Three-dimensional Nonlinear Model Research Articles

Magnetic reconnection in three-dimensional quasi-helical pinches

This paper deals with the phenomenology of magnetic reconnection during reversed-field pinch helical self-organization. Numerical results obtained by solving a three-dimensional nonlinear visco-resistive fluid model to describe the hot current-carrying plasma are summarized. Magnetic reconnection manifests itself during the plasma dynamics, interrupting the persistence of quasi-helical states. The main signatures of magnetic reconnection in reversed-field pinches are discussed: partial conversion of magnetic into kinetic energy, current sheet formation, steepening of plasma current profiles, locking of the angular phases between different Fourier components of the magnetic field. The latter is recognized as the three-dimensional trigger of the reconnection events. Then the paper deals with the temporal scales of the process: low visco-resistive dissipation in the model, corresponding to high plasma current in the experiments, results in longer characteristic time between reconnection events. Furthermore, it is confirmed that the scaling of the reconnection rate is compatible with a modified Sweet–Parker model. A discussion of magnetic reconnection during the 2D simplified tokamak internal kink mode evolution, showing the development of secondary tearing instabilities, is presented and the similarities with RFP evolution are highlighted.

Rapid postearthquake safety evaluation of buildings using sparse acceleration measurements

After a seismic event, buildings need to be inspected to confirm their safety prior to reoccupation. As such, the rapid evaluation of the condition of individual buildings is important for minimizing disruption to lives and business. However, traditional manual inspection by experts is laborious and time-consuming. Structural health monitoring provides the potential to accelerate the required evaluation. This article proposes a cost-effective approach for rapid safety evaluation of buildings after seismic events using sparse acceleration measurements. First, a damage-sensitive feature is defined that can be used to infer the condition of buildings. Herein, the maximum interstory drift angle is proposed as a reliable damage index to classify the safety of buildings after seismic events. A convolutional neural network is then employed to uncover the complex relationship between the damage-sensitive features and the building condition. A five-story steel building is considered to validate the proposed approach. First, a three-dimensional nonlinear model of the building is created. To generate the required training data, a simplified nonlinear model is developed, along with a corresponding linear model, as use of the three-dimensional model is too computationally expensive. The training data for the convolutional neural network incorporates uncertainties in both the analysis model and the ground motion. Initial evaluation is conducted using the simplified nonlinear model, while final validation of the proposed approach is performed using the results of the three-dimensional nonlinear analysis model subjected to historical earthquakes. The results demonstrate the ability of the proposed approach to accommodate differences between the in-situ structure and the analysis model, as well as the efficacy of this approach for rapid postearthquake safety evaluation of buildings.

Seismic performance of an existing RC structure retrofitted with buckling restrained braces

The use of buckling restrained braces (BRBs) represents one of the best solutions for retrofitting or upgrading the numerous existing reinforced concrete framed buildings in areas with a high seismic hazard. This study investigates the effectiveness of BRBs for the seismic retrofit of reinforced concrete (RC) buildings with masonry infills. For this purpose, an advanced non-linear three-dimensional model of an existing building in L'Aquila is developed in OpenSees, by accounting for the effect of infill walls through an equivalent strut approach, and by using a recently developed hysteretic model for the BRBs. The seismic performance of the building before and after the retrofit with BRBs is evaluated by performing both non-linear static analyses and incremental dynamic analyses under a set of real ground motion records along the weak direction of the frame. Seismic demand hazard curves are built for different response parameters before and after the retrofit, by accounting for and by disregarding the contribution of the infill walls. The study results shed light on the effect of the BRBs and of the infill walls on the seismic performance of the various components of the system, and on the effectiveness of the retrofit with BRBs for a real case study.

Experimental and numerical research on the nonlinear creep response of polymeric composites under humid environments

The aim of this work is to study the nonlinear creep response of polymeric composites under humid environments. A three-dimensional orthotropic nonlinear creep constitutive model that considers the moisture effect is derived by introducing the moisture shift factor into Schapery’s nonlinear equation. Hygrothermal-mechanical coupling moisture absorption tests, as well as static mechanical property tests and short-term tensile creep-recovery tests with different moisture contents were performed to obtain the hygroscopic parameters and the moisture and stress dependent nonlinear creep parameters. A fully coupled numerical prediction model was developed in Abaqus with a user-defined material subroutine (UMAT) and user-defined field variable subroutine (USDFLD) to simulate the coupled diffusion-nonlinear creep behaviour. Good agreement was observed between the numerical and experimental results.

Modeling of damage behavior of carbon fiber reinforced plastic composites interference bolting with sleeve

Interference-fit is getting increasing attentions in the aerospace field owing to its excellent enhancement on the sealing and fatigue life of composites assembly, but the severe damage around the hole caused by installation is still a huge challenge. In this paper, a three-dimensional anisotropic non-linear progressive damage model based on continuum damage mechanics was developed to reveal the damage mechanism of carbon fiber reinforced plastic (CFRP) composites interference bolting with sleeve. The proposed model adopted strain-based failure criteria and non-linear damage evolution law to predict damage initiation and propagation of composite laminates. A cohesive model taking into account the traction-separation constitutive response was employed to capture the delamination behavior between the composite plies. The elastoplastic model was utilized to characterize the sleeve's deformation behavior. Numerical simulations of different installation modes are performed and compared with experiments. The inserting load, damage modes and damage positions predicted by the proposed model agree well with the experimental results. Moreover, it is also verified that the interference installation of sleeved fasteners can remarkably reduce the intra-laminar damage and avoid the inter-laminar delamination of composite laminates compared to the conventional bolt.

The effect of follower load on the range of motion, facet joint force, and intradiscal pressure of the cervical spine: a finite element study.

Follower loads are used to simulate physiological compressive loads on the human spine. These compressive loads represent the load-carrying capacity of the human cervical spine and play an important role in maintaining its stability. However, under different follower loads the biomechanical response of the cervical spine is unknown. Therefore, the aim of this study was to determine the effect of follower load on the biomechanics of the cervical spine. A three-dimensional nonlinear finite element (FE) model of the cervical spine (C3-C7) was developed and validated. Using this FE model, we evaluated the effect of different follower loads (0 N, 50 N, 100 N, and 150 N) on the range of motion (ROM), facet joint forces (FJFs), and intradiscal pressure (IDP) in the cervical spine. In addition, a moment of 1 Nm was applied in three anatomical planes (sagittal, coronal, and transverse planes) to simulate different postures. The results indicate that as follower load was increased, the ROM of the cervical spine in extension decreased (4.06°-0.95°), but increased in other postures (flexion 4.19°-6.04°, lateral bending 1.74-3.03°, axial rotation 2.64°-4.11°). Follower loads increased the FJF in all postures (0 N-52 N). In lateral bending (LB), FJFs were only generated in the ipsilateral facet joints. In axial rotation (AR), there was large asymmetry in the FJF, which increased as follower load increased. The IDP of each segment increased nonlinearly with increasing follower load in all postures (0.01 MPa-1.23 MPa). In summary, follower loads caused changes in motion and loading patterns in the cervical spine (C3-C7). Therefore, in common daily activities, we should pay attention to the muscle strength of the neck through exercise to adapt to the biomechanical changes in the cervical spine following an increase in follower load. Graphical Abstract Follower load is defined as the compressive load directed approximately along the axis of the spine. The purpose of this investigation was to determine the effect of the follower compressive load on biomechanics of the cervical spine. To do so, a three-dimensional nonlinear FE model of the cervical spine (C3-C7) was built and validated. Using this FE model of the cervical spine, we evaluated the effect of different follower loads (0 N, 50 N, 100 N, 150 N) on range of motion, facet joint force, and IDP in the cervical spine. In this study, the follower load was applied to the finite element model by connector elements. At the same time, a moment of 1 Nm was applied in the three anatomical planes to simulate different postures.

Creep prediction of GFRP directors in a multiple launch rocket system under long-term stacking storage

During long-term stacking storage, creep deformation of polymeric composite directors used in multiple launch rocket systems can appear, which affects rocket launch. In this work, E-glass/epoxy 6509 composite laminates were prepared and 60/60 min creep/creep-recovery tests were carried out in the transverse and shear directions at different stress levels. Parameters of the Schapery’s nonlinear viscoelastic equation were obtained based on the test data. Then, a three-dimensional nonlinear viscoelastic constitutive model based on Schapery’s equation was implemented in the standard finite element code UMAT and a finite element model was developed to predict the creep deformation of the composite directors after 15 years of stacking storage. The effect of creep deformation on rocket launching was also studied. The results show that the residual deformation of the directors is a saddle-shaped distribution in three-dimensional space, the maximum residual deformation is 0.24 mm, and the minimum residual deformation is 0.22 mm. The creep deformation of the director causes a significant increase in the contact-collision force during launching, resulting in a decrease in the rocket run-off track velocity.

Estimation of wire strength based on residual stresses induced during wire electric discharge machining

Frequent breakages of wire electrode during wire electric discharge machining (WEDM) adversely affect the productivity and surface quality of the finished products. Uncontrolled thermal loads and large thermal stresses generated during the discharge phenomenon reduce the strength of the wire which eventually leads to wire rupture. Thermal residual stresses retained in the wire can cause the formation of microcracks, voids and pits which increases the probability of wire rupture. Thus, it is essential to predict and prevent the wire breakage phenomenon for better machining productivity. This paper presents an approach to estimate the wire safety index based on thermal residual stresses that generate on the wire electrode by using a finite element method based model. A three-dimensional nonlinear transient thermo-mechanical model for a molybdenum wire used during WEDM has been developed to compute the temperature and the induced stresses. The influence of the wire velocity has been incorporated. The computational ability of the developed model has been verified by conducting systematic experiments. The experimental values of the residual stresses were obtained by using X-ray diffraction (XRD) technique. The stresses produced on the wire were observed to reach values beyond the yield stress (600 MPa) of the molybdenum wire at certain process conditions, which causes the reduction in strength of the wire. The wire safety index was evaluated by calculating a ratio (X) between the maximum value of residual stress induced and the yield stress of the wire. Formation of microcracks on the wire surface was considered as an indicator of wire breakage to estimate the threshold value of wire strength beyond which the wire is considered to be unsafe for machining.

Nonlinear random seismic analysis of 3D high-speed railway track-bridge system based on OpenSEES

A new nonlinear track-bridge random model was established based on OpenSEES, of which the random seismic responses is systematically studied by using probability density evolution method (PDEM). First, a three-dimensional detail nonlinear random dynamic model of the track-bridge coupled system in high-speed railway is established considering the earthquake as the random excitation. The dynamic model is composed with the rail, CRTS II slab ballastless track, the simple supported bridges, bearing, pier and the pile foundation, from which the random dynamic equation of the random model is formulated. In order to evaluate the seismic performance of track structures from a random perspective, the random seismic responses of high-speed railway bridge under random seismic excitations are investigated and analyzed by using the PDEM. Eventually, the Newmark β integration method and the double edge difference method of TVD format are adopted to obtain the random responses involving the probability functions, which can be translated to get the mean value and the standard deviation of responses. Thus, the abundant probability information of seismic responses of the high-speed railway bridge under random seismic excitations can be obtained. The PDF and CDF of the sliding layer are obtained; thus, the failure probability and reliability of different damage grades of sliding layer are obtained. Discussions and significant conclusions on the random dynamic responses are presented.

Crack Cause in the High Slope of Chinese Ancient Copper Mine Relics: A Three-Dimensional Non-Linear Finite Difference Analysis

Preservation of world heritage and archaeological sites depends largely on better understanding of the soil and rock conditions and their alterations caused by natural and anthropogenic forces. This study took the Tonglushan Ancient Copper Mine (TACM), a key cultural relic site under the state protection in China, as an example to discuss that detailed field and numerical studies of rock mechanics can help understand the crack genesis of high slopes at the site, thus better protecting the relic site from damage. Several cracks occurred in the high slopes at TACM, thus in-situ investigations have been conducted to figure out the factors inducing the cracks. After that, a three-dimensional non-linear finite difference numerical model was applied to investigate the factors affecting the deformation and rupture of the high slopes at TACM. The numerical study revealed that certain mining activities in the copper mines around the TACM relic site could be responsible for the generation of cracks. Five typical mining and excavation plans have been simulated via numerical models; meanwhile rational deformation and failure criterions were determined, according to which, case-5, including eight horizontal tunnels sequentially excavated at different elevations, was found to be the most reasonable hypothesis to explain the generation of cracks and failure of slopes. Case-5 involved applying the SPSC (Sill Pillars Sublevel Caving) method to excavate the ore bodies located at the foot of the slopes and to subsequently backfill the empty chambers after the closure of mining activity. Finally, recommendations were given based on this study to remedy the generation of cracks and better preserve the TACM.

Numerical Investigation on Steel Square HSS Columns Strengthened with Polymer-mortar

This paper presents the results of finite element (FE) analysis of axially loaded square hollow structural steel (HSS) columns, strengthened with polymer-mortar materials. Three-dimensional nonlinear FE model of HSS slender columns were developed using thin-shell element, considering geometric and material nonlinearity. The polymer-mortar strengthening layer was incorporated using additional layers of the shell element. The FE model has been performed and then verified against experimental results obtained by the authors [1]. Good agreement was observed between FE analysis and experimental results. The model was then used in an extended parametric study to examine selected AISC square HSS columns with different cross-sectional geometries, slenderness ratios, thicknesses of mortar strengthening layer, overall geometric imperfections, and level of residual stresses. The effectiveness of polymer-mortar in increasing the column’s axial strength is observed. The study also demonstrated that polymer-mortar strengthening materials is more effective for higher slenderness ratios. An equivalent steel thickness is also accounted for the mortar strengthened HSS columns to discuss the effectiveness of polymer-mortar strengthening system. The polymer-mortar strengthening system is more effective for HSS columns with higher levels of out-of-straightness. Level of residual stress has a slight effect on the gain in the column’s axial strength strengthened with polymer-mortar.

Analysis of circulation near the coast of Western Crimea and the region of Sevastopol with assimilation of temperature and salinity observations

Hydrophysical fields which are continuous in time and space are reconstructed in the coastal zone of the Black Sea (near the coast of Western Crimea and the region of Sevastopol) by a three-dimensional nonlinear hydrodynamic model with assimilation of observational data of the 2007 hydrological survey. A sequential optimal interpolation of temperature and salinity observations is used as the assimilation procedure. We use real atmospheric forcing and a high resolution (a horizontal grid of ~1.6×1.6 km and 31 vertical layers from 1 m to 1300 m). Mesoscale features of the currents are obtained, and coastal upwelling in the Kalamitsky Bay is reconstructed and registered in satellite observations.

Modal properties variation and collapse assessment of masonry arch bridges under scour action

This paper investigates the problem of flood-induced scour on masonry arch bridges through the analysis of a real case study, Rubbianello Bridge. This is a multi-span masonry arch bridge located in Central Italy, which suffered the collapse of two of the seven spans due to foundation scour during a severe flood in December 2013. The study has a twofold aim: to evaluate with a numerical model the level of scour which led to the bridge failure in 2013 and the corresponding collapse mechanism, and to assess the sensitivity of the bridge’s modal properties (vibration frequencies and mode shapes) to different levels of scour. An accurate nonlinear three-dimensional model of the bridge is developed, whose elastic properties are calibrated to match the results of dynamic identification tests performed via Operational Modal Analysis (OMA) on the remaining portion of the bridge. A numerical simulation of the effects of the scour hole progression is also performed on the full bridge, according to recently proposed techniques. The study results provide useful insights on both the cause of collapse of the bridge and the suitability of OMA for bridge scour monitoring.

Mechanical Parameter Inversion in Sandstone Diversion Tunnel and Stability Analysis during Operation Period

A large number of experimental studies show that the mechanical parameters of deep buried surrounding rock show significant attenuation characteristics with the increase of strain from the rheological acceleration stage to the attenuation stage. However, the existing numerical models all take mechanical parameters as constants when describing the rheological behavior of surrounding rocks, which can only be applied to the stability analysis of the shallowly buried tunnel. Therefore, this work proceeding from the actual project, improved the sandstone rheological constitutive model and optimized the algorithm of parameter inversion, and put forward a long-term stability analysis model that can accurately reflect the rheological characteristics of surrounding rocks under the complex geological condition including high stress induced by great depth and high seepage pressure. In the process, a three-dimensional nonlinear rheological damage model was established based on Burgers rheological model by introducing damage factors into the derivation of the sandstone rheological constitutive model to accurately describe the rheological behaviors of the deep buried tunnel. And BP (Back Propagation) neural network optimized by the multi-descendant genetic algorithm is used to invert the mechanical parameters in the model, which improves the efficiency and precision of parameter inversion. Finally, the rheological equation was written by using parametric programming language and incorporated into the general finite element software ANSYS to simulate the rheological behavior of the tunnel rock mass at runtime. The results of the model analysis are in good agreement with the monitoring data in the later stage. The research results can provide a reference for the stability analysis of similar projects.

Three-Dimensional Propagation Simulation and Parameter Analysis of Rock Joint with Displacement Discontinuity Method

Displacement discontinuities method (DDM) is convenient for and efficient at dealing with discontinuity problems such as fracture and fault. However, the known method of ease iteration is not available for nonlinear joint surface problems. This paper introduces Barton-Bandis nonlinear joint deformation failure criterion, figures out the propagation model of joint through the maximum energy release rate theory of rock fracture mechanics, and establishes three-dimensional nonlinear displacement discontinuity model for rock joint. This paper gives results of the joint propagation pattern and its distribution law under tension and compression with different parameters and side pressure coefficients via compiled program.

Investigation of a nonlinear three-dimensional diffusion model of a porous medium

We study a general three-dimensional nonlinear diffusion model of porous medium with non-stationary source or absorption. For the model, admitting the widest group Lie of the transformations we found some invariant solutions of rank 1. These include the following solutions: the generalizations of “a layered circular pie”, “a layered plane pie”, a generalization of “a layered spiral pie”, “a layered conical pie”, a solution with a radial distribution of the pressure, “a layered spherical pie”. The obtained results can be used to study the processes associated with a underground fluid or gas flow, with water filtration, with the engineering surveys in the construction of the buildings, and also with shale oil and gas production.

Prediction of biomechanical behavior of lumbar vertebrae using a novel semi-rigid stabilization device.

The work investigates the effect of proposed novel semi-rigid stabilization device on lumbar segment L2-L3 so as to preserve motion at vertebral level. Here, the biomechanical behavior of intact spine with three instrumented spinal models (semi-rigid stabilization device, rigid implant and dynamic stabilization system NFlex) have been compared under the motion conditions of flexion, extension, bending and twist. Three-dimensional non-linear finite models of intact spine, semi-rigid stabilization device, rigid implant and dynamic stabilization system NFlex were developed in the present study. All the four models were subjected to a combined load of 400 N in axial compression along with 2, 4, 6, 8 and 10 N m as bending moment individually. Dynamic stabilization system NFlex shows the maximum variation in motion and reflects range of motion as 89.7% during lateral bending, 53.4% in flexion, 34.6% in twist and 28.0% in extension with respect to intact spine. However, semi-rigid stabilization device and rigid implant shows the range of motion of 60%, 48.7%, 32% and 21.8% and 60%, 32.3%, 22.3% and 21.7% of intact, respectively, during bending, flexion, twist and extension. Finite element simulation results reveal that semi-rigid stabilization device shows comparatively lower values than dynamic stabilization system NFlex and higher as compared to rigid implant for measured intradiscal pressure and von Mises strain at intervertebral disc-23.

Finite Element Based-Analysis for Pre and Post Lumbar Fusion of Adult Degenerative Scoliosis Patients

Study DesignPre-post cohort finite elements (FE). ObjectivesTo investigate the effect of adjacent load transfer pre and post fusion surgery of lumbar scoliotic spines using FE models. Summary of Background DataAdult degenerative scoliosis (ADS) results from age-related changes, leading to segmental instability, deformity, and stenosis. FE study is capable of capturing the biomechanical parameters internal to the bones and connective soft tissues of the spine, which is difficult to measure by experimental approaches. Literature that describes the underlying mechanisms responsible for spinal fusion in scoliosis patients is limited, and FE study with larger subject sample size should be conducted. MethodsTwenty three-dimensional nonlinear FE models of the lumbosacral spine were created from pre (Cobb angle: 28.1° ± 10.5°) and post scoliosis surgery in vivo CT scans. During surgery, pedicle screws and rods were implanted at lumbar and sacral levels. A compressive load and six different moments (flexion, extension, right lateral bending, left lateral bending, right axial rotation, left axial rotation) were applied to the top level of each model. Outcome measures were range of motion (RoM), intradiscal pressure (IDP), and facet joint forces (FJF). Spinal fusion did alter the mechanical function of the scoliotic spine. ResultsScoliotic spine presented abnormal and asymmetrical kinetic and kinematic behavior. RoM: At the adjacent level, spinal fusion surgery produced a statically significantly increased left and right later bending intersegmental rotation (p < .006) in comparison to presurgical scoliosis models. At the fused level, spinal fusion surgery produced a statically significantly reduced intersegmental rotation in all the loading conditions (p = .001) in comparison to presurgical scoliosis models. IDP: At the fused level, spinal fusion surgery produced a much lower IDP in all of the loading conditions (p = .001). FJF: At the adjacent level, spinal fusion surgery produced a considerably larger left lateral rotation FJF (p = .001) in comparison to presurgical scoliosis models. At the fused level, spinal fusion surgery produced considerably lower FJF in all the loading conditions (p = .001) in comparison to presurgical scoliosis models. ConclusionsThis study was the first to investigate the effect of adjacent load transfer before and after fusion surgery using in vivo CT scans of 10 scoliotic spines. A posterior fusion has only a minor effect on mechanical behavior and a large effect on pressure and forces at the adjacent level. As expected, a large effect in the kinematics and kinetics was found at the fused level. Level of EvidenceLevel 3.

Effect of pounding on nonlinear seismic response of torsionally coupled steel structures resting on flexible soil

The effects of earthquake induced pounding on the nonlinear response of torsionally coupled buildings resting on flexible soil are investigated in the current study. Three steel moment-resisting frame buildings with the same symmetric plan having 4, 7 and 10 stories are considered. Three-dimensional nonlinear models with different eccentricity ratios are created. The soil-structure interaction phenomenon is taken into account using the Winkler beam on nonlinear springs. The pair of adjacent structures spaced at different clear distances resting on a flexible soil are analyzed under a consistent set of ground motion records and the effects of seismic pounding, torsional eccentricity and soil-structure interaction are studied by comparison of nonlinear dynamic responses of buildings. The results show that the peripheral frames experienced the most critical conditions during earthquake-induced pounding and the combined effect of soil-structure interaction, torsional eccentricity and pounding results in the most severe nonlinear responses of the studied buildings in certain cases.

Dynamic response of soil–pile–structure system subjected to lateral spreading: shaking table test and parallel finite element simulation

This paper investigates the dynamic response of soil–pile–structure interaction (SPSI) system behind a quay wall in liquefiable soil and laterally spreading ground through both large-scale shaking table test and parallel finite element (FE) simulation. A three-dimensional (3D) nonlinear FE model is developed to simulate the target SPSI system using the parallel modeling technique with high computational efficiency. This FE model of the SPSI system is validated by the shaking table test results. The validated FE model is firstly used to further explore the dynamic behavior of the SPSI system with details on the global responses of the SPSI system and the local responses. Secondly, the validated FE model is used for global sensitivity analysis (GSA) to fully assess the effects of uncertain parameters on the interested dynamic responses of the SPSI system. The experimental and numerical investigations show that liquefaction-induced lateral spreading significantly affects the movement of the clay crust at the landside and the internal forces in piles behind the quay wall. GSA results show that the relative importance of system parameters depends on the dynamic responses of interest, while the interaction effects among system parameters on dynamic responses are not evident.