐蚀的双金属材料。SEM分析了双金属材料的微观结构,发现结构内存在NbC、TiC和MoC碳化物,且枝晶定向凝固并平行于热梯度排列。用透射电镜分析了显微组织中的位错。通过EBSD分析晶粒尺寸和取向,热影响区的晶粒尺寸平均约为10µm。化学分析表明,与第二层Inconel 625层叠加后,Fe的化学成分从3.5 ~ 1.2%的平均值下降。显微ct分析表明,由于适当的焊接参数,双金属材料的内部缺陷最小。显微硬度测试表明,焊接层之间的硬度最高,为398 HV0.1。基体16Mo3材料的平均硬度为210 HV0.1。结论是,由Inconel 625和16Mo3钢组成的双金属材料为焚烧炉等需要高强度,耐腐蚀性和热稳定性的工业环境提供了强大的解决方案。
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引用次数: 0
Axial compression damage mode and energy absorption mechanism of CFRP/metal composite class origami thin-walled infill members CFRP/金属复合材料类折纸薄壁填充构件轴压损伤模式及能量吸收机理
IF 3.6 3区 材料科学 Q2 ENGINEERING, MECHANICAL Pub Date : 2026-02-24 DOI: 10.1007/s10999-026-09881-w
Yong Xiao, Ning Tong, Yu Liu, YiHang Shi, HaiYang Gao, QianWen Wu

CFRP/metal composite class origami thin-walled square tubes filled with polyurethane foam are a new energy-absorbing component. This paper uses a combination of numerical simulation and quasi-static axial compression test to study the damage modes and energy-absorbing mechanisms of metal square tubes, metal class origami square tubes, and carbon fiber square tubes. It also explores the effects of factors such as foam filling, fiber winding angle, fiber circumferential-axial winding ratio, dihedral angle degree, and number of essential pattern layers on the damage modes and energy absorption mechanisms of the components. The results show that introducing the class origami pattern into a single metal square tube can change its damage mode from non-compact crushing to compact crushing. Filling the composite tube with polyurethane foam can result in more complete destruction of the carbon fiber tube and reduce the effective length of wrinkles on the metal tube, thereby significantly improving the total energy absorption of the composite tube. The fiber winding angle has a significant impact on the components: when the fiber winding angle is less than 45°, the potential energy release of the composite tube is incomplete, with low energy absorption efficiency and poor overall stability; when the fiber winding angle is greater than 45° and less than 90°, the potential energy release of the composite tube is sufficient and it has good axial folding and buckling consistency. The appropriate increase in the fiber circumferential-axial winding ratio, dihedral angle degree, and number of essential pattern layers can all improve the energy absorption capacity of CFRP/metal composite class origami thin-walled filled members. This study demonstrates the potential of CFRP/metal composite class origami thin-walled filled members as energy absorbers, aiming to provide a reference for origami design and composite energy-absorbing structure design.

CFRP/金属复合材料类填充聚氨酯泡沫的折纸薄壁方管是一种新型吸能材料。采用数值模拟与准静态轴压试验相结合的方法,对金属方管、金属类折纸方管和碳纤维方管的损伤模式和吸能机理进行了研究。探讨了泡沫填充、纤维缠绕角、纤维周轴缠绕比、二面角度、基本图案层数等因素对构件损伤模式和吸能机理的影响。结果表明,在单金属方管中引入类折纸图案可以使其由非紧致破碎转变为紧致破碎。用聚氨酯泡沫填充复合管,可以使碳纤维管破坏更彻底,减少金属管上起皱的有效长度,从而显著提高复合管的总吸能。纤维缠绕角对组件的影响显著:当纤维缠绕角小于45°时,复合管的势能释放不完全,能量吸收效率低,整体稳定性差;当纤维缠绕角大于45°,小于90°时,复合材料管的势能释放充分,具有良好的轴向折叠和屈曲一致性。适当增加纤维周轴缠绕比、二面角度和基本图案层数,均能提高CFRP/金属复合材料类折纸薄壁填充构件的吸能能力。本研究论证了CFRP/金属复合材料类折纸薄壁填充构件作为吸能材料的潜力,旨在为折纸设计和复合材料吸能结构设计提供参考。
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引用次数: 0
Memory-dependent and size-dependent effects on nonlinear electro-magneto-thermo-viscoelastic vibration analysis of a polymer spherical nanoshell with fractional order strain 分数阶应变聚合物球形纳米壳非线性电磁-热-粘弹性振动分析中的记忆依赖和尺寸依赖效应
IF 3.6 3区 材料科学 Q2 ENGINEERING, MECHANICAL Pub Date : 2026-02-21 DOI: 10.1007/s10999-025-09826-9
Wei Peng, Jingsong Luan, Ashraf M. Zenkour

The stress–strain prediction for viscoelastic materials using integer-order thermoviscoelastic models faces challenges due to the limitations of integer-order derivatives.With the miniaturization of devices, size-dependent effects on elastic deformation become more significant. Additionally, experiments and theories indicate that thermal conductivity in materials should not be treated as a constant in practical analyses. This study develops a fractional-order thermoviscoelastic model by integrating the fractional three-phase-lag heat conduction model, the fractional strain model and the nonlocal elasticity theory. The proposed model is then applied to analyze the nonlinear electro-magneto-thermo-viscoelastic response of a polymer spherical nanoshell under ramp-type heating and an external magnetic field. Taking into account the variable thermal conductivity, the nonlinear governing equations are derived. The Laplace and Kirchhoff transformations are employed to derive and solve the governing equations. The dimensionless temperature, induced magnetic field, displacement and stress are obtained and illustrated graphically. The results show that the nonlinear thermoviscoelastic response of the polymer spherical shell can be adjusted by the suitably modified parameters, which strongly depend on the size-dependent effect, memory-dependent effect and the variable thermal conductivity.

由于整数阶导数的局限性,用整阶热粘弹性模型进行粘弹性材料的应力应变预测面临挑战。随着器件的小型化,尺寸对弹性变形的影响越来越显著。此外,实验和理论表明,在实际分析中,材料的导热系数不应被视为常数。本文将分数阶三相滞后热传导模型、分数阶应变模型和非局部弹性理论相结合,建立了分数阶热粘弹性模型。然后应用该模型分析了聚合物球形纳米壳在斜坡加热和外加磁场作用下的非线性电磁-热-粘弹性响应。考虑变导热系数,导出了非线性控制方程。利用拉普拉斯变换和基尔霍夫变换推导和求解控制方程。得到了无因次温度、感应磁场、位移和应力,并用图形表示。结果表明,聚合物球壳的非线性热粘弹性响应可以通过适当修改参数来调节,这些参数强烈依赖于尺寸依赖效应、记忆依赖效应和变热导率。
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引用次数: 0
Impact of hydrospheric density variation and atmospheric thermal jumps on heat transfer between two concentric spheres with temperature-dependent fluid properties 水圈密度变化和大气热跳变对具有温度依赖流体性质的两个同心球之间传热的影响
IF 3.6 3区 材料科学 Q2 ENGINEERING, MECHANICAL Pub Date : 2026-02-19 DOI: 10.1007/s10999-026-09869-6
A. F. Isarinade, A. M. Obalalu, Umair Khan, Dalia H. Elkamchouchi, Anuar Ishak

Heat transfer between the Earth’s hydrosphere and atmosphere is influenced by density variations within water masses and thermal-jump effects in rarefied atmospheric layers. Traditional continuum-based models often neglect these coupled mechanisms, leading to inaccurate predictions of temperature transport across spherical earth regions. To address this limitation, this study investigates the combined effects of hydrospheric density variation and atmospheric thermal-jump conditions on heat transfer between two concentric spherical layers. A two-region mathematical model with temperature-dependent fluid properties is formulated in spherical coordinates, and the governing nonlinear momentum and energy equations are solved using the finite element method. The findings show that increasing hydrospheric density variation enhances thermal retention, producing up to a 14–18% reduction in temperature attenuation near the inner sphere. A reduction in the Grashof number weakens convective circulation, resulting in a 22% decrease in peak momentum intensity and a smoother thermal field. Furthermore, imposing thermal-jump conditions at the interface significantly alters heat exchange between the layers, causing a 10–15% variation in the interfacial heat flux, demonstrating the sensitivity of atmospheric–hydrospheric coupling to jump phenomena.

地球水圈和大气之间的热传递受水团内部密度变化和稀薄大气层中的热跳效应的影响。传统的基于连续体的模式往往忽略了这些耦合机制,导致对地球球形区域温度传输的预测不准确。为了解决这一局限性,本研究探讨了水圈密度变化和大气热跳条件对两个同心球层之间传热的综合影响。在球坐标系下建立了具有温度相关流体性质的两区域数学模型,用有限元法求解了非线性动量方程和能量方程。研究结果表明,水圈密度变化的增加增加了热保留,使内球附近的温度衰减降低了14-18%。格拉什夫数的减少使对流环流减弱,峰值动量强度降低22%,热场更加平滑。此外,在界面处施加热跃条件会显著改变层间的热交换,导致界面热通量变化10-15%,表明大气-水圈耦合对跃变现象的敏感性。
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引用次数: 0
Dynamics of bistable nonlinear energy sinks and their application in monopile offshore wind turbines 双稳态非线性能量汇动力学及其在单桩海上风力发电机组中的应用
IF 3.6 3区 材料科学 Q2 ENGINEERING, MECHANICAL Pub Date : 2026-02-14 DOI: 10.1007/s10999-026-09872-x
Jianwei Zhang, Shiju E, Cailiang Zhang

To explore the coupling effect of the bidirectional bistable nonlinear energy sink (BBNES), this study examines the dynamics of both BBNES and dual bistable nonlinear energy sinks (BNESs), with their application in monopile offshore wind turbines (OWTs). The research methodology involves: (1) establishing physical models of both absorbers with corresponding force and potential energy analyses; (2) developing separate dynamic analysis models for host structure (HS)-mounted and nacelle-mounted absorber configurations; (3) comparing harmonic forced vibration responses between the BBNES and dual BNESs installed on the HS to preliminarily reveal the BBNES’s coupling effect. This study culminates in evaluating both absorbers’ performance under wind-wave loads, paying attention to the emergency shutdown scenario characterized by significant tower vibrations. Under harmonic excitation, the BBNES demonstrates superior vibration mitigation with the strongly modulated response when excitations are equal in both directions, but shows complex coupling effects under asymmetric excitations. During emergency shutdown conditions with wind-wave loads, the BBNES matches the performance of the dual BNESs in the fore-aft direction but exhibits inferior side-to-side damping performance due to its bidirectional energy coupling and limited adaptability to amplitude variations. Notably, the BBNES reduces nacelle space requirements by 1.24 m, and its performance is highly sensitive to slight changes in the proportionality factors but robust against variations in the mass ratio, frequency ratio, damping ratio, and pre-compressed spring’s original length. The research reveals that while the BBNES has greater application potential than the dual BNESs, its coupling effect suggests optimization opportunities through bidirectional decoupling as well as bidirectional stiffness and damping inequality designs. This work not only provides deep insights into the dynamics of the BBNES but also lays the foundation for its future optimization design.

为了探讨双向双稳态非线性能量汇(BBNES)的耦合效应,本文研究了双向双稳态非线性能量汇(BNESs)和双向双稳态非线性能量汇(BNESs)的动力学特性,并将其应用于单桩海上风力发电机(OWTs)。研究方法包括:(1)建立吸收体的物理模型,并进行相应的力和势能分析;(2)分别建立主结构式和机舱式减振器的动力分析模型;(3)对比安装在HS上的BBNES与双BBNES的谐波强迫振动响应,初步揭示BBNES的耦合效应。该研究最终评估了两种吸波器在风浪荷载下的性能,并关注了以显著塔振动为特征的紧急关闭场景。在谐波激励下,当两方向激励相等时,BBNES表现出较好的减振效果,具有强调制响应,但在非对称激励下,BBNES表现出复杂的耦合效应。在具有风浪荷载的紧急停机条件下,BBNES在前后方向上的性能与双BNESs相匹配,但由于其双向能量耦合和对振幅变化的适应性有限,其侧向阻尼性能较差。值得注意的是,BBNES将机舱空间要求降低了1.24 m,其性能对比例因子的微小变化高度敏感,但对质量比、频率比、阻尼比和预压缩弹簧的原始长度的变化非常稳定。研究表明,虽然BBNES比双BNESs具有更大的应用潜力,但其耦合效应通过双向解耦以及双向刚度和阻尼不等式设计提供了优化机会。这项工作不仅为BBNES的动力学提供了深入的见解,也为其未来的优化设计奠定了基础。
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引用次数: 0
Lightweight design of double-decker ball bearing based on loofah bionic characteristics 基于丝瓜仿生特性的双层滚珠轴承轻量化设计
IF 3.6 3区 材料科学 Q2 ENGINEERING, MECHANICAL Pub Date : 2026-02-13 DOI: 10.1007/s10999-026-09870-z
Jing Hu, Puyi Wang, Xinming Zhang, Xin Zhang, Yiwen Zhang, Jingran Zhang, Chunmin Shang

Compared with traditional single-decker bearings, double-decker ball bearings exhibit advantages such as higher limiting rotational speed and longer service life. However, the additional bearing stage inevitably increases the overall mass, which restricts their application in weight-sensitive fields such as aerospace. To address this issue, this study proposes a bionic design for one of the key components of the double-decker ball bearing-the adapter ring. Inspired by the three-dimensional network structure of loofah sponge, characterized by its extremely low specific density and high mechanical strength, a loofah-inspired adapter ring structure has been developed. A finite element static analysis model for the loofah-inspired double-decker ball bearing was established to perform strength analysis on various adapter ring configurations. Furthermore, the mechanical behavior of the bearing under compressive load was theoretically analyzed, and the energy transfer mechanisms in this process was elucidated. Different adapter ring structures were fabricated using additive manufacturing technology, and experimental validation was conducted. By comparing the results of multiple experimental groups, the optimal adapter ring configuration for the double-decker ball bearing was determined. Optimization results indicate that, in the case study, the mass of the adapter ring was reduced by 25.97% and the maximum equivalent stress decreased by 7.74% compared with the unoptimized design. The proposed design approach provides a theoretical foundation for subsequent structural optimization of double-decker ball bearings and their application in lightweight-demanding scenarios such as aerospace.

与传统的单层轴承相比,双层球轴承具有更高的极限转速和更长的使用寿命等优点。然而,额外的承载级不可避免地增加了整体质量,这限制了它们在航空航天等重量敏感领域的应用。为了解决这一问题,本研究提出了双层球轴承关键部件之一的适配环的仿生设计。受丝瓜海绵具有极低比密度和高机械强度的三维网络结构的启发,开发了一种丝瓜海绵适配器环结构。建立了丝瓜型双层球轴承的有限元静力分析模型,对各种转接头环配置进行了强度分析。在此基础上,对轴承在压缩载荷作用下的力学行为进行了理论分析,阐明了压缩载荷作用过程中的能量传递机理。采用增材制造技术制作了不同的适配器环结构,并进行了实验验证。通过对多组实验结果的比较,确定了双层球轴承的最佳转接头环配置。优化结果表明,与未优化设计相比,优化后的接箍环质量降低了25.97%,最大等效应力降低了7.74%。提出的设计方法为后续双层球轴承的结构优化及其在航空航天等轻量化要求场合的应用提供了理论基础。
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引用次数: 0
Artificial neural network modeling of rotary flow around a permeable sphere in Jeffrey fluid with magnetic field effects 磁场作用下杰弗里流体中可渗透球体旋转流场的人工神经网络建模
IF 3.6 3区 材料科学 Q2 ENGINEERING, MECHANICAL Pub Date : 2026-02-12 DOI: 10.1007/s10999-026-09871-y
P. Aparna, M. Pavan Kumar Reddy, Rajani Indrakanti, MD. Shamshuddin, V. Ganesh Kumar

This study investigates the slow, steady rotation of a permeable sphere in an incompressible Jeffrey fluid under the influence of a magnetic field using an analytical approach and an artificial neural network (ANN) framework. In order to train and validate the ANN, high-quality reference data is generated by using exact analytical solutions to the governing equations. The suggested ANN reliably forecasts the swirl and external couple for a variety of controlling parameters, such as the magnetic and Jeffrey fluid characteristics. The ANN model converges quickly, maintains high accuracy, and greatly reduces the amount of computation that is required. These findings support the ANN’s efficacy as a trustworthy surrogate model for challenging non-Newtonian MHD flow issues. The governing dynamics of the flow are represented through nonlinear partial differential equations (PDEs) articulated in the form of swirl velocity, subject to the relevant boundary conditions. The conventional no-slip condition is imposed at the spherical surface, while the regularity condition for the fluid velocity is applied outside of the sphere in the far-field area. Azimuthal direction is used to apply a constant magnetic field. For both the inside and outside of the sphere, the velocity field is represented by the swirl function. A new method for estimating Navier–Stokes equation solutions has been created, based on artificial neural networks. The scheme’s performance and result correctness are assessed by comparison with established analytical methods and solutions in the literature. To create and analyze the solution for controlled fluid flow, Feed-Forward Neural Network (FFNN) approaches are used. A multilayer perceptron (MLP) neural network is used to construct the sample functions, and the adaptive moment estimation (ADAM) algorithm is applied to optimize the adjustable parameters. The mathematical calculations for both ANN and precise solutions are shown in tables and graphs for different values of physical parameters. The numerical results obtained from both the ANN and analytical solutions are presented in tabular form and further illustrated graphically for a range of physical parameter values. The accuracy of the ANN-based solution is found to improve with rise in both the amount of neurons and the volume of training data used in the network. The swirl velocity predicted by the ANN approach achieved a high coefficient of determination, with an R-Squared value of 0.99951. Additionally, the suggested ANN model shows better adaptation to more complicated mathematical frameworks than the analytical method, and it drastically reduces the amount of computation and resources needed to solve problems.

本研究使用解析方法和人工神经网络(ANN)框架研究了不可压缩杰弗里流体中可渗透球体在磁场影响下的缓慢、稳定旋转。为了训练和验证人工神经网络,使用控制方程的精确解析解生成高质量的参考数据。所提出的人工神经网络在各种控制参数(如磁特性和杰弗里流体特性)下可靠地预测了涡流和外部耦合。该模型收敛速度快,保持了较高的精度,大大减少了所需的计算量。这些发现支持了人工神经网络作为挑战非牛顿MHD流动问题的可靠替代模型的有效性。流动的控制动力学是通过非线性偏微分方程(PDEs)来表示的,以旋涡速度的形式表达,并受相关边界条件的约束。常规的无滑移条件是施加在球面上,而流体速度的规则性条件是施加在球外的远场区域。用方位方向施加恒定磁场。对于球内外,速度场均用旋流函数表示。提出了一种基于人工神经网络估计Navier-Stokes方程解的新方法。通过与文献中已有的解析方法和解的比较,评估了该方案的性能和结果的正确性。为了创建和分析控制流体流动的解决方案,采用了前馈神经网络(FFNN)方法。采用多层感知器(MLP)神经网络构造样本函数,并采用自适应矩估计(ADAM)算法对可调参数进行优化。对于不同的物理参数值,人工神经网络的数学计算和精确解以表格和图表的形式显示。从人工神经网络和解析解中得到的数值结果以表格形式呈现,并进一步以图形形式说明了一系列物理参数值。发现基于人工神经网络的解决方案的准确性随着神经元数量和网络中使用的训练数据量的增加而提高。人工神经网络预测的旋流速度具有较高的确定系数,其r平方值为0.99951。此外,与分析方法相比,所提出的人工神经网络模型对更复杂的数学框架具有更好的适应性,并且大大减少了解决问题所需的计算量和资源。
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引用次数: 0
Stress relaxation behavior and springback prediction of Ti-6Al-4V alloy under triple-layer-sheet hot stamping condition Ti-6Al-4V合金三层板热冲压应力松弛行为及回弹预测
IF 3.6 3区 材料科学 Q2 ENGINEERING, MECHANICAL Pub Date : 2026-02-09 DOI: 10.1007/s10999-026-09874-9
Lida Yu, Xiaoming Yang, Shengqiang Liu, Xiaomin Huang, Baoyu Wang, Hongchao Ji

The traditional single-layer hot stamping process has a significant temperature drop during sheet metal transfer and forming, and the springback of the formed parts is relatively large. The new hot stamping forming process that adopts a triple-layer plate stacking method can effectively reduce the springback after forming. In order to predict the springback behavior of Ti-6Al-4V alloy after hot stamping of triple-layer plates, this paper studies the stress relaxation (SR) behaviors and microstructure evolution of Ti-6Al-4V alloys were investigated at different temperatures (500 °C, 550 °C, 600 °C and 650 °C) and pre-strains (2%, 4% and 8%). The SR constitutive model was also established and embedded in the simulation software to analysis the sheet springback. The prediction accuracy of the simulation model was verified by hot forming experiments. The results show that high temperature and high pre-strain jointly affect the SR process. The initial relaxation stress (IRS) difference with a pre-strain of 2% and 8% decreased from 130 MPa at 500 °C to 2 MPa at 650 °C, and the stress relaxation limit (SRL) has been reduced from 204 MPa to 4.1 MPa. By observing the microstructure of the SR samples, it was found that the content of low-angle grain boundaries (LAGBs 2°–15°) decreased from 57.3% to 49.1% with the increase of temperature. The dislocation slip and climb are the main mechanism of SR at low temperature, and mechanism of SR becomes grain boundary slip and diffusion creep under high temperature conditions. The springback angle increases with the die radius and sheet temperature increasing. In the triple-layer sheet hot stamping process, U-shaped parts experienced stress relaxation behavior during the quenching process. The springback angle decreases by 82.8% increasing by the sheet temperature. Compared with the experimental results, the simulation prediction model has a higher prediction accuracy.

传统的单层热冲压工艺在板料传递和成形过程中温度下降明显,成形件回弹较大。新型热冲压成形工艺采用三层板堆积法,可有效降低成形后回弹。为了预测三层板热冲压后Ti-6Al-4V合金的回弹行为,研究了Ti-6Al-4V合金在不同温度(500°C、550°C、600°C和650°C)和预应变(2%、4%和8%)下的应力松弛(SR)行为和组织演变。建立了SR本构模型,并将其嵌入到仿真软件中,对板料回弹进行分析。通过热成形实验验证了仿真模型的预测精度。结果表明,高温和高预应变共同影响SR过程。预应变为2%和8%时,初始松弛应力(IRS)差值从500℃时的130 MPa减小到650℃时的2 MPa,应力松弛极限(SRL)从204 MPa减小到4.1 MPa。通过观察SR试样的显微组织发现,随着温度的升高,低角晶界(LAGBs 2°~ 15°)的含量从57.3%下降到49.1%。低温条件下,位错滑移和攀爬是SR的主要机制,高温条件下,SR的机制为晶界滑移和扩散蠕变。回弹角随模具半径和板料温度的升高而增大。在三层板料热冲压过程中,u形件在淬火过程中出现应力松弛行为。随着板料温度的升高,回弹角减小82.8%。与实验结果相比,仿真预测模型具有更高的预测精度。
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International Journal of Mechanics and Materials in Design
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