Dynamic Finite Element Method Research Articles

Construction of multi-component finite element model to predict biomechanical behaviour of breasts during running and quantification of the stiffness impact of internal structure.

This study aims to investigate the biomechanical behaviour and the stiffness impact of the breast internal components during running. To achieve this, a novel nonlinear multi-component dynamic finite element method (FEM) has been established, which uses experimental data obtained via 4D scanning technology and a motion capture system. The data are used to construct a geometric model that comprises the rigid body, layers of soft tissues, skin, pectoralis major muscle, fat, ligaments and glandular tissues. The traditional point-to-point method has a relative mean absolute error of less than 7.92% while the latest surface-to-surface method has an average Euclidean distance (d) of 7.05mm, validating the simulated results. After simulating the motion of the different components of the breasts, the displacement analysis confirms that when the motion reaches the moment of largest displacement, the displacement of the breast components is proportional to their distance from the chest wall. A biomechanical analysis indicates that the stress sustained by the breast components in ascending order is the glandular tissues, pectoralis major muscle, adipose tissues, and ligaments. The ligaments provide the primary support during motion, followed by the pectoralis major muscle. In addition, specific stress points of the breast components are identified. The stiffness impact experiment indicates that compared with ligaments, the change of glandular tissue stiffness had a slightly more obvious effect on the breast surface. The findings serve as a valuable reference for the medical field and sports bra industry to enhance breast protection during motion.

Dynamic large strain formulation for nematic liquid crystal elastomers

AbstractLiquid crystal elastomers (LCEs) are a class of materials which exhibit an anisotropic behavior in their nematic state due to the main orientation of their rod-like molecules called mesogens. The reorientation of mesogens leads to the well-known actuation properties of LCEs, i.e. exceptionally large deformations as a consequence of particular external stimuli, such as temperature increase. Another key feature of nematic LCEs is the capability to undergo deformation by constant stresses while being stretched in a direction perpendicular to the orientation of mesogens. During this plateau stage, the mesogens rotate towards the stretching direction. Such characteristic is defined as semisoft elastic response of nematic LCEs. We aim at modeling the semisoft behavior in a dynamic finite element method based on a variational-based mixed finite element formulation. The reorientation process of the rigid mesogens relative to the continuum rotation is introduced by micropolar drilling degrees of freedom. Responsible for the above-mentioned characteristics is an appropriate free energy function. Starting from an isothermal free energy function based on the small strain theory, we aim to widen it into the framework of large strains by identifying tensor invariants. In this work, we analyze the isothermal influence of the tensor invariants on the mechanical response of the finite element formulation and show that its space-time discretization preserves mechanical balance laws in the discrete setting.

Dynamic propagation of moving cracks in brittle materials by field-enriched finite element method

We propose a field-enriched finite element model to simulate the dynamic growth of moving cracks in brittle solids. The paper introduces the dynamic model and verifies its accuracy by analyzing dynamic stress intensity factors during the propagation of a mode-I moving crack. We also simulate crack bifurcation using a specific criterion. Our numerical method successfully reproduces experiments, including the Kalthoff-Winkler experiment, three-point bending test under impact load, and compact compression specimen (CCS) experiment. Finally, we investigate how the location of a circular hole influences the propagation paths of a pre-existing straight crack using a numerical model including both the hole and the crack (COSSCC). Several numerical examples demonstrate the ability of dynamic field-enriched finite element method in simulating dynamic moving cracks.

Dimension-Reduction Spectral Representation of Soil Spatial Variability and Its Application in the Efficient Reliability Analysis of Seismic Response in Tunnels

Reliability analysis of tunnels considering soil spatial variability was traditionally carried out using Monte Carlo simulations, which are computationally expensive. This study proposes a dimension-reduction spectral representation method (SRM) for simulating parameter stochastic fields to capture uncertainties in soil properties, which can be coupled with the probability density evolution method (PDEM). Additionally, the PDEM is employed to conduct seismic reliability assessments of tunnels in a more efficient manner. By integrating a non-intrusive dynamic random finite element method (FEM), this study explores the horizontal drift angle and vertical relative settlement of tunnel dynamic response under different coefficient of variations (COVs) and horizontal autocorrelation lengths of elastic modulus (E). Results show the changes in COVs have more pronounced effects on the mean and standard deviation of horizontal drift angle and vertical relative settlement of tunnel than alterations in horizontal autocorrelation lengths. A limit state pertaining to the horizontal drift angle and vertical relative settlement is established through the use of a probability density function (PDF) and cumulative distribution function (CDF). The results suggest that the combination of soil spatial variability and PDEM can serve as an effective approach for practical tunnel design.

Non-bracket oblique traction-hoisting construction strategy for cable-truss structures

This study describes the non-bracket oblique traction-hoisting construction strategy for cable-truss structures, which is to assemble the upper and lower radial cables, hoop cables, sling cables, and compression rods without stress at a low altitude, then hoist the cable-strut system to a high altitude by oblique traction of the upper radial cables through the jack fixed on the upper radial anchorage nodes, and finally actively tension the lower radial cables to achieve the designed shape and prestress level of the entire structure. This strategy assembles at a low altitude, requires simple operations, results in high tensioning efficiency, and does not require brackets, which could guarantee both quality and quantity in terms of completing the construction of cable-truss structures. The semilune-shaped canopy of Yueqing Stadium is constructed using this strategy. The construction simulation and disturbance stability analyses of the structure in the traction-hoisting state and prestress tensioning state are conducted using a nonlinear dynamic finite element method. In the traction-hoisting stage, the deformation changes sharply, and the hoop cables and upper radial cables make up the primary bearing substructure, while the lower radial cables are in a suspended hanging state. In the forming process, the forces of the radial and hoop cables increase gradually, and the structure finally reaches the designed state. For cable-trusses with crossed upper and lower radial cables, the additional stabilizing tooling ropes should be tied at the top of the middle rods to ensure geometric stability because they are susceptible to excessive out-of-plane displacement or even overturning, which is the least desirable at the beginning of traction hoisting.

Evaluation of stability of fixation using conventional miniplate osteosynthesis in comminuted and non-comminuted Le Fort I, II, III fractures – A dynamic finite element analysis

Purpose: The purpose of the present study was to evaluate and compare the stability of fixation using conventional miniplate osteosynthesis in comminuted and non-comminuted Le Fort I, II, and III fractures in open and closed jaw movements under masticatory loading conditions.Materials and Methods: About 23 dimensional models of comminuted and non-comminuted Le Fort I, II, and II with traditional miniplate fixation were simulated virtually using a CT scan of the patient and analyzed using ANSYS Workbench 2020 R1 software. The dynamic finite element method was applied by the simulation of the forces of the muscles of mastication upon the fractured midface. The von Mises stress was analyzed and collated for each model; thereby, the stability of conventional miniplate fixation was interpreted.Results: The von Mises stress over the regions of fixation were compared and the tabulated data was interpreted. Considerable von Mises stress was generated on the bone and deformation over the hardware was noted on the pyriform rim in the Le Fort I model, infraorbital rim in the Le Fort II model, and frontonasal region in the Le Fort III model in the closing phase of jaw movement.Conclusion: The findings implicated that the biomechanical stability of conventional miniplate osteosynthesis is insufficient to secure the midface fractured bone under masticatory load.

Comparison of Hexcore and Poly-Hexcore computational meshes in the aspect of air flow modeling based on the actual geometry of mining excavations

Discrete models are used in industry for many applications. In one of the most frequently used Finite Element Method (FEM) for Computational Fluid Dynamics (CFD) calculations, discrete models may be two-dimensional or three-dimensional. 2D models are used as a simplification to achieve satisfied results in the shortest computational time. 3D models, on the other hand, are used for more complex calculations. These models constitute a representation of real-world objects that have been appropriately simplified to make the calculations accurate and correct. The calculation time of a 3D model is significantly longer compared to a 2D model. For this reason, to reduce the calculation time, different types of simplifications and various types of discrete model meshes are used. In this paper, the authors made a comparison of two computational meshing technologies: Hexcore and Poly-Hexcore in the aspect of airflow modeling in mining excavations using CFD. The geometry considered in this case came from real-world excavations captured by laser scanning in the Gertruda Slant, Zloty Stok. Point cloud data was processed through feature extraction, which was subsequently utilized to create structured models of mining excavations. The results of the simulations show that taking into account such a diverse and complicated geometry and its significant lengths, reaching tens of kilometers, better results are obtained with the use of Poly-Hexcore mesh. This type of mesh allows simulations to be performed with similar accuracy in a shorter computation time. Utilizing a more modern type of mesh makes work more dynamic, which is of particular importance when conducting numerical simulations of air distribution in large and complex computational domains.

Direct spatio-temporal stress field determination combining full-field deformation measurements and explicit finite element method: Concept verification

High strain rate loading of materials with spatially heterogeneous properties produces non-homogeneous and transient stress-strain states. Such stress-strain states are atypical of classical split Hopkinson pressure bar (SHPB) analysis that assumes homogeneous deformation and dynamic force equilibrium. To determine spatio-temporal stress fields in heterogeneous materials, a novel concept combining digital image correlation (DIC) full-field deformation measurements and explicit dynamic finite element method (EFEM) is described in this paper. The concept utilizes measured boundary forces and DIC measurements including both displacements and accelerations as input. The measured input is used to calculate internal forces, and hence the stress fields, within each continuum finite element by solving the governing equations of motion using the framework of EFEM. The DIC+EFEM concept procedure is verified using simulated synthetic data considering one-dimensional stress wave propagation in a bar. The reconstructed axial stress fields match identically with the exact EFEM solution for both homogeneous and heterogeneous materials that are elastic or elastic-plastic. The influence of DIC measurement noise on the reconstructed stresses is also studied.

A study on mechanical properties of 1H-type crystalline nickel ditelluride

We used the molecular dynamic finite element method with Stillinger-Weber potential to study the mechanical behavior of monolayer 1H-type nickel ditelluride (1H-NiTe2) sheets under uniaxial tension. As the size of the pristine 1H-NiTe2 sheet increases, the Young’s modulus in the armchair direction increases by 6.2 %, while that in the zigzag one decreases by 6.0 %. Both tend to be size-independent in larger sheets and approach the same value at around 54 N/m. The ultimate stress in the armchair direction remains almost unchanged but that in the zigzag one reduces by about 9.5 % as the size inclines. Besides the influence of size, our results show that single vacancy defects strongly affect the ultimate stress and strain while having no effect on Young’s modulus and Poisson’s ratio. When a Te atom is missing at the sheet’s center, the ultimate stress in the armchair direction is reduced by 11.7 %, while a decrease of 16.0 % is caused by a Ni atom vacancy

Tensile Stress Reduction and Strain Concentration of Epoxy Resin Caused by Heterogeneity: A Multiscale Approach Combining Molecular Dynamics Simulation and Finite Element Method.

In this study, we investigated the effect of heterogeneity on the mechanical properties of epoxy resin by combining coarse-grained molecular dynamics (CG-MD) and finite element method (FEM) simulations. To evaluate the heterogeneity effect in the uniaxial elongation, heterogeneous and homogeneous FEM models of micrometer-scale cubic epoxy resin were constructed. For the heterogeneous FEM model, parameters of nanometer-scale elements were determined by CG-MD simulations, where nanometer-scale blocks have different cross-linked structures. For the homogeneous FEM model, the averaged parameters were used for all elements. The calculated stress-strain (S-S) curves of the heterogeneous model exhibit similar tensile stress values when compared to the experimental data, whereas the homogeneous model yields notably higher values. Moreover, a clear strain concentration associated with the formation of the shear band-like structure was observed in the heterogeneous model and not in the homogeneous model.

Comparative study of shell element formulations as NLFE parameters to forecast structural crashworthiness

Abstract This work made a comparison of the effects of selected element formulations (EFs) through nonlinear finite element analysis (NLFEA) and physical configurations in scenario design, particularly target locations. The combined results help in quantifying structural performance, focusing on crashworthiness criteria. The analysis involves nonlinear dynamic finite element methods, using an explicit approach applied to an idealized system. This system models ship-to-ship collisions, specifically the interaction between Ro and Ro and cargo reefer vessels, with one striking the other. Summarizing initial NLFEA results reveals that the chosen EF significantly influences the crashworthiness criteria. Notably, differences in formulations lead to different calculation times. The Belytschko–Tsay (BT) EF is the quickest, followed by the Belytschko–Leviathan (BL), with around a 36% difference. Conversely, formulations such as the Hughes–Liu involve much longer processing times, more than twice that of BT. To address the potential impact of shear locking and hourglassing on calculation accuracy during impact, the fully integrated (FI) version of the EF is used. It mitigates these undesired events. For formulations with the same approach, the FI BT formulation suppresses hourglassing effectively, unlike others that show orthogonal hourglassing increments. To ensure reliability, rules were set to assess hourglassing. The criterion is that the ratio of hourglass energy to internal energy should be ≤10%. All formulations meet this criterion and are suitable as geometric models in NLFEA. Regarding reliability and processing time, analyzing the computation time offers insights. Based on calculations, BL is the fastest, followed by Belytschko–Wong–Chiang, while the FI BT formulation takes more time for the same collision case.

Effect of expanded polyethylene (EPE) foam packing net design on the mechanical damage resistance of strawberry fruit during transportation

Fresh strawberries are susceptible to mechanical damage during transportation, leading to high loss rates. This problem can be addressed through the development of appropriate packaging designs. The initial collision velocity of the fruit and the external packaging would also influence the mechanical damage resistance of the expanded polyethylene (EPE) foam packing net. The dynamic finite element method (FEM) was used to investigate the effect of EPE foam packing net on resisting mechanical damage to strawberry fruits. The results showed that the elastic modulus and diameter of the EPE foam packing net material, as well as the hole size of the net, were key factors affecting the maximum impact force and contact time of the collision process. The initial collision velocity of the fruit and the external packaging also influenced the mechanical damage resistance of the EPE foam packing net. Our results showed that the EPE foam packing net material should have a slightly smaller elastic modulus than that of the strawberry cortex tissue, and the hole size of the net should not be too large. Moreover, when the initial collision velocity and environmental temperature increased by 1 m·s−1 and 1 ℃, the collision damage volume of the fruit increased by 37.6433, and 6.4658 mm3, respectively. This study presents a numerical simulation method that evaluates the collision damage resistance of packed fresh fruit. The findings of this study can serve as a valuable guide for designing packaging solutions and optimizing transportation environments for the long-distance transport of fresh fruit.

Folding, stowage, and deployment of composite thin-walled lenticular tubes

Composite thin-walled lenticular tube (CTLT) is a lightweight foldable and deployable structural material that enables large-scale deployable mechanisms for various space missions. A key step toward the structural design of CTLT is to understand its folding, stowage, and deployment behaviors. This work presents an integrated experimental and numerical investigation of the dynamic deployment behavior of CTLT that wraps around a central hub, with emphasis on the effect of long-term storage. A two-meter-long CTLT prototype was manufactured, and a gravity compensation system was designed and built for the on-ground dynamic deployment experiments. The deployment experiments were performed on the CTLT prototype both before and after it had been stowed for extended storage periods. The results indicate that after being stowed for 6 and 10.5 months the CTLT is deployed slower and the deployment time increases by 8.2% and 15.0%, respectively. Furthermore, a high-fidelity numerical model was constructed using the explicit dynamic finite element method, where the CTLT was modeled as a deformable part and the folding/deployment mechanisms were modeled as rigid bodies to perform the folding, stowage, and deployment simulations. The long-term storage effect was accounted for in the numerical analyses with the use of a viscoelastic fiber-reinforced composite material model, and a good agreement has been achieved between the experimental and numerical results.

Numerical study on crushing damage and energy absorption of multi-cell glass fibre-reinforced composite panel: Application to the crash absorber design of tsunami lifeboat

Abstract During an evacuation, the tsunami lifeboat should be able to withstand the possible external loads that might be occurred, such as collisions, violent crashes, and capsizing events. Special structural reinforcement and improvement, such as a crash absorber, are attached to prevent damage due to the impact load. Therefore, this article focuses on the crushing behaviour of the tsunami lifeboat crash absorber made of the multi-cell glass fibre-reinforced composite panel. The effect of the cross-section geometry design of the cell on the damage mechanism and energy absorption behaviour was investigated. The explicit dynamic finite element method was used to identify the multi-cell configuration’s crashworthiness performance. Experimental studies such as tensile and three-point bending tests were conducted to define the material properties and validation of the FE model. The simulation results showed that the explicit dynamic finite element method has effectively estimated the crash absorber crushing damage. The circular cross-section has shown the most significant crash absorption capability compared to the others, namely the honeycomb, the square, and the triangular cell. Furthermore, the 4CSM laminate type has revealed a lower energy absorption than the 4WRC45 and 4WRC laminates. Otherwise, the study exhibits that the cross-sectional geometry and the laminate type significantly influence the crash absorber performance for improving the tsunami lifeboat crashworthiness.

Modelling fracture of rock masses around tunnels and slopes by field-enriched finite element method

The dynamic response and mechanical behaviors of rock masses are mainly governed by discontinuities. The field-enriched finite element method is proposed to study the mechanism of crack propagation in rock mass, and the multiaxial perfectly matched layer (M-PML) is introduced to absorb the reflected wave due to the existence of artificial boundary. The fundamental theory and numerical implementation of the proposed numerical method are described in detail. By comparing two numerical models, namely one with the absorbing boundary and the other without the absorbing boundary, the necessity of considering an absorbing boundary and the ability to verify the absorption effect of the absorbing boundary on the reflected waves are demonstrated. In addition, a numerical example of underground tunnel is established to investigate the influence of dynamic waves from the hole in underground space on the crack propagation in adjacent surrounding rocks of the tunnel. Finally, a numerical model of rock slope with cracks is considered, and the influence of the combination forms of rock bridge inclination angle and fissure spacing on the crack evolution patterns of rock slope with fissures under dynamic load is studied. The research in this paper demonstrates that the dynamic field-enriched finite element method with M-PML absorbing boundary can effectively simulate the dynamic behaviors of fractured rock masses under dynamic load.

Numerical validation of analytical solutions for tunnels and their applicability evaluation index

Analytical solutions are widely adopted in the preliminary seismic design of tunnels, which gives credit to their quick response and convenience to provide the internal forces and displacements of tunnels. In the first part of this paper, five analytical solutions are extensively verified by comparing them with the reference solution which obtained by the dynamic finite element method. Some suggestions are given for their application in design according to the prediction results. The analytical solutions contain some assumptions, which may not be applicable to all possible scenarios. Therefore, the application scope of analytical solution in practical engineering is limited, and this application scope has not been discussed at present. In the second part of this paper, the applicability evaluation index is established for the first time to evaluate the critical condition for the application of analytical solution. Then, the applicability function is obtained by fitting the relationships between the critical condition and the flexibility ratios, which can be convenient to calculate the critical condition for the application of analytical solutions in engineering. Finally, the applicability of analytical solution in some engineering projects is correctly evaluated based on the proposed applicability evaluation index and applicability function.

Laser shock dynamic compaction of aluminum–copper (Al–Cu) composite metal powder

Laser impact dynamic compaction experiments and 2D multi-particle finite element method (MPFEM) simulations were carried out on aluminum–copper (Al–Cu) binary-based composite powders. Al–Cu compacts with densities of about 95% were successfully prepared at the maximum laser energy of 1.8 J. Research trends indicate that higher power lasers could nearly achieve the theoretical densities. Analysis of the influence laws of laser energy and copper powder mass fraction on the densities of Al–Cu compacts was carried out, and the effects of microstructure and microhardness of Al–Cu compacts on their mechanical properties were investigated, as well as the stresses and velocities in the dynamic compaction process of Al–Cu composite powders were analyzed. The results showed that the relative densities of composite powder compacts of Al-5 wt%Cu gradually exceeded those of Al-10 wt%Cu and Al-15 wt%Cu with the increase of laser energy. In laser impact dynamic compaction the mechanism of inter-particle joining was solid-state press-welding, and the increase in the hardness of the Al–Cu compacts could be attributed to the inherent hardness of the hard particles. The upper particles have a localized maximum velocity of more than 300 m/s, which met the explosion welding velocity, thus localized cold welding occurred and contributed to the inter-particle connection.

Accurate Modeling and Control System Simulation of Bearingless Brushless DC Motor

Background: Precise modeling and control system design are the basis of highperformance control of dual-winding bearingless brushless DC motors (BL-BLDCM), and the existing research is relatively few. Objective: This paper takes 12-slot/tooth 4-pole BL-BLDCM as the research object, establishes a set of a detailed mathematical model, and designs the control system of BL-BLDCM. Methods: Firstly, the structure of BL-BLDCM and the radial suspension force generation principle were introduced. Secondly, a set of an accurate mathematical model of BL-BLDCM was established which was finally verified by static and dynamic finite element method (FEM), the motor body model and control system were built by Matlab/Simulink software, and the simulation analysis of control performance was completed. Results: The established mathematical model is correct. The BL-BLDCM can generate stable electromagnetic torque and radial magnetic suspension force, and the control system has strong ability of resisting load torque disturbance and radial force load disturbance. Conclusion: It has certain reference significance for the accurate modeling and control system design of later BL-BLDCM.

Dynamic simulation of a motor longitudinally mounted on a centralized electric drive systems for pure electric vehicles under torque ripple and transmission error excitations.

The dynamic characteristics of electric drive systems are crucial in electric vehicles. Based on the dynamic finite element method and previous studies, this study proposes and analyzes a new mathematical model for a motor longitudinally mounted on a centralized electric drive system of a pure electric vehicle. First, we analyze the largest torque ripple of a fractional slot concentrated winding inner-mounted permanent magnet synchronous motor designed for commercial electric vehicles. This torque ripple is identified as one of the excitations influencing the dynamic performance of the electric drive system. Second, a new dynamic mathematical model for the electric drive system is established. Third, we investigate the linear vibration responses of the system subject to torque ripple and transmission error. Finally, the relationships between critical motor parameters and dynamic mesh force are revealed. The results demonstrate that the proposed theoretical method can effectively determine the dynamic characteristics of the electric drive system, thereby providing valuable theoretical guidance for the design and optimization of the motor and electric drive system.

Seismic damage characteristics of high arch dams under oblique incidence of SV waves

This study investigates the seismic damage characteristics of high arch dams considering the oblique incidence of seismic waves. Based on the dynamic implicit finite element method, a viscous-spring artificial boundary is applied to consider radiation damping of the infinite foundation, the seismic wave input is converted into an equivalent nodal force of the artificial boundary, and the equivalent nodal loads of the wave input under oblique incidence of the SV wave is deduced. Taking JP Ⅰ arch dam as an example, combined with the concrete damaged plasticity (CDP) model, the nonlinear dynamic response of the dam under 25° oblique incidence of the SV wave is conducted considering the geometrical nonlinearity of contraction joints and the dynamic mechanical properties of concrete materials. Based on the incremental dynamic analysis (IDA) method, the relative displacement and transverse joint opening are selected as the damage measures for fragility analysis of the arch dam. According to the damage distribution from the analysis of a large number of seismic time-history responses, the damage levels of the arch dam are classified. Three limit states of slight damage, moderate damage and severe damage are proposed for the arch dam. The average responses of the 10 earthquakes are considered as the limit values to quantitatively describe the damage of the arch dam. By fitting the results of incremental dynamic analysis, the seismic probabilistic demand model and seismic fragility curves for the two damage measures to predict the probability of the arch dam reaching damage levels under different seismic actions have been established. The fragility curve shows that the probability of severe damage is almost zero under the maximum design earthquake (PGA = 0.1971 g) and less than 5% under the maximum credible earthquake (PGA = 0.2299 g). It is concluded that JP Ⅰ arch dam has a high degree of safety redundancy and fully satisfies the “two levels” design requirements.