Explicit Finite Element Approach Research Articles

Influence of high-frequency vibrations on the wheel-rail creep curve at high speeds

Quasi-steady and transient rolling contact of a driving wheelset over tangent and curved tracks at a speed up to 500 km/h is simulated using an explicit finite element approach to derive creep curves. Quasi-steady curves corresponding to smooth wheel and rail are compared to those from traditional theories implying the steady rolling assumption for validation. Transient curves in the presence of rail corrugation with a wavelength of 10 ∼ 1000 mm are further analyzed to study the influence of middle/high-frequency vibrations. Cases where transient effects must be considered or traditional theories are inapplicable are identified.

An explicit finite element approach for simulations of transient meshing contact of gear pairs and the resulting wear

A 3D time-domain modelling approach is developed with the explicit finite element method to simulate transient meshing contact of gear pairs and the resulting wear. Taking a helical gear pair used in a locomotive as an example, the dynamic contact states of gear teeth are predicted for different speeds in consideration of actual geometries (including those of damaged teeth), time dependent torques, and structural and continuum vibrations of the gear system. The friction between mating teeth is taken into account by a non-Newtonian EHL friction model. A tiny time step of 4.5 × 10−8 s determined by conditional stability of the explicit time integration ensures the capture of transient effects. Based on detailed contact solutions during meshing, the dynamic wear on teeth is further calculated using an Archard wear model to predict tooth profile evolvement. Taking initial involute profiles and a speed of 120 km/h, the model is first validated for dynamic contact solutions. More results show that structural vibrations and worn profiles influence the dynamic meshing contact significantly, tooth wear increases as lubrication fails, and tooth pitting's influence is localized. This approach provides key load boundaries for detailed studies on mating gears, and may be employed for studies on tooth damages and as a reference for lumped parameter dynamic models of gear pairs.

Dynamic Structural Assessment of Blast Wall Designs on Military-Based Vehicle Using Explicit Finite Element Approach

Explosion load studies are an essential part of shield engineering design. This is especially true for explosion-proof plates, which are used in order to reduce the impact of explosions, which have the potential to cause substantial damage to structural elements. The purpose of this study is to detail the explosion phenomenon and the response of sandwich panel structures under explosive loading. The finite element method (FEM) is used to model the dynamic structural response to explosions. Explicit finite element modeling and analysis are performed using ABAQUS CAE software. An air explosion simulation code is used to determine the blast load on the lower skin plate of a test panel on a typical armored personnel vehicle. Structural analysis is carried out with respect to displacement, von-Mises stress, and internal kinetic energy. Three variations of explosive loads are considered in the simulation in order to better compare the responses of the structures. Three different design variants and materials are considered, including honeycomb, stiffener, and corrugated geometric models and mild steel, medium carbon steel, and alloy steel materials. The results provided by this study pave the way toward the development of guidelines for the design of lightweight structural reinforcement elements.

Fragility analysis of masonry wall subjected to blast loading

The present research focuses on developing the Fragility Curves (FC) of masonry panels subjected to various blast scenarios considering extensive parameters such as the effect of variation in types of masonry (unreinforced and reinforced) and blast explosion (air and surface). The Fragility Curve (FC) is a suitable way of illustrating the vulnerability of structure against blast load. Herein; fragility analysis of Solid Brick Masonry (SBM), Hollow Brick Masonry (HBM) and Reinforced Hollow Brick Masonry (RHBM) wall panels were carried out to assess their vulnerability against blast load using explicit finite element approach. The FC(s) were plotted considering uncertainties in blast parameters viz., weight of charge (W) and standoff distance (R). Two types of FC(s) were plotted: FC-1, with Probability of Failure (PF) as ordinate and W as abscissa; and FC-2, with PF on ordinate-axis and scaled distance Z [f (W, R)] on abscissa. Monte Carlo simulation (MCS) was adopted to generate random sample sets of variables based on the mean value and coefficient of variation. The failure criterion assumed in this study is based on the inelastic tension damage curve generated for the masonry in accordance with the experimental results. Also, a Damage Index was established having four levels of damage- Minor Damage (MD), Repairable Damage (RD), Non-Repairable Damage (NRD) and Total Damage (TD). In addition, limit state function was defined in terms of cracking strain for which the threshold values corresponding to each damage level was specified on the basis of tension damage curve. The various critical values of W and Z corresponding to the probability of TD being 90% were reported from the FC(s). It was found that percentage increase in demand of W critical for RHBM was about 100%–400% approximately for various standoff distances between 5 m and 40 m. Also, due to strengthening value of Z critical decreased to 21% and 27.5% respectively for surface and air blast scenario respectively.

An Efficient Reliability-Based Approach for Evaluating Safe Scaled Distance of Steel Columns under Dynamic Blast Loads

Damage to building load-bearing members (especially columns) under explosions and impact are critical issues for structures, given that they may cause a progressive collapse and remarkably increase the number of potential victims. One of the best ways to deal with this issue is to provide values of safe protective distance (SPD) for the structural members to verify, so that the amount of damage (probability of exceedance low damage) cannot exceed a specified target. Such an approach takes the form of the so-called safe scaled distance (SSD), which can be calculated for general structural members but requires dedicated and expensive studies. This paper presents an improved calculation method, based on structural reliability analysis, to evaluate the minimum SSD for steel columns under dynamic blast loads. An explicit finite element (FE) approach is used with the Monte Carlo simulation (MCS) method to obtain the SSD, as a result of damage probability. The uncertainties associated with blast and material properties are considered using statistical distributions. A parametric study is thus carried out to obtain curves of probability of low damage for a range of H-shaped steel columns with different size and boundaries. Finally, SSD values are detected and used as an extensive databank to propose a practical empirical formulation for evaluating the SSD of blast loaded steel columns with good level of accuracy and high calculation efficiency.

The Dynamic Impact Response of 3D-Printed Polymeric Sandwich Structures with Lattice Cores: Numerical and Experimental Investigation.

This paper proposes a dynamic drop weight impact simulation to predict the impact response of 3D printed polymeric sandwich structures using an explicit finite element (FE) approach. The lattice cores of sandwich structures were based on two unit cells, a body-centred cubic (BCC) and an edge-centred cubic (ECC). The deformation and the peak acceleration, referred to as the g-max score, were calculated to quantify their shock absorption characteristic. For the FE results verification, a falling mass impact test was conducted. The FE results were in good agreement with experimental measurements. The results suggested that the strut diameter, strut length, number and orientation, and the apparent material stiffness of the lattice cores had a significant effect on their deformation behavior and shock absorption capability. In addition, the BCC lattice core with a thinner strut diameter and low structural height might lead to poor shock absorption capability caused by structure collapse and border effect, which could be improved by increasing its apparent material stiffness. This dynamic drop impact simulation process could be applied across numerous industries such as footwear, sporting goods, personal protective equipment, packaging, or biomechanical implants.

Explicit nonlinear finite element approach to the Lagrangian-based coupled phase field and elasticity equations for nanoscale thermal- and stress-induced martensitic transformations

In this paper, a nonlinear finite element procedure is developed to solve the coupled system of phase field and elasticity equations at large strains for martensitic phase transformations at the nanoscale. The transformation is defined based on an order parameter which varies between 0 for austenite to one for martensite. The phase field equation relates the rate of change of the order parameter to the Helmholtz free energy. Both the Helmholtz free energy and the transformational strain tensor depend on the order parameter, and the coupling between the phase field and elasticity equations occurs due to the presence of elastic energy in the Helmholtz free energy and the transformational strain in the total strain. The deformation gradient tensor is introduced as a multiplicative decomposition of elastic and transformational gradient tensors. A staggered strategy is used to solve the coupled system of equations so that first, the principle of virtual work is utilized to obtain the integral form of the Lagrangian equation of motion. It is then discretized and solved using the Newton–Raphson method which gives the displacements and consequently, the deformation gradient tensor. Next, since the order parameter is obtained from the phase field equation from the previous time step, the elastic deformation gradient tensor and the first Piola–Kirchhoff stress can be calculated and substituted in the phase field equation to find the order parameter for the current time step. The weighted residuals method is used to derive the finite element form of the phase field equation and the explicit method is used for its time discretization. The finite element procedure is well verified by comparing the obtained results with those from other simulations. Examples of thermal- and stress-induced phase transformations are presented, including austenite–martensite interface propagation and growth of preexisting martensitic regions. The developed algorithm and code can be advanced to solve kinetic problems coupled with mechanics at large strains for phase transformations and similar phenomena at the nanoscale.

Explicit finite element analysis can predict the mechanical response of conical implant press-fit in homogenized trabecular bone

Prediction of primary stability is a major challenge in the surgical planning of dental and orthopedic implants. Computational methods become attractive to estimate primary stability from clinical CT images, but implicit finite element analysis of implant press-fit faces convergence issues due to contact and highly distorted elements. This study aims to develop and validate an explicit finite element method to simulate the insertion and primary stability of a rigid implant in a deformable bone while accounting for damage occurring at the bone-implant interface. Accordingly, a press-fit experiment of a conical implant into predrilled bovine trabecular bone was designed and realized for six samples. A displacement-driven cyclic protocol was used to quantify the reaction force and stiffness of the bone-implant system. Homogenized finite element analyses of the experiments were performed by modeling contact with friction and converting an existing constitutive model with elasto-plasticity and damage of bone tissue to be applicable to an explicit time integration scheme where highly distorted elements get deleted. The computed reaction forces and unloading stiffnesses showed high correlations (R2 = 0.95 and R2 = 0.94) with the experiment. Friction between bone and implant exhibited a strong influence on both reaction force and stiffness. In conclusion, the developed explicit finite element approach with frictional contact and element deletion accounts properly for bone damage during press-fit and will help optimizing dental or orthopedic implant design towards maximal primary stability.

Creep modelling for multi-physical simulation of mass concrete structures using the explicit finite element approach

In the context of increasingly required evaluation of existing critical concrete infrastructures, prediction of the long-term behaviour can sometimes be very sensitive to the proper consideration of physical phenomena that occur during the first weeks during construction. For the specific example of mass concrete structures, it is important to consider the heat of hydration process and the possible development of thermally induced stresses and cracking at an early age. Consideration of the early age to the long-term time spectrum to recreate the history of stress/crack development is a challenging task in the field of numerical simulation of concrete structures and involves a consideration of multiple non-linear and physical phenomena. This work constitutes a continuation of previous works involving multi-physical simulation of concrete structures using the explicit finite element solver algorithm, which is known for its efficiency in solving highly nonlinear problems compared to the conventional implicit solver. A simple and innovative framework was developed in previous studies and involves the decomposition of strain into mechanical, thermal, creep, shrinkage and a coupling chemo-physical strain. This work focuses on the development of a simple and feasible computational framework for considering the creep in the specific field of mass concrete structures. Verification and validation examples are considered at the material and element levels. Application at the structural level on a new numerical benchmark demonstrates the feasibility of the approach and the efficiency of the developed computational framework.

Finite element simulation of the braiding process

Braiding is one of the most common technique employed for the manufacture of fabrics and ropes. It is also commonly used to produce near-net shaped preforms for advanced fibre reinforced composites. This paper presents an explicit finite element approach to create and simulate the braiding process for the virtual manufacture of 2D braids. The process starts from the definition of an analytical function which describes the movement of the carriers on a braiding track plate. Models of idealised Maypole-type braiding machines are built and used to shape virtual yarns into braids. This procedure can be used in a parameter control fashion, to optimise or to create virtual braided structures, which can serve as input for other structural analyses. It is emphasised that multiple cylinders are required for the modelling of a multifilament yarn to achieve better correlation with the experimental results. A parametric study is presented to investigate the effect of the number of virtual cylinders to represent a real yarn and the shape of the final braid. Excellent correlation was found between the virtual models and the experimental results when comparing the braid angle and yarn width.

A Novel CAE Method for Compression Molding Simulation of Carbon Fiber-Reinforced Thermoplastic Composite Sheet Materials

Its high-specific strength and stiffness with lower cost make discontinuous fiber-reinforced thermoplastic (FRT) materials an ideal choice for lightweight applications in the automotive industry. Compression molding is one of the preferred manufacturing processes for such materials as it offers the opportunity to maintain a longer fiber length and higher volume production. In the past, we have demonstrated that compression molding of FRT in bulk form can be simulated by treating melt flow as a continuum using the conservation of mass and momentum equations. However, the compression molding of such materials in sheet form using a similar approach does not work well. The assumption of melt flow as a continuum does not hold for such deformation processes. To address this challenge, we have developed a novel simulation approach. First, the draping of the sheet was simulated as a structural deformation using the explicit finite element approach. Next, the draped shape was compressed using fluid mechanics equations. The proposed method was verified by building a physical part and comparing the predicted fiber orientation and warpage measurements performed on the physical parts. The developed method and tools are expected to help in expediting the development of FRT parts, which will help achieve lightweight targets in the automotive industry.

An explicit Lagrangian finite element method for free-surface weakly compressible flows

In the present work, an explicit finite element approach to the solution of the Lagrangian formulation of the Navier-Stokes equations for weakly compressible fluids or fluid-like materials is investigated. The introduction of a small amount of compressibility is shown to allow for the formulation of a fast and robust explicit solver based on a particle finite element method. Newtonian and Non-Newtonian Bingham laws are considered. A barotropic equation of state completes the model relating pressure and density fields. The approach has been validated through comparison with experimental tests and numerical simulations of free surface fluid problems involving water and water–soil mixtures.

Numerical procedure for fatigue life prediction for railway turnout crossings using explicit finite element approach

In this paper a numerical procedure for analysis of rolling contact fatigue crack initiation and fatigue life prediction for the railway turnout crossing is presented. To analyse wheel–rail interaction, a three-dimensional explicit finite element (FE) model of a wheelset passing a turnout crossing is developed to obtain the dynamic responses such as the contact forces, displacements and accelerations as well as the stresses and strain in the crossing nose. The material model accounting for elastic–plastic isotropic and kinematic hardening effects in rails is adopted. The fatigue life of the rails is defined as the time to rolling contact fatigue crack initiation. In predicting the fatigue life Jiang and Sehitoglu model is used, which is based on the critical plane approach. Using the FE simulation results the ten critical locations on the crossing nose susceptible to crack initiation are determined first. Then, using the fatigue model the critical planes in these locations are obtained and the number of cycles to fatigue crack initiation is calculated for each location, based on which the most decisive location and the crossing life is determined. The results of the numerical simulations are presented and discussed.

A wheel set/crossing model regarding impact, sliding and deformation—Explicit finite element approach

A dynamic finite element model for the process of a wheel passing the crossing panel of a turnout is presented. This model accounts for the dynamic process, the elastic deformations of the wheel and the elastic–plastic deformations of the crossing. The axle and the second wheel are accounted for in terms of their influence on the angular velocity of the wheel.The model provides the dynamical contact forces between the wheel and the crossing parts, the vertical wheel displacement, the development of the angular velocity of the wheel as well as the stress fields and the plastic deformations in the crossing. Results that indicate the loading of the surface, such as the contact pressure and the microslip, are also provided by the model. From them, the specific frictional work and the maximum of the specific frictional power are derived. Those values are associated with surface damage such as wear and Rolling Contact Fatigue (RCF). An empirical relationship between the frictional work and wear is widely used and called Archard's wear law. For the formation and propagation of surface cracks there is no simple relationship.Results for the wheel initially running on the wing rail and then impacting onto the crossing nose (facing move) and the other direction (trailing move) are presented for three velocities.The presented model can help in the optimization of crossings in terms of geometry, bedding and material, depending on the loading conditions such as train velocity, axle load and wheel profile for both the facing and trailing move.

Loosening Analysis for Swing Circle Tightening Body of Excavator Subjected to Impact Loading: Explicit Finite Element Approach

Loosening Analysis for Swing Circle Tightening Body of Excavator Subjected to Impact Loading: Explicit Finite Element Approach

An explicit finite element approach with patch projection technique for strain gradient plasticity formulations

Implicit and explicit finite element approaches are frequently applied in real problems. Explicit finite element approaches exhibit several advantages over implicit method for problems which include dynamic effects and instability. Such problems also arise for materials and structures at small length scales and here length scales at the micro and sub-micron scales are considered. At these length scales size effects can be present which are often treated with strain gradient plasticity formulations. Numerical treatments for strain gradient plasticity applying the explicit finite element approach appear however to be absent in the scientific literature. Here such a numerical approach is suggested which is based on patch recovery techniques which have their origin in error indication procedures and adaptive finite element approaches. Along with the proposed explicit finite element procedure for a strain gradient plasticity formulation some numerical examples are discussed to assess the suggested approach.

On attenuation of floating structure response to underwater shock

This paper presents an analysis on attenuation of floating structures response to underwater shock. An explicit finite element approach interfaced with the boundary element method is used for the shock-fluid–structure interaction. The bulk cavitation induced by underwater shock near the free surface is considered in this study. Two types of floating structural configurations are modeled: one is the two-layered panel and the other is the sandwich panel, both of which are extracted from the typical floating hulls—the former corresponds the single hull with coating material and the latter corresponds to the double hull with different material fillings. Their effective structural damping and stiffness are formulated and incorporated in the fluid–structure-coupled equations, which relate the structure response to fluid impulsive loading and are solved using the coupled explicit finite-element and boundary element codes. The cavitation phenomenon near free surface is captured via the present computational procedure. The attenuation effects of the floating structure response to underwater explosion are examined. From the results obtained, some insights on the improvement of floating structures to enhance their resistance to underwater shock are deduced.

Simulation of a knee joint replacement during a gait cycle using explicit finite element analysis

The stress distribution within the polyethylene insert of a total knee joint replacement is dependent on the kinematics, which in turn are dependent on the design of the articulating surfaces, the relative position of the components and the tension of the surrounding soft tissues. Implicit finite element analysis techniques have been used previously to examine the polyethylene stresses. However, these have essentially been static analyses and hence ignored the influence of the kinematics. The aim of this work was to use an explicit finite element approach to simulate both the kinematics and the internal stresses within a single analysis. A simulation of a total knee joint replacement subjected to a single gait cycle within a knee wear simulator was performed and the results were compared with experimental data. The predicted kinematics were in close agreement with the experimental data. Various solution-dependent parameters were found to have little influence on the predicted kinematics. The predicted stresses were found to be dependent on the mesh density. This study has shown that an explicit finite element approach is capable of predicting the kinematics and the stresses within a single analysis at relatively low computational cost.

Numerical Simulation of Cylindrical Laminated Shells Under Impulsive Lateral Pressure

The finite element approach used to investigate the behavior of cylindrical laminated shells when acted upon by sudden dynamic loads is described. When solving the dynamic buckling problem, two major time-integration techniques are used, namely, the implicit integration operator in its Newmark method implementation and the explicit central difference scheme. Their performance and efficiency are compared, and the conclusion is made that, unlike some other types of dynamic problems for dynamic shell stability, the explicit finite element approach shows good accuracy of results combined with an excellent computational efficiency. Therefore, this approach is applied in the present investigation. The loading acting upon the shell structure consists of lateral suddenly applied fluid pressure, which remains normal to the shell surface as the shell deforms. Two different dynamic buckling criteria are used and combined with the finite element method in the proposed solution procedure. A new approach for assessing shell stability by using the variation of the volume enclosed by the shell is proposed. A demonstration example is presented. The performance of the present approach is compared with previously published results.