Nonlinear Numerical Simulations Research Articles

Nonlinear numerical simulation of dynamic response of pile site and pile foundation under earthquake

AbstractTo study the influence of the nonlinear connection of pile and soil on the dynamic response characteristics of the pile foundation, this article proposes to study the dynamic response of the bridge pile foundation to the slope by combining the centrifugal shaking table test and OPENSEES open source finite element program. This article introduces the pressure-dependent multiyield surface model based on confining pressure. Through the inverse calculation of the similarity ratio of the centrifuge model test, the OPENSEES two-dimensional nonlinear finite element model of the pile group in the slope section can be established. The centrifuge shaking table test is to input the preset seismic wave horizontally at the bottom of the model box. The form of seismic wave is El Centro wave verification of two-dimensional finite element model of the pile group in slope section under earthquake. The reliability of the model is verified by comparing the test and calculated values of dynamic response (residual horizontal displacement and final bending moment) of the pile body under five different peak acceleration seismic wave loading conditions. In the dynamic response experiment of slope pile foundation, in the embedded part below the bedrock surface, the residual horizontal displacement of each pile body is zero. Constrained by the cap beam and tie beam, the displacement of the free section of the pile group at these two positions is basically the same. Through comprehensive analysis, the displacement of P1 and P2 piles is basically the same. The calculated value of the final bending moment of P1 and P2 piles shows the same change trend as the test value, and the test value is slightly larger than the calculated value. The relative errors of the maximum final bending moment of P1 pile under each loading condition are 7.4, 7.8, 12.6, 3.9, and 9.6%, respectively, and the relative errors of P2 pile are 4.6, 3.6, 12.5, 13.6, and 11.5%, respectively. The analysis relative error is caused by the elastic element used in the calculation of the pile body, which is different from the mechanical behavior of the simulated pile body material in the test. Dynamic response of slope site according to the existing centrifuge test results can be seen that the deformation at the slope shoulder of slope site is the most obvious under the earthquake. The inclined interface of soft and hard rock and soil layer will aggravate the dynamic response of the overburden layer on the slope, weakening its ability of seismic energy consumption.

Shape optimisation of stainless steel corrugated cylindrical shells for additive manufacturing

Axially compressed circular cylindrical shells with large diameter-to-thickness ratios are highly susceptible to local buckling, and their load-carrying capacities are known to be very sensitive to initial geometric imperfections. Hence, severe knock-down factors on their theoretical buckling loads are typically prescribed in design specifications, which greatly impair their structural efficiency. With the aim of enhancing load-bearing resistance and reducing sensitivity to imperfections, the shape optimisation and assessment of compressed free-form wavy cylindrical shells, the realisation of which is now viable through additive manufacturing, are the subject of the present study. The adopted optimisation framework employs the Particle Swarm Optimisation (PSO) algorithm, integrating computer-aided geometric design, nonlinear numerical simulations and imperfection sensitivity analyses. The structural performance of the optimised free-form wavy shells is analysed and compared to that of reference circular shells, as well as other types of non-circular shell profiles, including sinusoidally corrugated shells, Aster shells and stringer-stiffened shells. The optimised free-form wavy shell profiles are shown to exhibit increases in ultimate stress of up to 136% compared with the reference circular shell profiles; in general, greater benefits are achieved for more slender cross-sections. In future work, the proposed optimised shells will be manufactured in stainless steel by means of powder bed fusion (PBF), and their structural performance will be further verified through physical experiments.

Prediction of transverse stability of composite micro-curvature plates

This article is focused on the instability of marine composite micro-curvature plates subjected to transverse load, which is different from the axial loading case. The jump instability mechanism of orthogonal laminated plates has been analyzed, and transverse stability is predicted through the modified formula. Based on the classical elastic stability theory, suitable transverse stability analysis models for cylindrical and spherical shells are proposed. The instability load of the plate is predicted theoretically. The influential factors of the instability load are methodically analyzed based on an orthogonal experiment. Finally, according to the correlation analysis results of design variables, the calculation formula of the instability load is appropriately modified by considering the chord length of the plate. The obtained results show that the thickness has the most significant effect on the instability load, followed by the radius and the chord length. The instability load formula based on the elastic stability theory does not consider the chord length, which leads to low accurate results for the case of unclosed structures such as spherical crown plates. A comparison study confirms that the predicted results by the modified formula are generally closer to the experimentally observed data for the unclosed micro-curvature plate. In the present investigation, the load-bearing capacity of plates is evaluated in conjunction with the theory, nonlinear numerical simulation, and experimental research. Further, it can be applied to the theoretical prediction of the instability load for composite micro-curvature plates.

The nonlinear evolution of internal tides. Part 1: the superharmonic cascade

In non-uniform stratification, horizontally propagating internal waves with the vertical structure of a single mode self-interact to excite superharmonics. Baker & Sutherland (J. Fluid Mech., vol. 891, 2020, R1) showed that a vertical mode-1 parent wave of sufficiently small amplitude dominantly excites a vertical mode-1 superharmonic with double the horizontal wavenumber. Through theory, assuming a parent wave of sufficiently small amplitude, they showed that the superharmonics grew and decayed periodically due to the parent forcing frequency being off-resonant with the natural frequency of the superharmonic. Here, we extend this theory to allow for larger parent wave amplitudes and/or stronger resonant forcing, as would occur at lower latitudes, where the influence of background rotation is small. The resulting coupled system of nonlinear ordinary differential equations is shown to well predict the evolution of the internal tide as determined in fully nonlinear numerical simulations. With strong nonlinear forcing, successive superharmonics grow to non-negligible amplitudes in what we call the ‘superharmonic cascade’. The phase relationship between the superharmonics is such that when superimposed, the internal tide transforms into a solitary wave train, consistent with the predictions of well-established shallow-water models, particularly that of the Ostrovsky equation, which is an extension of the Korteweg–de Vries equation accounting for background rotation. This work thus gives new insight into internal solitary wave generation. The model equations have less restrictive assumptions than models based upon shallow-water theory, and because they are quickly solved, these provide a potentially powerful new tool to examine the nonlinear evolution of the internal tide.

Optimal control and nonlinear numerical simulation analysis of tunnel rock deformation parameters

Abstract In order to study the influence of nonlinear numerical simulation on the optimal control of the tunnel rock deformation parameters, the author proposes a numerical simulation study of the deformation characteristics of the layered rock tunnel, and determines the calculation model according to the thickness of the rock mass. The estimated thicknesses of the dolomite limestone surrounding the tunnel are 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, and 0.9 m. Select the vertical displacement to analyze as a result of the calculation. In order to study the influence of the structural slope on the tunnel stability, the thickness of the rock layer was 0.6 m, and the structural slopes of 5°, 15°, 30°, 45°, 60°, 75°, and 85° were used for simulation calculations. During on-site construction, focus on monitoring the tunnel section deformation before the construction of the secondary lining. Every 10–20 m and at the change of the surrounding rock, the observation section of the surrounding convergence and vault settlement shall be arranged, according to the observed deformation, the peripheral displacement rate and the vault subsidence rate are calculated. The results show that the vertical displacement of the top of the tunnel is generally in a “V” shape, that is, the maximum settlement in the tunnel; when the layer thickness is 0.3 m, the maximum vertical displacement of the rock layer is 7.2 mm, and the total settlement in the lining support tunnel is 8.23 mm. When the layer thickness is 0.9 m, the vertical displacement of the rock layer is 5.14 mm, and the total settlement in the lining support tunnel is 5.22 mm. When the layer thickness is from 0.9 to 0.3 m, the maximum vertical displacement of the rock layer increases by 140%, and the settlement at the vault increases by 158%. The focus of tunnel support at this time is the two sides of the lining structure and the vault with large vertical settlement. For the YK51 + 032 section, the phenomenon of first decreasing and then increasing is due to the sudden mud on the surrounding YK51 + 040, which causes the short-term deformation to increase. Only the ZK49 + 356 sections at the entrance of the spider has very good deformation due to the thin overlying stratum, and other sections are similar, which shows the reliability of the calculation results.

The nonlinear evolution of internal tides. Part 2. Lagrangian transport by periodic and modulated waves

We examine Lagrangian transport by a nonlinearly evolving vertical mode-1 internal tide in non-uniform stratification. In a companion paper (Sutherland & Dhaliwal, J. Fluid Mech., 2022, in press) it was shown that a parent internal tide can excite successive superharmonics that superimpose to form a solitary wave train. Despite this transformation, here we show that the collective forcing by the parent wave and superharmonics is effectively steady in time. Thus we derive relatively simple formulae for the Stokes drift and induced Eulerian flow associated with the waves under the assumption that the parent waves and superharmonics are long compared with the fluid depth. In all cases, the Stokes drift exhibits a mixed mode-1 and mode-2 vertical structure with the flow being in the waveward direction at the surface. If the background rotation is non-negligible, the vertical structure of the induced Eulerian flow is equal and opposite to that of the Stokes drift. This flow periodically increases and decreases at the inertial frequency with maximum magnitude twice that of the Stokes drift. When superimposed with the Stokes drift, the Lagrangian flow at the surface periodically changes from positive to negative over one inertial period. If the background rotation is zero, the induced Eulerian flow evolves non-negligibly in time and space for horizontally modulated waves: the depth below the surface of the positive Lagrangian flow becomes shallower ahead of the peak of the amplitude envelope and becomes deeper in the lee of the peak. These predictions are well-captured by fully nonlinear numerical simulations.

Observation of Axisymmetric Standard Magnetorotational Instability in the Laboratory.

We report the first direct evidence for the axisymmetric standard magnetorotational instability (SMRI) from a combined experimental and numerical study of a magnetized liquid-metal shear flow in a Taylor-Couette cell with independently rotating and electrically conducting end caps. When a uniform vertical magnetic field B_{i} is applied along the rotation axis, the measured radial magnetic field B_{r} on the inner cylinder increases linearly with a small magnetic Reynolds number Rm due to the magnetization of the residue Ekman circulation. Onset of the axisymmetric SMRI is identified from the nonlinear increase of B_{r} beyond a critical Rm in both experiments and nonlinear numerical simulations. The axisymmetric SMRI exists only at sufficiently large Rm and intermediate B_{i}, a feature consistent with theoretical predictions. Our simulations further show that the axisymmetric SMRI causes the velocity and magnetic fields to contribute an outward flux of axial angular momentum in the bulk region, just as it should in accretion disks.

Seismic failure behavior of masonry domes under strong ground motions

General stability and failure behaviors of masonry domes under static loads have been investigated extensively in literature. However, a few studies have been done on the seismic failure behavior of masonry domes under strong ground shaking. This study aims to investigate the seismic failure behaviors and failure angles of masonry domes with support system including drum and buttresses using advanced 3D nonlinear numerical simulations. Four types of masonry domes with thickness-to-span ratios t/R = 0.092, such as a dome with circular drum (Dome A), a dome with circular drum and buttress (Dome B), a dome with dodecagon drum (Dome C), a dome with dodecagon drum and buttress (Dome D), built on historical structures are selected. Three-dimensional solid finite element models of the selected masonry domes are created using isotropic continuum macro modelling technique with homogenized properties. The finite element models are utilized to simulate the seismic behaviors of the masonry domes under three different strong ground motion acceleration records matched according to the target response spectrum with a return period of 475 years in the Turkish Building Earthquake Code. The seismic failure behaviors of four masonry dome models are evaluated by comparing mode shapes, displacements, maximum principal stresses, damage propagation patterns and failure angles. It is determined that the average angle intervals of hoop tension failure regions of Dome A, Dome B, Dome C and Dome D models under strong ground motions vary between 39, 25, 35 and 26 degrees, respectively.

Research on Bending Performance of Concrete Sandwich Laminated Floor Slabs with Integrated Thermal and Sound Insulation

In this study, a full-scale test on the bending performance of concrete sandwich laminated floor slabs with integrated thermal and sound insulation was carried out, and the effects of different reinforcement ratios on the bending performance of concrete sandwich laminated floor slabs were investigated as well as the variation law of the failure modes, characteristic loads, load-mid span deflection, load-rebar strain curves, and anti-slip performance. The results indicate that the concrete sandwich laminated floor slabs present typical bending failure characteristics. According to bending failure characteristics, the damage process can be divided into three stages, i.e., elasticity, cracking, and failure. The bearing capacity significantly increases with the increase in reinforcement ratio. The normal service, yield, and ultimate loads of bearing capacity of the floor slabs with a larger reinforcement ratio increase by 54.55%, 52.94%, and 46.46%, respectively. Moreover, the mid-span deflection decreases significantly with the increase in reinforcement ratio, and the cracking expansion is also delayed. Before cracking, the prefabricated layer and laminated layer can realize load bearing together, and the floor slab is in a state of complete interaction. When the floor slabs reach the ultimate state, the superimposed surface produces a sliding effect, and the floor slab is in a state of partial interaction. The finite element analysis software ABAQUS (with the version number of ABAQUS 2020, the chief creator of David Hibbitt, and the sourced location of the United States) was used to perform nonlinear numerical simulation. The test results accord well with the simulation results, which verifies the correctness of the finite element model. Based on finite element simulation, the influence of post-cast concrete strength on the ultimate load can be ignored.

Scientific Model of Vocational Education Teaching Method in Differential Nonlinearity

Abstract This paper uses nonlinear differential equations to establish a relationship model between enrollment, education, and employment in vocational education. In this paper, the local stability of the vocational education system is analyzed utilizing nonlinear differential theory and numerical simulation. At the same time, we carried out a numerical simulation of the system’s dynamic behavior. Through numerical simulation research, it is found that the model has peculiar nonlinear behavior and dynamic characteristics when its parameters take some specific values. Finally, we get the critical condition of the stability of the vocational education system according to the model established in the article.

Topological design of strain sensing nanocomposites

High-performance piezoresistive nanocomposites have attracted extensive attention because of their significant potential as next-generation sensing devices for a broad range of applications, such as monitoring structural integrity and human performance. While various piezoresistive nanocomposites have been successfully developed using different material compositions and manufacturing techniques, current development procedures typically involve empirical trial and error that can be laborious, inefficient, and, most importantly, unpredictable. Therefore, this paper proposed and validated a topological design-based methodology to strategically manipulate the piezoresistive effect of nanocomposites to achieve a wide range of strain sensitivities without changing the material system. In particular, patterned nanocomposite thin films with stress-concentrating and stress-releasing topologies were designed. The strain sensing properties of the different topology nanocomposites were characterized and compared via electromechanical experiments. Those results were compared to both linear and nonlinear piezoresistive material model numerical simulations. Both the experimental and simulation results indicated that the stress-concentrating topologies could enhance strain sensitivity, whereas the stress-releasing topologies could significantly suppress bulk film piezoresistivity.

The Cooperative Control of Subgrade Stiffness on Symmetrical Bridge–Subgrade Transition Section

In the field of civil engineering and architecture, the concept of symmetry has been widely accepted. The bridge can be treated as a typical symmetrical structure of civil engineering buildings. Among them, the Subgrade can be identified as an important part to bear the vehicle loads. Severe pavement problems and bridge service capabilities will be caused by problems of the bridge–subgrade transition section. Therefore, setting the rigid–flexible transition is an important method to solve this problem. The bridge–subgrade transition section has been set at both ends of the bridge, which can be regarded as a typical symmetrical structure. Based on nonlinear finite element numerical simulation and synergistic theory, the cooperative control problems of the bridge–subgrade transition section were studied in this work. The change rule of the stiffness of the transition section was discussed and the influence of stiffness variation of the bridge–subgrade transition section on the stress state of the structure was also analyzed. Furthermore, the influence of subgrade stiffness change on the stress and strain field was analyzed. A permanent strain prediction model was established and stiffness or subsidence difference coordination control was also discussed.

Nonlinear numerical simulation and experimental verification of bondline strength of CFRP strips embedded in concrete for NSM strengthening applications

AbstractThis article presents results of an investigation that focuses on assessing bondline strength of carbon/epoxy fiber reinforced polymeric (CFRP) precured strips embedded in concrete for near‐surface‐mounting (NSM) strengthening applications. In this study, experimental evaluation and nonlinear numerical analysis of CFRP/concrete interfacial bond behavior are investigated. In this study, 15 pull‐out tests were performed on different reinforced concrete (RC) U‐shaped column specimens with different NSM groove configurations to evaluate the effect of groove size, groove depth, and adhesive bondline thickness on overall performance of the CFRP‐NSM system and to identify the optimum groove dimensions. Experimental results indicated that changing groove geometries of the NSM‐FRP reinforcements significantly affect bondline strength and associated mode of failures of NSM‐CFRP system. It was also shown that increasing bondline length lead to an increase in ultimate failure load and CFRP rupture strain. Based on results of this study, NSM materials with lower longitudinal moduli and higher rupture strains (e.g., E‐glass/epoxy or basalt/epoxy), may increase toughness and enhance performance of the NSM strengthening system.

Time-domain numerical analysis of single pedestrian random walks on laminated glass slabs in pre- or post-breakage regime

Mechanical performance assessment of load-bearing elements under ordinary design actions is a priority when material degradation or even severe damage may be experienced. This is especially the case of unconventional constructional materials, or assembled systems like laminated glass (LG) solutions, in which multiple load-bearing components may suffer of different mechanical issues. This turns out in potential risk for customers, and in the need of specific design assumptions to address the problem. For load-bearing elements with direct interaction with final users (as pedestrian systems), a reciprocal modification of mechanical and dynamic parameters should be properly taken into account in the early design process.This paper explores the sensitivity of human-structure interaction effects and performance indicators for LG slab modules subjected to various walking paths of single pedestrians. An extended set of Finite Element (FE) nonlinear dynamic numerical simulations is presented, in which the variation of conventional performance indicators (such as acceleration peaks, deflection, vibration frequency) is investigated for two in-service LG modular units with intact (LGU) or partially fractured (LGF) glass layers. Walking scenarios are described with the support of consolidated deterministic method in use for pedestrian loads, in which walking features do not account for the features of structural background. The comparative analysis of numerical results with earlier experimental outcomes for two reference LG slab modules subjected to random walking conditions shows that time-domain nonlinear simulations with simplified pedestrian loads can efficiently capture some major effects of pedestrians, as well as the presence of damage in glass. At the same time, it is shown that fractured glass layers in LG pedestrian modules can still provide partial post-breakage contribution to the resisting section.

Impact Loads on Tension Composite Multi-Strings of Insulator After a Single String Breaks

The dynamic impact load after a single insulator of a tension composite multi-strings of insulator (MSI) set has failed is a key factor that should be considered in design. In this paper, an experimental method to obtain the dynamic tensile impact factor (DTIF) is established by considering a typical double-strings set, which is commonly used in practical engineering. A nonlinear numerical simulation method based on the finite element model, which is convenient for cases that are more complex than the double-strings set, is proposed to calculate the DTIF and demonstrated through the experimental results. The values of the DTIF on the unbroken insulator string obtained by the experimental models fall between 2.6 and 3.3, which should be a very valuable reference for the design of composite MSI sets. The size of connection fittings is a key factor that influences the DTIF, and the yoke height between the insulator strings and the conductors is the most sensitive parameter. The application of the proposed method to calculate the DTIF can improve the existing design approach to ensure the safety of the tension composite MSI sets, especially for high voltage transmission lines.

Simulation and Optimization Design for Energy Absorption Characteristics of Multi-cell Thin-walled Structures

Abstract Based on muti-cell thin-walled structures, construct variety of circular, octagonal, hexagonal multi-cell thin-walled tubes, energy absorption characteristics were studied. Used ANSYS to 12 different cross-sectional shapes of thin-walled tubes axial compression characteristics to nonlinear numerical simulation. The best cross-sectional shape was determined by comparing the energy absorption of different cross-sectional shapes. The thickness of inner and outer walls of thin-walled tubes and stiffened ribs were taken as design variables. Taking the strain energy density and peak force as targets, a response surface model was fitted and multi-objective optimization was performed. The optimization results show that strain energy density and compression efficiency are improved under premise of small peak force.

Archaeoseismological project in Ostia: Tracking evidence on seismic damage by nonlinear numerical simulations

Within the framework of an archaeoseismological project in Ostia (Italy), this paper discusses archaeological evidence of historic seismic damage of one of the arcade pillars in a building originally used as a warehouse for goods - “Piccolo Mercato” - located in the North-West part of the archaeological site. This interdisciplinary study is aimed at providing an interpretation of the detected damage by performing some numerical simulations. One of the pillars was represented by a finite element (FE) model, considering natural ground motion records. FE model allowed to conduct complete nonlinear time-history analyses. The results cross-validate the already provided interpretation of the historic damage, and suggest a possible dateline.

Mooring system stiffness: A six-degree-of-freedom closed-form analytical formulation

A mooring system project is an iterative process, involving design and analysis with numerous parameters. In this context, analytical tools can help to reduce the use of expensive and time consuming full nonlinear numerical simulations based on high-order hierarchical models such as Finite Element models, mainly during early stages of the design. By employing Analytical Mechanics approaches, the present article brings an analytical and closed-mathematical-form formulation to determine the six-degree-of-freedom (DOF) mooring system stiffness matrix at any generic position of the floating body, provided mooring line forces are modeled as conservative ones. In order to demonstrate the use of these tools, the international benchmark of the OC4-DeepCwind platform is considered as a case study. The influence of the vessel mean position and design parameters in the stiffness, natural periods and oscillation modes is studied, revealing interesting coupling effects. Results are benchmarked against the commercial code OrcaFlexTM showing good agreement, observing that the analytical result requires much less computational cost.

Retraction of: algebro-geometric constructions of the Heisenberg hierarchy

Article Retraction of: algebro-geometric constructions of the Heisenberg hierarchy was published on February 1, 2022 in the journal International Journal of Nonlinear Sciences and Numerical Simulation (volume 23, issue 2).

Turbulence mitigation in maximum-J stellarators with electron-density gradient

In fusion devices, the geometry of the confining magnetic field has a significant impact on the instabilities that drive turbulent heat loss. This is especially true of stellarators, where the density-gradient-driven branch of the ‘trapped electron mode’ (TEM) is predicted to be linearly stable if the magnetic field has the maximum-J property, as is very approximately the case in certain magnetic configurations of the Wendelstein 7-X experiment (W7-X). Here we show, using both analytical theory and simulations, that the benefits of the optimisation of W7-X also serve to mitigate ion-temperature-gradient (ITG) modes as long as an electron density gradient is present. We find that the effect indeed carries over to nonlinear numerical simulations, where W7-X has low TEM-driven transport, and reduced ITG turbulence in the presence of a density gradient, giving theoretical support for the existence of enhanced confinement regimes, in the presence of strong density gradients (e.g. hydrogen pellet or neutral beam injection).