Three-dimensional Nonlinear Model Research Articles

Nonlinear dynamic performance of long-span cable-stayed bridge under traffic and wind

Long-span cable-stayed bridges exhibit some features which are more critical than typical long span bridges such as geometric and aerodynamic nonlinearities, higher probability of the presence of multiple vehicles on the bridge, and more significant influence of wind loads acting on the ultra high pylon and super long cables. A three-dimensional nonlinear fully-coupled analytical model is developed in this study to improve the dynamic performance prediction of long cable-stayed bridges under combined traffic and wind loads. The modified spectral representation method is introduced to simulate the fluctuating wind field of all the components of the whole bridge simultaneously with high accuracy and efficiency. Then, the aerostatic and aerodynamic wind forces acting on the whole bridge including the bridge deck, pylon, cables and even piers are all derived. The cellular automation method is applied to simulate the stochastic traffic flow which can reflect the real traffic properties on the long span bridge such as lane changing, acceleration, or deceleration. The dynamic interaction between vehicles and the bridge depends on both the geometrical and mechanical relationships between the wheels of vehicles and the contact points on the bridge deck. Nonlinear properties such as geometric nonlinearity and aerodynamic nonlinearity are fully considered. The equations of motion of the coupled wind-traffic-bridge system are derived and solved with a nonlinear separate iteration method which can considerably improve the calculation efficiency. A long cable-stayed bridge, Sutong Bridge across the Yangze River in China, is selected as a numerical example to demonstrate the dynamic interaction of the coupled system. The influences of the whole bridge wind field as well as the geometric and aerodynamic nonlinearities on the responses of the wind-traffic-bridge system are discussed.

8×8 Wheeled Vehicle Modeling in a Multibody Dynamics Simulation Software

The article describes a three-dimensional non-linear dynamic model of a 8×8 wheeled vehicle. The authors used the “Universal Mechanism” MBS software to build the model. The article also presents a tire – rigid terrain interaction model built in Matlab/Simulink. The authors tested the process of linking a Matlab/Simulink DLL to the vehicle MBS model. The authors used the developed model to analyze the wheeled vehicle dynamic behavior at different operation conditions. The article contains the results of the lane change test simulation. The simulation results confirmed the validity of the model. The developed model allows the estimation of the wheeled vehicle dynamic behavior at various operation conditions at the design stage.

New Analysis Theory and Method for Drag and Torque Based on Full-Hole System Dynamics in Highly Deviated Well

The research on calculation of torque and drag in highly deviated wells has demonstrated a significant gap against oil exploration and development; with the increasingly rigorous situation, the drill string dynamics and the contact or friction of drill pipe with borehole wall under the drill string action of dynamic need more attention and urgent research work. Based on full-hole system dynamics, three-dimensional nonlinear dynamic model and dynamic torque and drag model were established in highly deviated well by using the finite element method. An application of analyzing typical torque and drag problems presented here provides a means to more accurate description of the contact relation between drill string and wellbore. The results show that those models established in this paper have complete adaptability for a complex three-dimensional borehole trajectory. For the actual well application, it will help to evaluate security performance of drill string in complex working conditions.

Pulsed Bessel-Gauss beams: a depleted wave model for type II second-harmonic generation.

In this work, a three-dimensional and time-dependent nonlinear wave model to describe the generation of pulsed Bessel-Gauss second-harmonic waves (SHWs) is presented. Three coupled equations, two for ordinary and extraordinary fundamental waves and one for extraordinary SHWs, describing type II second-harmonic generation (SHG) in a KTiOPO4 (KTP) crystal were solved by considering the depletion of fundamental waves (FWs). The results examined the validity of nondepleted wave approximation against the energy of pulses, beam spot size, and interaction length. It was shown that for pulses with spot sizes of ωf=80 μm and energy of 0.8j, the nonlinear interaction was accomplished over a distance of ∼5 mm. Therefore, for KTP crystals with lengths longer than 5mm, the nondepleted wave approximation can no longer be valid. To be valid, the crystal must be shorter than the interaction length, i.e., 5mm.

Staged Construction Modeling of Steel Pipes Buried in Controlled Low-Strength Material Using 3D Nonlinear Finite-Element Analysis

AbstractSeveral complexities are inherent in numerical simulation of staged construction modeling of large-diameter steel pressure pipes. A comprehensive robust three-dimensional (3D) nonlinear finite-element analysis model was developed and verified using three experimental field tests conducted at the Rolling Hills Booster Pump Station, Fort Worth, Texas, to simulate the behavior of buried steel pipes during staged construction installation. Controlled low-strength material (CLSM) was used as the embedment material, and the depth of the CLSM embedment and the trench width varied. The developed numerical model includes three possible nonlinearities, including geometric, material, and contact nonlinear algorithms. A large deformation algorithm was considered in the finite-element model and its associated analysis using a total Lagrangian formulation. The contact between each soil layer, soil-to-trench wall, and soil to pipe was carefully implemented. The lateral effect of compaction was identified in prev...

Failure Behavior of a Top and Seat Angle Bolted Steel Connection with Double Web Angles

AbstractThe article presents a three-dimensional nonlinear finite-element model that was developed for the study of a top and seat angle bolted steel connection with double web angles. Unilateral contact and friction laws were used to simulate the interaction among the connected parts. Large displacements as well as the von Mises failure criterion were also considered for the steel parts and bolts. Numerical results were compared with the experimental research conducted on the same steel joint. This study finds yielding of the top angle as well as shear failure of the bolts connecting the beam bottom flange with the seat angle to be very important for the overall response of the structure. For this reason, a parametric investigation of the influence of the top angle on the behavior of the structure and the study of the prying forces developed at the top angle were conducted.

Using three-dimensional finite element analysis for simulation of residual stresses in railway wheels

One of the most important issues in railway wheels is residual stresses. It is desirable to produce less residual stresses when possible and to decrease the remaining residual stresses in the wheels. The objective of this paper is to provide an estimation of the residual stresses in the rail wheel caused by the stress field from heat treatment process of a railway wheel. A three-dimensional nonlinear stress analysis model has been applied to estimate stress fields of the railway mono-block wheel in heat treatment process. After forging or casting, railway wheels are heat-treated to induce the desirable circumferential compressive residual stress in the upper rim. Finite element analysis model is presented applying the elastic–plastic finite element analysis for the rail wheel under variable thermal loads. Calculative analysis applying a finite element method (FEM) has been used to predict residual stresses. The quenching and annealing segments of the wheel manufacturing process are simulated using a decoupled heat transfer and stress analysis. Three-dimensional finite element analysis results obtained show good agreement with those achieved in field measurements.

Modelling the nonlinear viscoelastic response of asphalt binders

In a recent article, Narayan et al. [Narayan, S.P.A., et al., 2012b. Nonlinear viscoelastic response of asphalt binders: experimental study of relaxation of torque and normal force in torsion. Mechanics Research Communications, 43, 66–74] recorded both torque and normal force in torsional relaxation experiments on asphalt binders. The data are three-dimensional and thus, require interpretation using three-dimensional constitutive relations. In this article, we develop such a three-dimensional nonlinear viscoelastic model for asphalt binder. The predictions of the model fit the experimental data reasonably well. While there are already some three-dimensional constitutive relations available in the literature for asphalt binders which can describe the normal forces that are developed during torsion, they do not capture the relaxation behaviour presented by Narayan et al. (2012b). This new model, however, captures most of the key features of the experimental data including the development of normal forces in torsion and the relaxation behaviour. In this respect, the new model performs considerably better than the existing models.

Seismic assessment of a steel braced plan mass symmetric/asymmetric building structure

This paper presents a seismic response investigation into a code designed concentrically braced frame structure that is subjected to but not designed for in-plan mass eccentricity. The structure has an accidental uneven distribution of mass in plan resulting in an increased torsional component of vibration. The level of inelasticity that key structural elements in plan mass asymmetric structures are subjected to is important when analysing their ability to sustain uneven seismic demands. In-plan mass asymmetry of moment resisting frame and shear wall type structures have received significant investigation, however, the plan asymmetric response of braced frame type structures is less well understood. A three-dimensional non-linear time history analysis model is created to capture the torsional response of the plan mass asymmetric structure to quantify the additional ductility demand, interstorey drifts and floor rotations. Results show that the plan mass asymmetric structure performs well in terms of ductility demand, but poorly in terms of interstorey drifts and floor rotations when compared to the plan mass symmetric structure. New linear relationships are developed between the normalised ductility demand and normalised slenderness of the bracing on the sides of the plan mass symmetric/asymmetric structures that the mass is distributed towards and away from.

MODELING AND OPTIMAL CONTROL FOR ANTIRETROVIRAL THERAPY

We consider a three-dimensional nonlinear control model based on the Wodarz HIV model. The model phase variables are populations of the uninfected and infected target cells and the concentration of an antiretroviral drug. The drug intake rate is assumed to be a bounded control function. An optimal control problem of minimizing the cumulative infection level (the infected cells population) on a given time interval is stated and solved, and the types of the optimal control for different model parameters are found by analytical methods. We thereby reduce the two-point boundary value problem (TPBVP) for the Pontryagin maximum principle to a problem of the finite-dimensional optimization. Numerical results are presented to illustrate the optimal solution.

Non-collinear phase-matching geometries in optical parametric chirped-pulse amplification

This study presents a full three-dimensional nonlinear pulse propagation and amplification model that includes considerations for phase-matching, diffraction, and walk-off effects. By using this model, two types of type I non-collinear phase-matching geometries in BBO based optical parametric chirped-pulse amplification are investigated theoretically and experimentally. The simulation results agree well with the experimental findings.

Performance evaluation of natural rubber seismic isolators as a retrofit measure for typical multi-span concrete bridges in eastern Canada

More than 46% of the 2672 multiple-span bridges in the Province of Quebec (Canada) are concrete girder bridges. Due to the advanced age and the lack of seismic detailing, these bridges may be vulnerable to earthquake events. In an effort to prevent an interruption of the transportation network, which could be catastrophic for Quebec, a comprehensive research program was conducted whose aims were to assess the seismic vulnerability of typical bridge classes retrofitted with natural rubber seismic isolator devices through the development of fragility curves. The understanding of the impact of various modeling parameters on structural-component responses is the first step in a forward-vulnerability assessment of bridges in Quebec. This paper presents part of a comparative study using detailed three-dimensional nonlinear models that was conducted to assess the longitudinal and transverse responses of multi-span continuous (MSC) and multi-span simply supported (MSSS) concrete bridges in their as-built and retrofitted configurations using different synthetic ground motions (SGM) for the eastern part of Canada. Deterministic responses in terms of column curvature demand, abutment footing deformations, and abutment wall deformations are provided for the longitudinal and transverse directions of bridge models. The influences of various modeling parameters were assessed using analysis of variance (ANOVA) and design-of-experiments (DOE) principles to perform screening of 12 structural parameters. This study revealed that the most important modeling parameters that affect critical components responses of MSC and MSSS bridges are the isolator effective stiffness, the abutment stiffness, and the gap between abutment and deck, in addition to the variation in gross bridge geometry and ground-motion contents. This screening study also gives an indication that the variation in other modeling parameters such as structural damping and skew angle affect the seismic response of MSC and MSSS bridges and should be considered carefully in a seismic-vulnerability assessment for these portfolios of concrete bridges. In addition, it was found that the use of seismic isolation devices effectively reduces the curvature demand placed on columns but has a negative impact on the deformation demand placed on abutment walls.

Finite element method for viscoelastic medium with damage and the application to structural analysis of solid rocket motor grain

This paper studies the damage-viscoelastic behavior of composite solid propellants of solid rocket motors (SRM). Based on viscoelastic theories and strain equivalent hypothesis in damage mechanics, a three-dimensional (3-D) nonlinear viscoelastic constitutive model incorporating with damage is developed. The resulting viscoelastic constitutive equations are numerically discretized by integration algorithm, and a stress-updating method is presented by solving nonlinear equations according to the Newton-Raphson method. A material subroutine of stress-updating is made up and embedded into commercial code of Abaqus. The material subroutine is validated through typical examples. Our results indicate that the finite element results are in good agreement with the analytical ones and have high accuracy, and the suggested method and designed subroutine are efficient and can be further applied to damage-coupling structural analysis of practical SRM grain.

Effects of viscosity and varying gravity on liquid sloshing in a carrier subjected to external excitations

The nonlinear dynamic behavior of liquid sloshing in a carrier is investigated in this research with consideration the effects of viscosity of the liquid and varying gravity on the carrier. Liquid sloshing in the tank of the carrier is analogized as a three-dimensional nonlinear conical pendulum model. The solutions of the coupled governing equations for the sloshing are developed and solved numerically. Both inviscid and viscous liquids are considered and compared for their effects on the sloshing. With the research results obtained, viscosity of the liquid plays a significant role in the nonlinear dynamic behavior of liquid sloshing. Also, the influence of gravitational acceleration on the 3D nonlinear sloshing of the liquid in the carrier is studied in details with a variety of system parameters.

Numerical Simulation of Artificical Hip Joint Movement for Western and Japanese-Style Activities

A numerical simulation model for observing the artificial hip joint movement with respect to the range of motion during human activities is presented in this paper. There were two human activities discussed, i.e. Western-style and Japanese-style. Previous investigation has reported the range of motion on the artificial hip joint for Western-style and Japanese-style, measured from the postoperative total hip arthroplasty patients. The aim of this investigation is to observe the probability of prosthetic impingement and to calculate the von Mises stress during these activities using finite element analysis (FEA). The Western-style activities consist of picking up, getting up and sitting, while the Japanese-style activities consist of sitting on legs with fully flexed at the knee (seiza), squatting and sitting on legs with fully flexed at the knee (zarei). The FEA uses a three-dimensional nonlinear model and considers the variation of the acetabular liner cup positions. Result shows that a prosthetic impingement is found in the Western’s picking up activity. This activity induces a prosthetic impingement in a certain the acetabular liner cup position. In the Japanese-style activities there is no prosthetic impingement observed. However, a critical value in the range of motion was observed for the Japanese’s Zarei activity for certain the acetabular liner cup position. The acetabular liner cup positions influences the probability of prosthetic impingement.

Three-dimensional connectivity in the Gulf of California based on a numerical model

Quantifying connectivity is useful for understanding the exchange and trapping of some tracers, such as fish larvae and nutrients. In the Gulf of California, connectivity studies have been limited to certain periods and regions. The current study investigated the connectivity among 17 areas, defined by the presence of eddies and weak or strong flows as obtained from a three-dimensional non-linear baroclinic model. The particles were released into the water column and advected for 28days using an advection–diffusion scheme. The results revealed a seasonal connectivity pattern. In the northern region, particle trapping was greater during the cyclonic circulation period (June to September) compared with the anticyclonic period (November to March). This high retention was due to both the presence of a cyclonic eddy in the central portion of the region and the intense northwestward flow off the coast of Sonora. Retentions were low for the large island region due to the intense exchange between the northern and southern regions. East of Ángel de La Guarda Island the transport occurred predominantly towards the northwest due to the nearly permanent deep flow in that direction and to a branching of the surface flow among the large islands during the anticyclonic period and the northwestward low during the cyclonic period. In the peninsular and central areas of the southern region, retentions were high due to weak flows and the presence of eddies, respectively. The greatest retention and low dispersion of particles in practically all of the provinces were recorded during the transition periods of the circulation.

Impact behaviour of pre-compressed hollow and concrete filled mild and stainless steel columns

This paper investigates the behaviour of hollow and concrete filled steel (CFST) mild and stainless steel columns subjected to transverse static and impact loading with a pre-compressive axial load. Transverse load was applied at the mid or quarter point of the columns. A total of three test series were carried out recently at the University of Western Sydney and the University of Wollongong to obtain the performance of mild and stainless steel hollow and CFST columns subjected to lateral static as well as impact loading with or without pre-compressive load. The test results reported in this paper are from the third test series, where both axial and lateral loads were applied to the columns. This paper also investigates the finite element (FE) modelling of hollow and CFST mild and stainless steel columns due to static and impact loads. Three-dimensional nonlinear FE models were developed using ABAQUS, where nonlinear material behaviour, enhanced strength corner properties of steel, pre-compressive loads were all included to simulate the static and impact experiments. The main objective of this paper is to compare the performance of experimental results with numerical results for mild and stainless steel hollow and CFST columns. Moreover, the behaviour of in-filled tubes under impact loading is also compared with that of hollow sections. Close agreement is achieved between the experimental and finite element results in terms of load–deflection response and ultimate strength. This paper also compares the results of hollow and CFST stainless steel columns with those of mild steel columns due to both static and impact loading. Generally, the stainless steel specimens showed higher strength and improved energy-dissipating characteristics compared with the mild steel columns.

Numerical Simulation of Heat Flow in Friction Stud Welding of Dissimilar Metals

Friction stud welding is a solid-state joining technique used for welding similar and dissimilar materials with high integrity. In friction stud welding, heat is generated by the conversion of mechanical energy into thermal energy at the interface of the work pieces during rotation under pressure. This complicated metallurgical process is accompanied by frictional heat generation, plastic deformation, cooling of high-temperature metal, and solid-state phase variation. Since the thermal cycle of friction stud welding is very short, simulation becomes a vital role to study the behaviour of materials. The simulations make it possible to observe the temperature distribution and heat transfer fields that take place during the process. In the present work, a three-dimensional nonlinear Finite Element-based heat flow model is developed for friction stud welding of aluminium and mild steel combination. The numerical model is validated with a temperature history at the weld interface measured using a non-contact-type infrared thermometer. During friction stud welding, temperature, temperature distribution, temperature gradient, heat transfer rate and their variations, govern welding parameters of a welding machine. Knowledge of them helps to determine optimum parameters and ways to improve the design and manufacture of welding machines. Hence, the developed numerical model could be used as a tool to study the thermal cycles during the process and it will be very much useful for the subsequent analysis of residual stress and distortion of welded joints.

Vehicle-bridge coupling vibration analysis based fatigue reliability prediction of prestressed concrete highway bridges

The extensive use of prestressed reinforced concrete (PSC) highway bridges in marine environment drastically increases the sensitivity to both fatigue-and corrosion-induced damage of their critical structural components during their service lives. Within this scenario, an integrated method that is capable of evaluating the fatigue reliability, identifying a condition-based maintenance, and predicting the remaining service life of its critical components is therefore needed. To accomplish this goal, a procedure for fatigue reliability prediction of PSC highway bridges is proposed in the present study. Vehicle-bridge coupling vibration analysis is performed for obtaining the equivalent moment ranges of critical section of bridges under typical fatigue truck models. Three-dimensional nonlinear mathematical models of fatigue trucks are simplified as an eleven-degree-of-freedom system. Road surface roughness is simulated as zero-mean stationary Gaussian random processes using the trigonometric series method. The time-dependent stress-concentration factors of reinforcing bars and prestressing tendons are accounted for more accurate stress ranges determination. The limit state functions are constructed according to the Miner's linear damage rule, the time-dependent S-N curves of prestressing tendons and the site-specific stress cycle prediction. The effectiveness of the methodology framework is demonstrated to a T-type simple supported multi-girder bridge for fatigue reliability evaluation.

Influence of Coarse Aggregates on the Shear Resistance of Perfobond Rib Shear Connector

This paper shows the effect of coarse aggregates in concrete with perfobond rib via experimental and FE analysis. First, the model of a single PBL in ordinary concrete was reproduced through a three-dimensional nonlinear FE model. Coarse aggregates were added to the model; it was found that the coarse aggregates around the perforation of PBL increased its initial load-carrying capacity. Furthermore, the interlocking of these coarse aggregates was found to affect PBL behavior after the peak of load-carrying capacity. Next, analytical numerical modeling of push-out tests of single PBL was performed to investigate the role of coarse aggregates. It was confirmed that the initial load-carrying capacity could be increased via the vertical loading stress from the steel to the coarse aggregates. Finally, the numerical modeling results were verified by actual push-out tests of single PBL with systematically sorted coarse aggregates.