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Damage Behaviors of Thin and Thick Laminated Composites Under Ballistic Effect 薄层和厚层复合材料在弹道效应下的损伤行为
IF 1.7 4区 材料科学 Q4 MATERIALS SCIENCE, COMPOSITES Pub Date : 2024-04-29 DOI: 10.1007/s11029-024-10187-1
R. Gunes, D. S. Al-Behadili

The damage stages of the ballistic impact effect on both thin and thick laminated composites were investigated. Thin and thick laminated composite plates were produced with unsymmetrical cross-ply [0/90], [–45/+45], and [30/60] layups consisting of 16 and 50 unidirectional layers, respectively. Ballistic tests of the composite plates were carried out by means of a single-stage gas gun system at different velocities in the range from 447 to 861 m/s. The thin composite plates were more damaged than the thick plates at ballistic tests with the same velocity. Relatively small strains were observed at low-velocity impact while the projectile rebounded in all thick specimens. All thick plate specimens, except the plates with [–45/+45] layup, were perforated at high velocity impacts. Tests showed an increase in the shear stress between layers with increasing projectile velocity.

研究了弹道冲击效应对薄层和厚层压复合材料的破坏阶段。薄层和厚层复合材料板的非对称交叉层[0/90]、[-45/+45]和[30/60]层叠结构分别由 16 层和 50 层单向层组成。复合材料板的弹道试验是通过单级气枪系统在 447 至 861 米/秒的不同速度范围内进行的。在相同速度的弹道试验中,薄复合板比厚复合板受损更严重。在所有厚板试样中,当弹丸反弹时,在低速冲击下观察到的应变相对较小。除[-45/+45]层叠结构的板材外,所有厚板试样在高速撞击时都被击穿。试验表明,随着弹丸速度的增加,层间剪应力也在增加。
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引用次数: 0
Application of Polyethylene Terephthalate as a Denture Base Material for Manufacturing Temporary Removable Complete Dentures 聚对苯二甲酸乙二醇酯作为义齿基托材料在制作临时可摘全口义齿中的应用
IF 1.7 4区 材料科学 Q4 MATERIALS SCIENCE, COMPOSITES Pub Date : 2024-04-27 DOI: 10.1007/s11029-024-10186-2
E. A. Chizhmakov, A. S. Arutyunov, S. A. Muslov, S. A. Bochkareva, I. L. Panov, G. D. Akhmedov, D. G. Buslovich, S. V. Panin, S. D. Arutyunov

The mechanical properties of both polymethyl methacrylate (PMMA) and polyethylene terephthate (PET) were examined in tensile and three-point bending tests, as well as their bond and interlayer shear strengths were assessed. The results obtained were employed in computer simulation of mechanical loading of temporary removable complete dentures (TRCDs). It was shown that the variations of the elastic moduli of the dental materials studied did not exceed 15.6%; the ultimate strength of PET was higher than that of PMMA by ~2.2 times in tension and by ~1.9 times in bending. Elongation at break was greater for the PET specimens than those for the PMMA ones by ~2.3 times in tension and by ~3.1 times in bending. Computer simulation has shown that when the load was applied at the angle of 90°, the tooth fractured in all cases. Stresses were much lower in the denture base concerning the critical levels. Therefore, the adhesion conditions considered did not affect the pattern of their failure, and the critical load was the same for both denture base materials. When the load was applied to canines at the angle of 45°, the critical load was below the specified level of 100 N in the PMMA denture base due to the peculiarities of TRCD design and the lower strength of PMMA. When both canines and incisors were loaded at the angle of 45°, the PET denture base could withstand the greater critical load than the PMMA one. Both mechanical tests and computer simulation results enabled to conclude that PET is the prospect denture base material for the manufacture of TRCDs and dental orthopedic treatment.

在拉伸和三点弯曲试验中检验了聚甲基丙烯酸甲酯(PMMA)和聚对苯二甲酸乙二醇酯(PET)的机械性能,并评估了它们的粘接强度和层间剪切强度。所得结果被用于临时活动全口义齿(TRCD)机械加载的计算机模拟。结果表明,所研究的牙科材料的弹性模量变化不超过 15.6%;PET 的拉伸极限强度比 PMMA 高 ~2.2 倍,弯曲极限强度比 PMMA 高 ~1.9 倍。PET 试样的断裂伸长率在拉伸时比 PMMA 试样高 ~2.3 倍,在弯曲时高 ~3.1 倍。计算机模拟显示,当负载以 90° 角施加时,所有情况下牙齿都会断裂。义齿基托的应力远低于临界水平。因此,所考虑的粘附条件并不影响其破坏模式,而且两种义齿基托材料的临界负荷是相同的。当对犬齿施加 45° 角的载荷时,由于 TRCD 设计的特殊性和 PMMA 的较低强度,PMMA 义齿基托的临界载荷低于 100 N 的规定水平。当犬齿和门齿都以 45° 角加载时,PET 义齿基托比 PMMA 义齿基托能承受更大的临界载荷。机械测试和计算机模拟结果都表明,PET 是制造 TRCD 和牙科矫形治疗的理想义齿基托材料。
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引用次数: 0
Fluid Coupled Structural Analysis and Optimization of Expanded Polystyrene-Fiber-Reinforced Composite Wing of an Unmanned Aerial Vehicle 无人机膨胀聚苯乙烯-纤维增强复合材料机翼的流体耦合结构分析与优化
IF 1.7 4区 材料科学 Q4 MATERIALS SCIENCE, COMPOSITES Pub Date : 2024-04-26 DOI: 10.1007/s11029-024-10185-3
T. Jamil, A. Iqbal, U. Allauddin, E. Ahmad, S. A. Hashmi, S. Saleem, M. Ikhlaq

The growing demand for unmanned aerial vehicles (UAVs) in the wide range of commercial applications has necessitated engineers to develop lightweight and economical models that are simple to manufacture. This study focuses on the analysis of UAV wing a unconventionally manufactured medium altitude long endurance (MALE) by performing transient and static fluid structure interaction analysis. The wing was made of an expanded polystyrene (EPS) foam core reinforced by a glass and carbon fiber-reinforced polymer composite. The current study utilizes the one-way fluid-structure interaction technique to obtain the pressure profile from a computational fluid dynamics study, which then is used as a load boundary condition for the static and dynamic structural analyses of an EPS-reinforced composite wing to observe its failure characteristics under loading conditions. Modeling the composite laminate was conducted in the ANSYS Composite PrePost module with varying ply orientations to obtain an optimum configuration. The topology optimization of the wing core led to a 30.5% reduction in its overall weight, offering an economical and feasible solution for manufacturing UAVs on small and medium scales.

在广泛的商业应用中,对无人驾驶飞行器(UAV)的需求与日俱增,这就要求工程师们开发出轻质、经济、易于制造的模型。本研究侧重于通过执行瞬态和静态流体结构相互作用分析,对非传统制造的中空长航时(MALE)无人机机翼进行分析。机翼由发泡聚苯乙烯(EPS)泡沫芯材和玻璃纤维及碳纤维增强聚合物复合材料制成。本研究利用单向流体-结构相互作用技术从计算流体动力学研究中获得压力曲线,然后将其用作 EPS 增强复合材料机翼静态和动态结构分析的载荷边界条件,以观察其在载荷条件下的失效特性。在 ANSYS Composite PrePost 模块中对复合材料层压板进行建模,并改变层间方向以获得最佳配置。翼芯的拓扑优化使其整体重量减轻了 30.5%,为中小型无人机的制造提供了经济可行的解决方案。
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引用次数: 0
Families of Stress-Strain, Relaxation, and Creep Curves Generated by a Nonlinear Model for Thixotropic Viscoelastic-Plastic Media Accounting for Structure Evolution Part 1. The model, Its Basic Properties, Integral Curves, and Phase Portraits 考虑结构演变的触变粘弹性介质非线性模型生成的应力-应变、松弛和蠕变曲线族 第 1 部分。模型、其基本特性、积分曲线和相图
IF 1.7 4区 材料科学 Q4 MATERIALS SCIENCE, COMPOSITES Pub Date : 2024-03-04 DOI: 10.1007/s11029-024-10174-6
A. V. Khokhlov, V. V. Gulin

A systematic analytical study of the mathematical properties of the previously constructed nonlinear model of the shear flow of thixotropic viscoelastic-plastic media, which takes into account the mutual influence of the deformation process and structure evolution, is carried out. A set of two nonlinear differential equations describing shear at a constant rate and stress relaxation was obtained. Assuming six material parameters and an (increasing) material function that control the model are arbitrary, the basic properties of the families of stress-strain curves at constant strain rates, stress relaxation curves (Part 2) and creep curves (Part 3) generated by the model, and the features of the evolution of the structuredness under these types of loading were analytically studied. The dependences of these curves on time, shear rate, stress level, initial strain and initial structuredness of material (for example, degree of physical crosslinking), as well as on material parameters and function governing the model, were studied. Several indicators of the model applicability are found, which are convenient to check with experimental data. It was examined what effects typical for viscoelastic-plastic media can be described by the model and what unusual effects (properties) are generated by structuredness changes in comparison to typical stress-strain, relaxation and creep curves of structurally stable materials. The analysis proved the ability of the model to describe behavior of not only liquid-like viscoelastoplastic media, but also solid-like (thickening, hardening, hardened) media: the effects of creep, relaxation, recovery, a number of typical properties of experimental relaxation curves, creep and stress-strain curves at a constant rate, strain rate and strain hardening, flow under constant stress, etc. The first part of the article is devoted to formulation of the model and preparation of basis for the second part: the proof of the uniqueness and stability of the equilibrium point of the nonlinear equations set, analytical study of the equilibrium point dependence on all material parameters, possible types of phase portraits and the properties of integral and phase curves of the model.

对之前构建的触变粘弹塑性介质剪切流非线性模型的数学特性进行了系统的分析研究,该模型考虑了变形过程和结构演变的相互影响。得到了一组描述恒定速率剪切和应力松弛的两个非线性微分方程。假定控制模型的六个材料参数和一个(递增)材料函数是任意的,对模型产生的恒定应变速率下的应力-应变曲线、应力松弛曲线(第 2 部分)和蠕变曲线(第 3 部分)系列的基本特性,以及在这些类型的加载下结构性演变的特征进行了分析研究。研究了这些曲线对时间、剪切速率、应力水平、初始应变和材料初始结构度(例如物理交联程度)的依赖关系,以及对材料参数和管理模型的函数的依赖关系。发现了模型适用性的几个指标,便于与实验数据进行核对。与结构稳定材料的典型应力-应变、松弛和蠕变曲线相比,该模型可以描述粘弹性-塑性介质的哪些典型效应,以及结构性变化会产生哪些异常效应(特性)。分析表明,该模型不仅能描述液态粘弹性介质的行为,还能描述固态(增厚、硬化、淬火)介质的行为:蠕变、松弛、恢复的影响,实验松弛曲线的一些典型特性,恒定速率下的蠕变和应力-应变曲线,应变速率和应变硬化,恒定应力下的流动等。文章的第一部分致力于模型的建立和第二部分基础的准备:非线性方程组平衡点唯一性和稳定性的证明、平衡点对所有材料参数依赖性的分析研究、可能的相图类型以及模型积分曲线和相曲线的特性。
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引用次数: 0
Dynamic Response of Sandwich Beam with Flexible Porous Core Under Moving Mass 带柔性多孔芯材的三明治梁在移动质量作用下的动态响应
IF 1.7 4区 材料科学 Q4 MATERIALS SCIENCE, COMPOSITES Pub Date : 2024-03-04 DOI: 10.1007/s11029-024-10181-7
H. Biglari, H. Teymouri, A. Shokouhi

The dynamic behavior of a sandwich beam with a porous core and carbon nanotube-reinforced polymer facesheets subjected to a moving mass on simple supports was investigated using the quasi-3D theory of shear deformation. The system of equations was determined using the energy technique. In order to solve the equations of motion, the analytical Navier’s approach in the space domain and the numerical Newmark’s method in the time domain were employed. Additionally, the natural frequencies of the free vibrations of beam were studied and evaluated. To validate the accuracy of the results obtained, comparisons were made with existing responses for specific circumstances reported in the literature. The effect of various parameters such as carbon nanotube volume percentage, porosity coefficient and distribution pattern, ratio of geometric and dimensional parameters, speed of moving mass, and facesheet-to-core thickness ratio on the dynamic response, critical speed of moving mass, and natural frequency of the sandwich beam with a porous core and nanocomposite surfaces were investigated. The results showed that by increasing the core porosity, the natural frequencies and critical speeds were increased. Because the intrinsic holes in the core structure get bigger, the stiffness and mass of the beam decrease. However, the effect of the mass reduction is greater than the effect of the stiffness reduction, so the frequency and critical speed of the system are increased.

采用准三维剪切变形理论研究了夹层梁的动态行为,该夹层梁具有多孔核心和碳纳米管增强聚合物面层,在简单支撑物上受到移动质量的作用。方程组是利用能量技术确定的。为了求解运动方程,采用了空间域的纳维分析法和时域的纽马克数值法。此外,还对梁自由振动的自然频率进行了研究和评估。为了验证所获结果的准确性,与文献中报道的特定情况下的现有响应进行了比较。研究了各种参数(如碳纳米管体积百分比、多孔系数和分布模式、几何和尺寸参数比、运动质量速度、面片与芯材厚度比)对多孔芯材和纳米复合材料表面夹层梁的动态响应、运动质量临界速度和固有频率的影响。结果表明,随着夹芯孔隙率的增加,固有频率和临界速度也随之增加。由于夹芯结构中的固有孔变大,梁的刚度和质量也随之降低。然而,质量减小的影响大于刚度减小的影响,因此系统的频率和临界速度都得到了提高。
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引用次数: 0
Bending Analysis of Laminated Composite and Sandwich Cylindrical Shells Using Analytical Method and Ansys Calculations 使用分析方法和 Ansys 计算对层压复合材料和三明治圆柱壳体进行弯曲分析
IF 1.7 4区 材料科学 Q4 MATERIALS SCIENCE, COMPOSITES Pub Date : 2024-02-29 DOI: 10.1007/s11029-024-10173-7
A. Attia, A. T. Berrabah, F. Bourada, A. A. Bousahla, A. Tounsi, M. H. Ghazwani, A. Alnujaie

The bending analysis of isotropic, laminated composite and cylindrical sandwich shells was carried out using a higher order shear deformation theory which incorporates undetermined integral in the displacement field. The model proposed involves only four variables. Moreover, unlike the conventional FSDTs, the shear correction factor is not necessary. The Hamilton’s principle and the Navier’s method are employed to determine and solve the equations of motion. The present analytical model was compared with other higher-order theories in the literature. In addition, finite element analysis methods were designed to calculate displacements and stresses of shells. Shells are subjected to uniform loads. Results are given for shallow and deep shells and thick to thin. According to the analysis, kinematics, based on the indeterminate integral component, are very effective and enable researchers to investigate laminated plates and shells more accurately than traditional models.

采用高阶剪切变形理论对各向同性层压复合材料和圆柱形夹层壳体进行了弯曲分析,该理论在位移场中加入了未定积分。所提出的模型只涉及四个变量。此外,与传统的 FSDT 不同,无需剪切修正系数。采用汉密尔顿原理和纳维叶方法来确定和求解运动方程。本分析模型与文献中的其他高阶理论进行了比较。此外,还设计了有限元分析方法来计算壳体的位移和应力。壳体承受均匀载荷。给出了浅壳和深壳、厚壳和薄壳的结果。根据分析结果,基于不定积分分量的运动学非常有效,使研究人员能够比传统模型更精确地研究层压板和壳。
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引用次数: 0
Mechanical Properties of Alfa, Sisal, and Hybrid Alfa/Sisal Fiber Satin Cloth Reinforced Epoxy 阿尔法、剑麻和混合阿尔法/剑麻纤维缎布增强环氧树脂的机械性能
IF 1.7 4区 材料科学 Q4 MATERIALS SCIENCE, COMPOSITES Pub Date : 2024-02-28 DOI: 10.1007/s11029-024-10180-8
B. R. Baali, M. T. Gherbi, A. Nour, J. B. Casimir, R. Saci, S. Aguib, N. Attia, C. Aribi

The mechanical behavior of composites, made of an epoxy resin matrix reinforced by 30 and 40% of a satin cloth from long Alfa, sisal and hybrid Alfa/sisal fibers was studied. The fibers are obtained by extraction with elimination of binders such as pectins and lignin. For each type of fibers, appropriate and optimal chemical and thermal treatments were conducted within NaOH solution, to enhance both the fiber surface quality and the interfacial bonding between fibers and matrix. Fourier transform infrared (FTIR), scanning electron microscopy (SEM), and chemical decomposition of treated and untreated fibers lead to prove the treatment efficiency. The thermogravimetric (TGA) and differential thermogravimetric (DTG) analyses showed better thermal stability. Differential scanning calorimetry (DSC) made it possible to quantify the enthalpy changes which showed an increase in the amount of heat as a function of the increase in weight fraction of natural fibers. The endothermic reaction of the composites studied containing 30 wt% fiber reinforcement was less than that containing 40 wt% fiber reinforcement. The composite materials were produced by vacuum assisted resin transfer molding (VARTM) method due to hydrophilic nature of the fibers. The results of static tests were compared to those of pure epoxy resin. It showed a significant increase for 40 wt% woven A1lfa/epoxy of about 333, 113, and 81% in tension, 3-points bending and compression tests respectively. SEM morphology analysis revealed good interfacial adhesion between the treated fibers and the matrix.

研究了由 30% 和 40% 的长阿尔法纤维、剑麻纤维和阿尔法/剑麻混合纤维缎布增强的环氧树脂基体制成的复合材料的机械性能。这些纤维是通过萃取去除果胶和木质素等粘合剂后得到的。对于每种纤维,都在 NaOH 溶液中进行了适当和优化的化学和热处理,以提高纤维表面质量以及纤维与基体之间的界面粘合力。傅立叶变换红外光谱(FTIR)、扫描电子显微镜(SEM)以及处理过和未处理纤维的化学分解结果都证明了处理效率。热重(TGA)和差热重(DTG)分析表明,纤维具有更好的热稳定性。差示扫描量热法(DSC)可以量化焓变,显示热量随天然纤维重量分数的增加而增加。所研究的复合材料中,纤维增强量为 30% 的内热反应低于纤维增强量为 40% 的内热反应。由于纤维具有亲水性,复合材料是通过真空辅助树脂传递成型(VARTM)方法生产的。静态测试结果与纯环氧树脂的结果进行了比较。结果表明,40 wt% A1lfa/环氧编织物在拉伸、三点弯曲和压缩试验中的性能分别提高了约 333%、113% 和 81%。扫描电镜形态分析表明,经处理的纤维与基体之间具有良好的界面粘附性。
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引用次数: 0
Loading Capacities of Bonded Composite Pipe Joints of Different Structures 不同结构的粘接复合管接头的承载能力
IF 1.7 4区 材料科学 Q4 MATERIALS SCIENCE, COMPOSITES Pub Date : 2024-02-27 DOI: 10.1007/s11029-024-10175-5
G. H. Zhao, S. H. Hu, C. Feng

Fiber-reinforced composite materials are increasingly used in oil and gas transmission, and joints are the areas prone to failure in pipelines. Damage evolution in the adhesive joints connecting pipes made for basalt-fiber-reinforced polymers (BFRPs) was analyzed. First, finite-element models for three types of adhesive joints (single-lap, sleeve, and scarf ones) were developed. Second, an optimal cohesive zone model (CZM) for the adhesive layer was developed based on the inverse analysis of the results of debonding experiments. Finally, the damage evolution in the adhesive joints was analyzed under internal pressure, tension, bending, and torque, and their pipeline loading capacities were evaluated. Results showed that the single-lap joint exhibited the highest ultimate load-carrying capacity at a unit overlapping length, followed by the sleeve joint, but the scarf joint had the lowest unit ultimate load. For sleeve and scarf joints, the presence of a gap or a weak interface between two pipe adherends led to a reduction in their load-carrying capacity. These findings provide a basis for the design of the composite pipe joints.

纤维增强复合材料越来越多地应用于石油和天然气的输送,而接头是管道中容易出现故障的部位。本文分析了连接玄武岩纤维增强聚合物(BFRP)管道的粘接接头的损伤演变。首先,针对三种类型的粘接接头(单搭接接头、套筒接头和围巾接头)建立了有限元模型。其次,在对脱粘实验结果进行反分析的基础上,建立了粘合层的最佳内聚区模型(CZM)。最后,分析了粘合接头在内压、拉伸、弯曲和扭矩作用下的损伤演变,并评估了其管道承载能力。结果表明,在单位重叠长度上,单搭接接头的极限承载能力最高,其次是套筒接头,但围巾接头的单位极限载荷最低。对于套筒接头和围巾接头,如果两个管道粘合剂之间存在间隙或薄弱界面,则会降低其承载能力。这些发现为复合管道接头的设计提供了依据。
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引用次数: 0
Deflection Behaviour of Hybrid Composite Shell Panels Under Dynamic Loadings 混合复合材料壳体面板在动态载荷下的挠度行为
IF 1.7 4区 材料科学 Q4 MATERIALS SCIENCE, COMPOSITES Pub Date : 2024-02-26 DOI: 10.1007/s11029-024-10171-9
S. Tiwari, C. K. Hirwani, A. G. Barman

Dynamic behavior of hybrid composite shallow shell panels was analyzed utilizing a high-order shear deformation theory (HOSDT) in conjunction with the finite-element method (FEM). To enhance the suitability of plant-fiber composites and to use them as substitutes for pure synthetic-fiber composites, the hybridization of banana-epoxy and glass-epoxy composites was performed, and different sets of hybrid composites were prepared by altering the layers of glass and banana fibers. The elastic constants of these composites were evaluated experimentally and utilized in the further numerical investigation. Simultaneously, a mathematical formulation was developed based on a HOSDT and the FEM. The governing equation of a transient analysis was derived using the Hamilton’s principle and Newmark’s direct integration scheme to get responses in the time domain. First, the consistency of the present model was checked via an element convergence test, and the accuracy of the model was established by comparing the transient responses obtained from the current model with those of published data. Afterwards, different parametric investigations were carried out to explore the influence of the curvature ratio, shell geometry, hybridization, end conditions, and loading rate on the time-dependent responses of the composites.

利用高阶剪切变形理论(HOSDT)和有限元方法(FEM)分析了混合复合材料浅壳板的动态行为。为了提高植物纤维复合材料的适用性并将其用作纯合成纤维复合材料的替代品,研究人员对香蕉-环氧和玻璃-环氧复合材料进行了杂化,并通过改变玻璃纤维和香蕉纤维的层数制备了不同的混合复合材料。实验评估了这些复合材料的弹性常数,并将其用于进一步的数值研究。同时,在 HOSDT 和有限元模型的基础上开发了数学公式。利用汉密尔顿原理和纽马克直接积分方案推导出瞬态分析的控制方程,从而得到时域响应。首先,通过元素收敛测试检验了当前模型的一致性,并通过比较当前模型获得的瞬态响应和已公布的数据,确定了模型的准确性。随后,进行了不同的参数研究,以探讨曲率比、壳体几何形状、杂交、端部条件和加载速率对复合材料随时间变化的响应的影响。
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引用次数: 0
One-Dimensional vs. Three-Dimensional Models in Free Vibration Analysis of Axially Functionally Graded Beams with Non-Uniform Cross-Sections 非均匀截面轴向功能梯度梁自由振动分析中的一维模型与三维模型对比
IF 1.7 4区 材料科学 Q4 MATERIALS SCIENCE, COMPOSITES Pub Date : 2024-02-26 DOI: 10.1007/s11029-024-10176-4

A comparison of one-dimensional (1D) and three-dimensional (3D) models for simulating free vibrations of axially functionally graded material (AFGM) beams with non-uniform cross-sections was carried out. Both models were constructed using ABAQUS and the eigenvalue problem was solved to determine the natural frequencies and their corresponding mode shapes. User-defined material model subroutines (UMAT) were developed using 1D beam or 3D hexagonal graded finite elements to implement material gradients into appropriate finite element models. The performance of both models was evaluated using data for beams with non-uniform cross-sections and material gradation profiles for which natural frequencies were available in the literature. The accuracy and effectiveness of each modeling approach proposed were estimated by comparing the results obtained. Generally, distinctions between the 1D and 3D models become more pronounced as the geometric complexity and material inhomogeneity of AFGM beams increases, especially for high-frequency modes.

在模拟横截面不均匀的轴向功能分级材料(AFGM)梁的自由振动时,对一维(1D)和三维(3D)模型进行了比较。两个模型均使用 ABAQUS 建立,并通过求解特征值问题确定固有频率及其相应的模态振型。使用一维梁或三维六边形分级有限元开发了用户自定义材料模型子程序(UMAT),以便在适当的有限元模型中实现材料梯度。这两种模型的性能都是通过非均匀横截面梁的数据和材料梯度剖面进行评估的,自然频率可从文献中获得。通过比较所获得的结果,估计了所提出的每种建模方法的准确性和有效性。一般来说,随着 AFGM 梁的几何复杂性和材料不均匀性的增加,一维模型和三维模型之间的区别变得更加明显,特别是对于高频模式。
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引用次数: 0
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Mechanics of Composite Materials
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