Three-dimensional Elastic Beam Research Articles

STUDY THE BEHAVIOR OF ELASTIC MODULUS FOR ZIGZAG AND ARMCHAIR SINGLE WALL CARBON NANOTUBE STRUCTURE WITH FEM

A three-dimensional finite element (FE) model for single-walled carbon nanotubes with armchair and zigzag shapes is proposed in this paper (SWCNTs). Nodes are positioned at the locations of carbon atoms to design the FE models. And three-dimensional elastic beam components are used to model the bonds between them. The effect of the diameter length/diameter ratio on the diameter length/diameter ratio, cross sectional aspect ratio and number of elements on the Young’s modulus of SWCNTs has been considered herein. From the conducted experiments it can be observed that, the larger tube diameter can lead to higher Young’s modulus for carbon nanotubes. Such that, maximum elastic modulus for the armchair and the zigzag models has been obtained to be 1.0285TPa and 1.0396TPa when the diameters for the armchair and the zigzag models were 2.034nm and 1.957nm respectively. Increasing the length/diameter ratio has led the Young’s modulus to be increased for armchair and zigzag models such that its values can reach 1.0451TPa and 1.0191TPa respectively. The cross sectional aspect ratio of SWCNTs showed an inversely proportional effect on the elastic modulus in this work. As a result of rising the cross sectional aspect ratio to be2, the Young's modulus for armchair and zigzag models has decreased to 0.7991TPa and 0.8873TPa, accordingly. The change in geometry has been observed to be a defect and it is in general can decrease the modulus of elasticity. The number of elements in the armchair model considered as prominent factor that increases the young’s modulus to be 1.0280TPa when the number of element is 10836. In zigzag model, the number of element has no effect on the elastic modulus since the number of nodes that exposed to the applied load is fixed in this case. The findings showed that the proposed FE model may be useful for studying carbon nanotube mechanical action in the future.

Experimental and multiscale quantum mechanics modeling of the mechanical properties of PVC/graphene nanocomposite

In current work, we developed mechanical properties of PVC (polyvinyl chloride)/graphene nanocomposite theoretically and experimentally. In our theoretical model, a multi-scale finite element model was used to predict Young’s modulus of the stated nanocomposite. The molecular structure of pristine graphene was treated using the density functional theory (DFT) method. By assuming graphene as a space-frame structure that preserves the discrete nature of graphene, they were modeled by the use of three-dimensional elastic beam elements for the Carbon-Carbon covalent bonds and point mass elements for the atoms. Then interfacial van der Waals interaction that exists between PVC and graphene was modeled using the general form of Lennard–Jones potential and simulated by a nonlinear truss rod model. The Lennard–Jones parameters and van der Waals forces were determined versus separation distance for the stated nonlinear truss rod via the DFT method. Finally, we prepared PVC/graphene samples with different weight percentages of graphene nanoplatelets experimentally using the melt-mixing procedure. Our computational modeling demonstrated that the magnitudes of Young’s modulus PVC/graphene were close to the experimentally obtained results until 1 wt% with an average difference of about 25%. Finally, we justified the obtained mechanical results by investigating the morphology of experimental samples using Transmission electron microscopy (TEM) and Scanning Electron Microscopy (SEM) images.

The random vibration and force transmission characteristics of the elastic propeller-shafting system induced by inflow turbulence

Random vibration and force transmission characteristics of an elastic propeller-shafting system induced by the inflow turbulence are analytically studied. Both the propeller blades and the shafting are simplified as three-dimensional elastic beam, which are connected by lumped spring elements. Based on the Timoshenko beam theory, an analytical model considering both the longitudinal and transverse responses of the propeller-shafting system is developed. The random pressure spectrum induced by inflow turbulence is computed by the correlation method and is mapped onto the blades as exciting source. By virtue of the frequency response function matrix, the random vibration characteristics of the propeller-shafting system and forces transmitted through different bearings are obtained. Analytical results show that the elasticity of the propeller blades cannot be neglected and the bending modes of the propeller blades amplify both the longitudinal and transverse transmitted forces. The longitudinal force transmission is mainly controlled by the propeller elasticity and the longitudinal stiffness of the thrust bearing, while the frequency and magnitude of the transverse force is mainly controlled by the bending modes of the shafting and the system elasticity, respectively.

Proposal of FEM analysis model with three-dimensional elastic beam element in order to design the support structure for ground installation type of photovoltaic power generation system

Proposal of FEM analysis model with three-dimensional elastic beam element in order to design the support structure for ground installation type of photovoltaic power generation system

Numerical method for analyzing the nonlinear dynamic response of tubing running in a cased borehole

With the development of deeper and longer wells, the environment of the borehole becomes much more complex, leading to a higher risk of tubing failure. To accurately describe the contact force between the tubing and the borehole, a new method is developed to analyze the non-linear dynamic response of the tubing under complex loading condition. Based on the finite element method, the equilibrium equation of tubing segment is established, where the tubing is simulated by three-dimensional elastic beam elements and the contact between the tubing and borehole is represented by two no-linear springs. The element stiffness matrix was assembled under nodal coordinate system, and the modified square root algorithm was adopted to solve the large-scale banded systems of linear equations. Then, the contact force and position were solved by multi-step iterative method, and thus a new numerical method for analyzing the non-linear dynamic response of tubing was developed. Results show that, the new method could greatly improve the counting rate for analyzing the large deformation of tubing, and also could accelerate the convergence of the non-linear contact problem. This makes it describe well the no-linear dynamic behavior of the tubing, which is helpful for the optimization design and security evaluation of the tubular assembled in complex conditions. This method has been widely applied on the high angle deviated wells in the Shengli oilfields.

Contact Between 3D Beams with Deformable Circular Cross-Sections – Numerical Verification

In this paper a numerical analysis of contact between three-dimensional elastic beams with deformations at the contact zone is carried out. The authors propose a new model of beam-to-beam contact which is the continuation of ideas presented in [6, 7, 10]. The results of beam-to-beam contact analysis are compared with the ones for full 3D problem solved in the abaqus/enviroment. The aim of the conducted numerical simulations was to select the most appropriate 3D model and to use it as a reference to verify the accuracy of the proposed beam-to-beam contact definition. The verifications were carried out for contact between beams with circular cross-sections. The obtained contact forces and the displacements of beams tips for different beams arrangements and boundary conditions showed a satisfactory correlation.

Combining density functional theory-finite element multi-scale method to predict mechanical properties of polypropylene/graphene nanocomposites: Experimental study

In this paper a multi-scale finite element model is developed to study the tensile modulus of graphene reinforced polypropylene (PP/graphene) nanocomposites and compare the results with experimental tensile tests. Herein, the graphenes are modeled and optimized using density functional theory (DFT). By treating graphene as space-frame structures, in which the discrete nature of graphene is preserved, they are modeled using three-dimensional elastic beam elements for the C-C covalent bonds and point mass elements for the atoms. Our calculations reveal that the force constants of stated elastic beam obtained from DFT method are in best agreement comparing to the results of previous MD study which was equal to kr = 6.41 × 10−7 N/nm, kθ = 8.47 × 10−10 N nm/rad2 and kτ=2.7×10-10 N nm/rad2. The interlayer van der Waals forces between graphene and PP matrix are represented by Lennard–Jones potential and simulated by a nonlinear truss rod model. According to our DFT results we found that interaction energy between graphene and PP matrix decreased by increasing in the number of polymer matrix monomers and reached to a constant value when six monomer of polymer adsorbed onto the surface of graphene which was equal to −0.0044 eV/monomer. Our FE results showed that the moduli of the nanocomposites were close to the experimental results until 1 wt% of graphene and also were predictable. The Young's modulus obtained from combined model and experimental test were about 2.85 Mpa and 2.21 Mpa for 0.25 wt%, 3.88 Mpa and 3.22 Mpa for 0.5 wt%, 4.83 Mpa and 4.30 Mpa for 0.75 wt% and also 5.86 Mpa and 5.19 Mpa for 1 wt% of graphene, respectively.

Experimental and mechanical analysis of cement–nanotube nanocomposites

Composites of multi-walled carbon nanotubes (MWCNTs) and cement layers were manufactured by grinding carbon nanotubes and cement powder in a planetary ball mill. Tiny cement nanoparticles were fabricated using an ethylene-glycol-assisted synthesis procedure with successive hydrolysis and condensation reactions. Cement–nanotube nanocomposites were then produced by adding functionalized nanotube powder to the colloidal cement nanoparticles suspended in ethylene glycol (weight ratio of nanotubes to cement $$=$$ 1:1). Modal analysis of five-walled carbon nanotube nanocomposites with 1–5 cement layers was performed via the finite-element method. The five-walled carbon nanotube nanocomposites with different shapes were modelled using three-dimensional elastic beams of carbon bonds, nodal carbon point masses and cement layer shell elements. The natural frequency, von Mises stress and strain energy of the elements were calculated by considering the Van der Waals forces between the carbon atoms in the hexagonal lattice. In the modal analysis, the greatest variation in displacement was observed along the x-axis, and the maximum values of the total displacement appeared to be larger at the cement layers than at the MWCNTs. The cement–nanotube nanocomposites exhibited a gradual decrease in deformation and vibration as the number of cement layers was increased.

An approach to modelling and simulation of single-walled carbon nanocones for sensing applications

In the present manuscript an approach to modelling and simulation of nanocones has been suggested for their use as sensing mediums. The vibrational behaviours of bridged and cantilever Single-Walled Carbon nanocones are modelled using three-dimensional elastic beams of carbon- carbon bonds and atomic masses. Also, the dynamic analysis of bridged and cantilever configurations of these nanocones with different disclination angles of 60°, 120°, 180°, and 240° is performed to evaluate the variation in stiffness with different configurations. The analysis also exhibits the effect of change in the length of nanocones on the vibrational frequencies. For the said purpose a mass equivalent to a carbon atom has been added at the nodes. It is observed that increasing side length of a Single-Walled Carbon nanocones with a constant apex angle results in a reduction in the fundamental frequency. It is also clear from the results that Single-Walled Carbon nanocones with larger apex angles exhibit smaller values of fundamental frequencies. The results suggest that smaller lengths of nanocones are better candidates for sensing applications as they exhibit substantial change in the fundamental frequencies. It can be stated that with higher number of bonds and atoms Single-Walled Carbon nanocones undergoes substantial bending with large declination angle which can be considered as an important finding.

Numerical analysis of fibers tensions in the Siro-spinning triangle using finite element method

Siro-spinning is a new kind of modified ring spinning method and achieved by feeding two rovings simultaneously, which have three spinning triangles including two primary spinning triangles and one final spinning triangle. In this paper, by using finite element method (FEM), the quantitative relationships between the fiber tension in the Siro-spinning triangle and some chosen important spinning parameters are investigated. The constituent fibers in the Siro-spinning triangle are considered as three-dimensional elastic beam elements with tensile, compressive, torsion, and bending capabilities. Then, the finite element model of Siro-spinning triangle is constructed under the assumption that the ends of all fibers gripped in the front roller nip distribute evenly, and the initial strain of the central fiber in each primary triangle is set as zero. Finally, the effects of some more important parameters of the Siro-spinning triangle, including the spinning yarn count, spinning tension, yarn twist, the distance between two feeding bell mouths on fiber tension distributions, are numerically examined and their quantitative relationships are discussed in detail. The accuracy of the proposed FEM model in calculating the fiber tension distribution of the Siro-spinning triangle has been validated by comparing it with our earlier theoretical models. Furthermore, the spinning experiments with different progress parameters were made, and the properties of spun yarns were evaluated and analyzed.

Discrete element modeling of brittle crack roughness in three dimensions

The roughness exponent is reported in numerical simulations with a three-dimensional elastic beam lattice. Two different types of disorder have been used to generate the breaking thresholds, i.e., distributions with a tail towards either strong or weak beams. Beyond the weak disorder regime a universal exponent of 0.59(1) is obtained. This is within the range 0.4-0.6 reported experimentally for small scale quasi-static fracture, as would be expected for media with a characteristic length scale.

Wave propagation in carbon nanotube intramolecular junctions: finite element calculations

The dispersion of longitudinal and transverse waves in (n,0)–(2n,0) intramolecular junctions (IMJs) are investigated using an atomistic finite element method (FEM). The transient responses of IMJs with different connection types subjected to harmonic incident wave were modelled using three-dimensional elastic beams of carbon bonds and point masses. The linkage between the force-field constants of molecular mechanics and input parameters of beam and mass elements was established through the molecular structural mechanics approach. The wave dispersion simulated by FEM shows good agreement with that of the non-local elastic model in a wide frequency range up to the terahertz region. It is shown that both the microstructure of conical part (connection part) and the coupling of longitudinal vibration and transverse vibration brought by the conicity play important roles in the dispersion of longitudinal and transverse wave in a single-walled IMJ. The amplitude decay of longitudinal wave depended on the distance propagating; the wavelength and the structure in connection part are examined. The results show that the dispersion of the decay of the wave amplitude in IMJ with less pentagon–heptagon defects has a better agreement with analytical results of macroscopic conical shell.

Research on mechanical properties of the Siro-spinning triangle using the Finite Element Method

Siro-spinning (two-strand yarn spinning) is a new kind of modified ring spinning method, which is achieved by feeding two rovings into the apron zone at a predetermined separation simultaneously. There are three spinning triangles, including two primary spinning triangles and one final spinning triangle, in Siro-spinning. Therefore, in this paper, the quantitative relationships between the mechanical performance of a Siro-spinning triangle and the spinning parameters are investigated by using the Finite Element Method. The finite element model of the Siro-spinning triangle is constructed under the assumption in which the constituent fibers are considered as three-dimensional elastic beam elements with tensile, compressive, torsion, and bending capabilities. Three different cases where the ends of all fibers, the initial strain of all fibers, and the angle between any two adjacent fibers gripped in the front roller nip distribute evenly are discussed. Meanwhile, in each case, three different cases where the initial strains of the shortest boundary fiber, the central fiber, and the virtual fiber on the direction of yarn spinning tension are set as zero are discussed respectively. Then, taking the spinning triangle in Ne40 (14.6 tex) cotton Sirospun yarn as an example, the fiber tension distribution and fiber torsion distribution in the corresponding Siro-spinning triangle with and without fiber buckling are numerical simulated. It is shown that the fiber tension distributions are influenced by the setting of the fiber initial strain, while the magnitudes of fiber tension are not affected. Finally, Ne40 cotton ring yarns were spun on an EJM128K ring spinning machine, and the properties of spun yarns were evaluated and analyzed according to the simulation results.

AN EFFICIENT FINITE ELEMENT MODEL FOR ANALYSIS OF SINGLE WALLED BORON NITRIDE NANOTUBE-BASED RESONANT NANOMECHANICAL SENSORS

In this paper, the dynamics analysis of single walled boron nitride nanotubes (SWBNNT) as a resonant nanomechanical sensor by using the finite element method has been reported. Molecular structural mechanics-based finite element model (FEM) has been developed by using three-dimensional elastic beams and point masses, such that the proximity of the model to the actual atomic structure of nanotube is significantly retained. Different types of armchair layups of SWBNNTs are considered with cantilevered and bridged end constraints. By implementing the finite element simulation approach, the resonant frequency shift-based mass sensitivity analysis is performed for both types of end constraints for considered armchair form of the SWBNNTs with different aspect ratios. For both types of end constraint, continuum mechanics-based analytical formulations, considering effective wall thickness of nanotubes are used to validate the present FEM-based simulation approach. The intermediate landing position of the added mass is analyzed, considering variations in resonant frequency shifts of the different fundamental modes of vibrations for both types of end constraints. The FEM-based simulation results for both types of end constraints found in good agreement with the continuum mechanics-based analytical results for the aspect ratio of range of 9–15. The mass sensitivity limit of 10-1 zg is achieved for SWBNNT-based resonant nanomechanical sensors. The resonant frequency shift for higher-order fundamental vibrational modes become stable as the attached mass moves away from the fixed ends for particular magnitude of attached mass. The present finite element-based approach is found to be effectual in terms of dealing different atomic structures, boundary conditions and consideration of added mass to analyze the dynamic behavior of the SWBNNT-based resonant nanomechanical sensors.

Graphene in Edge-Carboxylated Graphite by Ball Milling and Analyses Using Finite Element Method

Edge-carboxylated graphite (ECG) was produced by grinding pristine graphite in a planetary ball-mill machine. Transmission electron microscope was used to confirm the layers of graphene in ECG. The elemental analyses showed that the oxygen contents are different between ECG samples. The vibrational analysis of single- and five-layered graphene was conducted using finite element method within ANSYS. The vibrational behaviors of cantilevered and fixed graphene with one or five layers were modeled using three-dimensional elastic beams of carbon bonds and point masses. The dynamic analysis was conducted using nonlinear elastic elements within LS-DYNA. The natural frequencies, strain and kinetic energy of the beam elements were calculated considering the van der Waals forces between the carbon atoms in the hexagonal lattice. The natural frequencies, strain and kinetic energy of the graphene sheets were estimated based on the geometrical type and the layered sheets with boundary conditions. In the dynamic analysis, the change in displacement over time appears larger along the x- and y-axes than along the z-axis, and the value of the displacement vector sum appears larger in the five-layer graphene than in the single-layer graphene.

Vibrational and dynamic analysis of C60 and C30 fullerenes using FEM

Vibrational analysis of C60 and C30 fullerenes was performed using a finite element method (FEM). The vibrational behaviors of 10ea C60 and C30 fullerenes with 600ea and 300ea for each atomic carbon, respectively, were modeled using three-dimensional elastic beams of carbon bonds and point masses. Furthermore, dynamic analysis of fullerenes was performed using the nonlinear elastic elements. The natural frequencies, strain and kinetic energy were calculated by considering the van der Waals force between the carbon atoms in the hexagonal and pentagonal lattice. The natural frequencies strain and kinetic energy of fullerenes were estimated depending on the geometric fullerene type with boundary conditions. The natural frequencies of the 10ea C60 fullerenes increased significantly at higher modes of vibration. In the dynamic analysis, the change in displacement over time occurs more significantly along the z-axis than the x-, y-axis, and the value of a displacement vector sum is somewhat larger in the C30 than in the C60 fullerenes.

Nonlinear Modeling of the Dynamical Behavior of the Three-Dimensional Elastic Beam

AbstractThe paper outlines a dynamic model of the nonlinear elastic beam. The investigated model in this paper is based on a linear model and considers additional relevant geometrical nonlinear couplings. The developed model considers terms up to the 3rd order. Furthermore, complex couplings between the guided motion of the beam in combination with external forces and the geometrical nonlinear relations are considered. A finite element method is used for discretization. The complex behavior is shown using known benchmark as well as with new complex simulation examples. Simulations of the flexible beam are used to show the coupling effects between the rotating motion including external effects and the axial, transverse deformations with geometrical nonlinear terms.

Atomistic finite element model for axial buckling and vibration analysis of single-layered graphene sheets

In this article, an atomistic model is developed to study the buckling and vibration characteristics of single-layered graphene sheets (SLGSs). By treating SLGSs as space–frame structures, in which the discrete nature of graphene sheets is preserved, they are modeled using three-dimensional elastic beam elements for the bonds. The elastic moduli of the beam elements are determined via a linkage between molecular mechanics and structural mechanics. Based on this model, the critical compressive forces and fundamental natural frequencies of single-layered graphene sheets with different boundary conditions and geometries are obtained and then compared. It is indicated that the compressive buckling force decreases when the graphene sheet aspect ratio increases. At low aspect ratios, the increase of aspect ratios will result in a significant decrease in the critical buckling load. It is also indicated that increasing aspect ratio at a given side length results in the convergence of buckling envelops associated with armchair and zigzag graphene sheets. The influence of boundary conditions will be studied for different geometries. It will be shown that the influence of boundary conditions is not significant for sufficiently large SLGSs.

Modal analysis of carbon nanotubes and nanocones using FEM

Modal analysis of single-walled carbon nanotubes (SWCNTs) and nanocones (SWCNCs) was performed using a finite element method (FEM) with ANSYS. The vibrational behaviors of fixed beam and cantilever SWCNTs with different section types of a circle and an ellipse were modeled using three-dimensional elastic beams of carbon bonds and point masses. Also, the vibrational behaviors of fixed beam and cantilever SWCNCs with different disclination angles of 120°, 180°, and 240° were modeled using the same method. The beam element natural frequencies were calculated by considering the mechanical characteristics of the covalent bonds between the carbon atoms in the hexagonal lattice. Each mass element of the carbon atoms was assigned as a point mass at the nodes of the FEM elements. The natural frequencies of zigzag and armchair SWCNTs and SWCNCs were also computed. There were some differences between the findings obtained in this study and the molecular structural mechanics data available in the literature. The natural frequencies of SWCNCs were estimated depending on the geometrical type and disclination angle with different boundary conditions. The natural frequencies of the SWCNCs with disclination angles of 120°, 180°, and 240° increased significantly at higher modes of vibration.

Three-point bending tests-Part I: Mathematical study and asymptotic analysis

The goal of this work is to study the static behaviour of a three-dimensional elastic beam when is subjected to a three-point bending test. In the first part, under suitable compatibility conditions on the applied forces and on the geometry of the beam, we will prove the existence of a unique solution for the associated contact elastic problem; these conditions of compatibility on the data come from the absence of a Dirichlet condition on the beam boundary. In the second part, we will study the asymptotic behaviour of this problem; in particular, we will deduce the one-dimensional models associated with the displacement components, and we will give the existence and uniqueness of solution for them. Moreover, we will give an expression for the normal axial stress in the beam which is related to the modulus of rupture of brittle materials. In the final part of the work, we will deal with the regularity of the solution for the bending problem and we will prove some properties of the coincidence set. Copyright © 2011 John Wiley & Sons, Ltd.