Two-dimensional Finite Element Model Research Articles

Finite element analysis on the propagation characteristics of laser-generated surface acoustic wave in V-groove weld

Thick-walled structures, such as marine engineering and rail transportation, are widely used in modern society. V-groove welding is a common welding method in thick structures. At the same time, the V-groove weld is also the area of a thick-walled structure in which defects are most easily formed. Laser-generated surface acoustic waves are a promising non-destructive testing method in most fields. This study examined the propagation characteristics of laser-generated surface acoustic waves in a V-groove weld. A two-dimensional finite element model with Q345 steel was constructed. A thermoelastic mechanism was adopted to generate the wave. The temperature and displacement fields were analyzed in detail. The results showed that wave transmission, reflection, and mode conversion are generated with an R wave at the junction, and the dispersion phenomenon of the R wave occurred in the welded area.

Prediction of long-term differential track settlement in a transition zone using an iterative approach

A methodology for the simulation of long-term differential track settlement, the development of voided sleepers leading to a redistribution of rail seat loads, and the evolving irregularity in vertical track geometry at a transition between two track forms, is presented. For a prescribed traffic load, the accumulated settlement is predicted using an iterative approach. It is based on a time-domain model of vertical dynamic vehicle–track interaction to calculate the contact forces between sleepers and ballast in the short-term. These are used in an empirical model to determine the long-term settlement of the ballast/subgrade below each sleeper. Gravity loads and state-dependent track conditions are accounted for, including a prescribed variation of non-linear stiffness of the supporting foundation along the track model. In parallel, a two-dimensional (2D) non-linear finite element model of layered soil is verified versus field measurements and used to determine the support stiffness of each sleeper in the track model. The methodology is applied to a transition zone between a ballasted track and a slab track that is subjected to heavy haul traffic. Analyses of the influence of higher axle loads and the implementation of under sleeper pads on sleeper settlement are demonstrated.

Homogenization modeling and numerical simulation of piezolaminated lattice sandwich structures with viscoelastic material

Lattice sandwich structures have the advantage of high strength-to-weight and stiffness-to-weight ratios. The laminated structures filled with viscoelastic materials have active and passive damping properties and have great potential for applications in aerospace engineering. To overcome numerical modeling challenges, the paper first proposes a homogenization approach for periodic lattice core filled with viscoelastic materials using periodic boundary conditions. Based on the homogenized elastic and viscoelastic material parameters, a two-dimensional finite element modeling method based on the zig-zag hypothesis is proposed for piezolaminated lattice sandwich structures, where continuous interlayer shear stresses are satisfied due to independent shear strains in each layer. The homogenization approach is applied to corrugated and honeycomb core structures for obtaining orthotropic elastic and viscoelastic material parameters. Additionally, the two-dimensional finite element modeling method is implemented to the simulation of piezolaminated sandwich structures filled with viscoelastic materials.

Study on the electric resistance method in crack depth measurements

Obtaining geometric parameters, especially depth, and describing the morphological characteristics of cracks are of great significance to control engineering disasters and accidents caused by cracks. The electric resistance method is based on the principle of differences in electrical properties between cracks and soil, which could be used to measure the single crack depth at project sites. There exists an Rmin value corresponding to a specific electrode distance d value at each Rf-d value obtained by laboratory experiments. Furthermore, a two-dimensional finite element model of soil with a single crack is established to carry out numerical simulation analysis considering the crack width W, crack depth D and complex crack conditions. The results reveal dynamic variation rules of soil resistance after crack development, and for each Rf-d value, the electrode distance d value corresponding to the Rmin value is approximately equal to the crack depth D. In the range of the electric field, the offset and rotation of the crack have little effect, while the measurement results have a strong dependence on relocation movement. The regulation gives guidance to the inversion analysis of crack depth D at project sites and has been applied in crack depth measurements of an expansive soil slope. The electric resistance method as a proposed integrated approach is of great significance and brings new perspectives into the study of crack depth measurements for field applications.

Factors influencing fault-propagation folding in the Kuqa Depression: Insights from geomechanical models

Understanding the rock mass deformation and strain state is critical to a range of endeavors. Geomechanical modeling is an excellent approach simulating the formation processes of faulting and folding, which can reproduce the geometry of fold structures and track strain and stress through the whole deformation process. In this study, five series of two-dimensional (2D) elastic-plastic finite element models were built to investigate the influences of shortening distance, ramp cutoff angle, interlayer slip, fault friction, fault number and fault slice width on structural styles and strain distribution patterns during fault-propagation folding in the Kuqa Depression of Tarim Basin. The results indicate that, i) All above mentioned factors can influence the structural style and strain distribution of fault-propagation fold (FPF) to varying degrees. Fault friction, interlayer slip and fault slice width are the most important parameters influencing the deformation geometry and strain patterns of FPF; ii) There are critical values for fault friction coefficient and shortening distance to create a secondary fold besides the FPF; iii) A “step pattern” occurs both in the forelimb and backlimb of the FPF when fault slice width reaches a certain high value; iv) Structural position in the FPF controls volumetric changes. The evolution of FPF can be divided into two stages: layer parallel shortening and volume loss, and folding; v) The steep forelimb region of FPF develops more natural fractures, which may serve as a favorable location for potential reservoirs in the Kuqa Depression. The results are also expected to provide clues for the exploration and development of oil and gas in regions with similar geological conditions.

Two-dimensional study of the inclusions of skirt sand and deep cement piles to improve the load‒displacement behavior of circular foundations on soft clay soil

The bearing capacity of clayey soils is low, and the induced settlements play an important role in estimating the stability of structures built on these weak soils. Therefore, these clayey soils need improved mechanical strength. In this study, a two-dimensional finite element model was used to improve the bearing capacity and settlement of soft clay soil by employing skirt sand piles, and the results were compared with reinforced cement piles. Skirt sand piles consisting of thick sand cores and closed tubes placed under a circular shallow foundation with a steel plate of suitable dimensions, as well as reinforced cement piles of different lengths and in nondrained situations were studied. These calculations were carried out using PLAXIS 2D software, and a series of finite element analyses were performed. The Mohr‒Coulomb and hardening soil models were used to model the fine-grained and granular soils, respectively. A linear elastic model was used to simulate the circular plate and skirt components. Previous experimental studies were used to validate the numerical model. The experimental test and the 2D axisymmetric model agree well. According to the assumptions, the efficiency of skirt sand piles is superior to that of deep cement piles. In addition, increasing the length of SSP skirt sand piles has a significantly greater effect on improving the bearing capacity than increasing the length of deep cement piles. As a consequence, the failure modes of piles with skirt sand were determined. It was found that the failure mode when skirt sand piles were tied into clayey soils occurred in the underlying sandy soil layer as a general shear failure.

Edge-driven asthenospheric convection beneath the North China Craton: A numerical study

The North China Craton (NCC) is one of the most tectonically active cratons in the world today. Its scattered late Cenozoic volcanism, as well as small-scale low-velocity anomalies in the upper mantle, suggests a major role of asthenospheric upwellings in the NCC tectonism. Such asthenospheric upwellings, however, cannot be readily explained by the Indo-Asian continental collision or subduction of the Pacific plate, two of the plate boundary processes previously suggested for causing the Cenozoic tectomagmatism in the NCC. Here we propose that edge-driven convection, resulting from the large changes of lithospheric thickness under the NCC, is likely a major cause of the observed upper mantle structure and late Cenozoic volcanism in the NCC. Using a two-dimensional thermo-mechanical finite element model, we found that the contrast of lithospheric thickness between the Eastern and Western blocks of the NCC can cause significant edge-driven small-scale convection, especially if the viscosity of the asthenosphere is reduced by melts and volatiles from dehydration and decarbonization of the stagnant slabs of the subducted Pacific plate under the NCC.

LEGO-Inspired and Digitally-Fabricated steel reinforcement cage for Ultra-High performance concrete (UHPC) beams

Reinforced concrete is one of the most used structural configurations in the world, but the production of reinforcement cage is a labor-intensive, time-consuming and strenuous task. This study develops a new LEGO-inspired reinforcement cage system that is digitally fabricated through waterjet cutting, which can be assembled in three steps. The experimental program tests two ultra-high performance concrete (UHPC) beams reinforced by this LEGO-cage system, one with smooth surface and one with deformed ribs. Results show that including deformed ribs slightly increase the post-cracking stiffness of the beams while both beams exhibit a post-yielding plateau and a displacement ductility ratio over 8. An existing UHPC flexural model predicts the flexural strength (both yield and maximum strength) of the LEGO-cage-reinforced beams with errors below 4%. A two-dimensional finite element model, which is originally developed for rebar-reinforced UHPC, is found to well predict the load–displacement responses of LEGO-reinforced UHPC beams. A cost analysis reveals that adopting this new cage system can reduce the production cost and manual labor time by over 17% and 86%, respectively.

Two-dimensional finite element modeling of long-term frost heave beneath chilled gas pipelines

Proper estimation of frost heave over the lifetime of a buried chilled gas pipeline is a key design concern. Previously conducted full-scale and centrifuge tests were continued for a limited period of time. Similarly, the numerical analyses with modeling of the coupled thermo-hydro-mechanical process of frost heave were limited to less than half of the design life of typical pipelines. Few studies estimated the long-term frost heave based on decoupled analyses where the heat transfer and frost heave were calculated separately, although both are interrelated processes. This study presents a two-dimensional coupled finite element (FE) modeling of frost heave under chilled gas pipelines buried in frost susceptible soil. The Konrad–Morgenstern segregation potential (SP) model is implemented in commercially available software using user subroutines. Simplified elastic-plastic models that recognize the key influencing factors, including temperature and volumetric ice fraction of frozen soil, are used for modeling the mechanical behaviour of soil. The present numerical approach can properly calculate the temperature gradient in the frozen fringe, which is essential in the SP model to define the volumetric expansion due to water migration to the frozen fringe. The FE calculated heave and frost front penetration are compared with the Calgary full-scale test results. The moisture content profiles obtained from FE simulation show a similar pattern as reported from a full-scale test. The challenges in modeling long-term heave resulting from continued ice accumulation in front of the final ice lens and potential warming of the leading part of the frozen bulb when the pipe moves further up are discussed.

The semi-automated development of plant cell wall finite element models

This study presents a methodology for a high-throughput digitization and quantification process of plant cell walls characterization, including the automated development of two-dimensional finite element models. Custom algorithms based on machine learning can also analyze the cellular microstructure for phenotypes such as cell size, cell wall curvature, and cell wall orientation. To demonstrate the utility of these models, a series of compound microscope images of both herbaceous and woody representatives were observed and processed. In addition, parametric analyses were performed on the resulting finite element models. Sensitivity analyses of the structural stiffness of the resulting tissue based on the cell wall elastic modulus and the cell wall thickness; demonstrated that the cell wall thickness has a three-fold larger impact of tissue stiffness than cell wall elastic modulus.

Thermal and Mechanical Properties of Plain Woven Ceramic Matrix Composites by the Imaged-Based Mesoscopic Model

The mesoscopic finite element model of ceramic matrix composites is developed by reconstructing computed tomography images. The relationship between microstructure and macroscopic properties and their dispersion are explored. Firstly, a three-dimensional reconstructed computed tomography model was carried out to calculate the orientation of the components. Secondly, the orientation and gray value of images were used to identify the basic structure of composites including fiber tows, matrix, and porosities. Finally, the two-dimensional finite element model was developed to analyze the macroscopic thermal and mechanical properties. The numerical results showed that: (1) the geometries and distributions of pores had a significant effect on the through-thickness modulus and thermal conductivity; (2) the stress and heat flow concentration area on the material surface usually occurred in narrow gaps between closely spaced longitudinal tows; (3) the elastic modulus and thermal conductivity were dispersive, and their distribution followed by two-parameter Weibull distribution.

Effect of pulse duty ratio on temperature rise induced by focused ultrasound combined with magnetic microbubbles

Development of acoustic/magnetic contrast agent microbubbles with various diagnostic and therapeutic functions has attracted more and more attention in medical ultrasound, biomedical engineering and clinical applications. Superparamagnetic iron oxide nanoparticles (SPIO) have unique magnetic characteristics and wonderful biocompatibility, so they can be used as MRI contrast agents to improve image contrast, spatial resolution and diagnostic accuracy. Our previous work shows that the multimodal diagnostic and therapeutic microbubble agents can be successfully constructed by embedding SPIO particles into the coating shell of conventional ultrasound contrast agent (UCA) microbubbles, which in turn changes the size distribution and shell properties of UCA microbubbles, thereby affecting their acoustic scattering, cavitation and thermal effects. However, previous studies only considered the influence factors such as acoustic pressure and microbubble concentration. The relevant investigation regarding the influence of ultrasound temporal characteristics on the dynamic response of magnetic microbubbles is still lacking. This work systematically measures the temperature enhancement effect of the SPIO-albumin microbubble solution flowing in the vascular gel phantom exposed to pulsed ultrasound with various temporal settings (e.g. duty cycle, PRF and single pulse length). Meanwhile, a two-dimensional finite element model is developed to simulate and verify the experimental observations. The results show that the increase of duty cycle of pulse signal should be the crucial factor affecting the temperature enhancement effect of flowing SPIO-albumin microbubble solution under the exposure to high-intensity focused ultrasound. The current results help us to better understand the influence of different acoustic setting parameters on the thermal effect of dual-modal magnetic UCA microbubbles, and provide useful guidance for ensuring the safety and effectiveness of the application of SPIO-albumin microbubbles in clinics.

A simulation method for the electromagnetic railgun based on equivalent circuit

As a typical electromagnetic launcher, electromagnetic railguns have attracted widespread attention for their broad military application prospects. It is known that skin effects occur during electromagnetic railgun launch. How to quickly and accurately simulate these skin effects is of importance for the application of electromagnetic launch technology. This paper proposes a static two-dimensional finite element model in series with one variable equivalent inductance and three resistances for simulating the dynamic electromagnetic railgun launch. Two skin effects are presented by changing equivalent inductance and resistances. For an electromagnetic railgun including two rails of length of 2 m and width of 0.3 m and square armature of 0.3 m long, after 4.23 ms under a pulse current of a peak of 1 MA, the simulation results based on this proposed static 2D model show that the armature can leave the rails with a velocity and acceleration increasing to 1,464 m/s and 614,876 m/s2, respectively. For an equivalent circuit connected in series, the equivalent inductance, AC resistance, velocity skin effect resistance, and back EMF resistance are 0.49 μH, 2.5 mΩ, 7.1 mΩ, and 4.44 mΩ, respectively, whereas the breech voltage can increase to 1.36 kV. The proposed method simplifies the meshing in the finite element model, saves computational cost, and is conducive to study electromagnetic railgun design and projectile magnetic field shielding. Key words: Electromagnetic railgun, equivalent inductance, equivalent resistance. Tables 1, Figs 7, Refs 10.

Does the model reflect the system? When two-dimensional biomechanics is not 'good enough'.

Models are mathematical representations of systems, processes or phenomena. In biomechanics, finite-element modelling (FEM) can be a powerful tool, allowing biologists to test form-function relationships in silico, replacing or extending results of in vivo experimentation. Although modelling simplifications and assumptions are necessary, as a minimum modelling requirement the results of the simplified model must reflect the biomechanics of the modelled system. In cases where the three-dimensional mechanics of a structure are important determinants of its performance, simplified two-dimensional modelling approaches are likely to produce inaccurate results. The vertebrate mandible is one among many three-dimensional anatomical structures routinely modelled using two-dimensional FE analysis. We thus compare the stress regimes of our published three-dimensional model of the chimpanzee mandible with a published two-dimensional model of the chimpanzee mandible and identify several fundamental differences. We then present a series of two-dimensional and three-dimensional FE modelling experiments that demonstrate how three key modelling parameters, (i) dimensionality, (ii) symmetric geometry, and (iii) constraints, affect deformation and strain regimes of the models. Our results confirm that, in the case of the primate mandible (at least), two-dimensional FEM fails to meet this minimum modelling requirement and should not be used to draw functional, ecological or evolutionary conclusions.

Numerical investigation on DE-strengthened-RC beams without steel shear reinforcement

This study presents a two-dimensional nonlinear finite element (FE) model for Deep Embedment (DE) strengthened reinforced concrete (RC) beams without existing steel shear links. The FE model was developed and validated against experimental results reported in published literature. The parametric study was thereafter conducted to examine important parameters influencing the strengthened behavior. The parameters were concrete compressive strength, beam width, beam size, and tension reinforcement ratio. The FE model accurately predicted experimental results with a mean predicted-to-experimental value of 1.04. The FE results showed that the percentage of shear strength provided by embedded steel bars was almost constant once both concrete strength and tension reinforcement ratio were increased. However, an increase in the beam width resulted in a decrease in the percentage of shear strength gain due to embedded steel bars. Shear stress at failure decreased once beam size was increased for both unstrengthened (control) and DE-strengthened beams. The percentage of shear strength provided by embedded steel bars decreased from 47.9% to 27.6% as effective depth was increased from 261.5 mm to 523 mm.

Deformation of Sandy Ground Induced by Tunneling of Super-Large-Diameter Shield—Influence of Buried Depth of Tunnel and Relative Density of Sand

The mechanical properties of sandy soil depend on both the confining pressure and the state of compactness. Therefore, both the buried depth of the tunnel and the relative density of the sand are key factors that affect the ground deformation induced by the tunneling of a super-large-diameter shield. In this study, the parameters of the SANISAND constitutive model are first calibrated based on triaxial test data for Foshan silty fine sand. Then, based on the actual project, a two-dimensional finite-element analysis model is established to investigate the ground deformation induced by the tunneling of a super-large-diameter shield. The width and maximum value of the settlement trough, the volume loss ratio, and the deformation characteristics of the soil are summarized and analyzed for 13 cases. The results show that as the ratio of the buried depth to the diameter and the relative density of sand increases, the anti-disturbance ability of the sand layer to the tunnel construction increases and the volume loss ratio of the stratum reduces correspondingly. The denser the sand and the smaller the confining pressure of the soil around the tunnel, the more significant the shear-induced expansion of the sand at the tunnel haunch; this expansion partially makes up the volume loss caused by the tunnel excavation and reduces the loss ratio of the stratum at the arch crown.

Nonlinear Fe Model for Shear Strengthening of Simply Supported RC Beams with FRP DE Bars

Deep embedment (DE) is emerging as a potential and effective shear strengthening approach for existing reinforced concrete (RC) structures. A two-dimensional nonlinear finite element (NLFE) model for simply supported RC T-beams strengthened in shear with embedded carbon fibre reinforced polymer (CFRP) and steel bars is presented in this study. VecTor2, version 4.2, was used to create a two-dimensional NLFE model. To validate the nonlinear FE models, three sets of six simply supported RC T-beams from Breveglieri et al. (2015) are employedEach set consists of two beams with vertical and inclined (45) DE bars. Set one strengthens the beams with steel DE bars without vertical steel stirrups in the shear span. In the shear span, the beams of Sets two and three are reinforced with CFRP DE bars with vertical steel stirrups @180 mm c/c and @300 mm c/c, respectively. The above-mentioned NLFE model is validated by comparing experimental and predicted results for failure load, deflection, and failure mode. For both experimental and simulated beams, the fracture pattern is diagonal, and the failure mode is shear failure. The overall mean predicted/experimental loads at failure and deflection at failure ratios are 1.09 and 1.00, respectively, with corresponding standard deviations of 0.03 and 0.04. Following the validation of the proposed NLFE model's correctness, numerical parametric tests are conducted to determine the influence of concrete compressive strength and effective depth of RC T-beams on shear capacity of simply supported RC T-beams. The parametric analysis findings reveal that enhancing the cylinder compressive strength increases the predicted failure load while increasing the effective beam depth decreases it

The study of mixed mode fatigue crack growth mechanism of 25CrNiMo compact tensile specimens by experiment and finite element simulation

Fatigue cracking is the most common failure mode that endangers the safety and service life of parts. Initial manufacturing flaws are a critical factor affecting the growth of fatigue cracks. Currently, mixed-mode crack growth research frequently applies a simplistic two-dimensional finite element model, which cannot adequately represent the crack growth mechanism. An improved finite element method is proposed in this paper to overcome this drawback. Fatigue fracture propagation investigations on 25CrNiMo compact tensile specimens are conducted in this study, and the crack propagation rate is calculated using the Paris formula. Moreover, the special element modeling method and second-order Runge-Kutta integration method are utilized to perform finite element calculations on the 3D model. The results are highly consistent with the experimental test results. The propagation mechanism of cracks with varied initial inclination angles is explored depending on the finite element method. The relationship between the stress intensity measures KI, KII, and KIII is discovered to be competitive. The results have significant application value for the crack growth path prediction and crack life in parts with initial flaws.

Seismic fragility analysis for subway station considering varying ground motion ensembles

The seismic fragility analysis involves employing an ensemble of ground motion records to establish the seismic performance. This paper investigates the effect of number of ground motion records in the considered ensemble on the calculated post-earthquake failure probability of subway structure. A two-dimensional (2D) finite element model was established considering the soil-subway station underground structure interaction. The cloud and incremental dynamical analysis (IDA) methods are employed to compute the seismic demand of the structure and the seismic fragility curves considering different ensembles of ground motion records. The results revealed that the number of records have a significant influence on the structure seismic fragility analysis in both cloud and IDA methods. It is suggested that the optimal ensemble size should comprise 300 ground motion records in the cloud-based seismic fragility analysis, and 24 ground motion records in the IDA method. The results also showed that the failure probability of structure predicted by the cloud method is greater than that predicted by the IDA method. These findings provide practical guidance for the performance-based seismic design of underground structures.

Numerical Simulation of Grounding Characteristics and Temperature Field of Mine Tires under Multiple Working Conditions

Mine tires are an essential and expensive component of heavy mining machinery. This study explored the grounding characteristics and temperature field distribution of mining tires during driving as well as the relationships between the maximum temperature and tire inflation pressure, load, and speed. Two-dimensional and three-dimensional finite element models of mine tires were established. Steady-state rolling simulation analysis was conducted based on inflation and static load simulations. Temperature field simulation analysis was conducted with the tire section as a research object. The accuracy of the finite element model was verified. Analysis results demonstrated that the grounding contact area decreased with an increase in charging pressure and increased with an increase in load. With an increase in inflation pressure, the maximum normal grounding stress increased in the middle part of the tread and decreased near the shoulder. The maximum normal grounding stress continuously deviated in the shoulder direction with an increase in load. Temperature field analysis indicated that the tire had the maximum temperature at the binder position, where the first belt layer was connected to the second belt layer, which corresponds to the maximum stress position in the steady-state rolling simulations. Tire temperature increased with driving speed. The maximum temperature increased with an increase in tire deflection, whereas the deflection decreased with an increase in inflation pressure and increased with an increase in load. Speed had the greatest influence on the maximum temperature, followed by load, with inflation pressure having the smallest influence. The results of this research can be used to improve the service life of mine tires to improve productivity and reduce costs.