Explicit Finite Element Method Research Articles

Transient Dynamic Characteristics of a Non-Pneumatic Mechanical Elastic Wheel Rolling Over a Ditch

The transient dynamic characteristic of a tire, which has a significant effect on vehicle handling stability and ride comfort, is difficult to study in detail because of its highly non-linear behavior. In this study, the transient dynamic characteristics of a non-pneumatic wheel, called the mechanical elastic wheel (MEW), which was rolling over a ditch were investigated by the explicit dynamic finite element (FE) method. A three-dimensional FE model of MEW considering geometric nonlinearity, material nonlinearity and large contact deformation between the wheel and the road, was established. For the validation of the accuracy and reliability of the FE model of MEW, the simulation and the experimental results of the radial stiffness and footprint of MEW were compared and analyzed. A dynamic simulation of the validated FE model of MEW rolling over a ditch was conducted using the ABAQUS/Explicit program. The equivalent stress and the contact stress generated during the process of the rolling MEW impacting the ditch were studied in detail. The effect of the rolling speed on the transient dynamic characteristics was also analyzed based on the simulation results. The simulation results could provide guidance for the optimization of the MEW structure and vehicle dynamics.

A simple and systematic scheme implemented in explicit FEM solver for surface tension effects in powder injection moulding process

In order to simulate more accurately the powder injection moulding process, the explicit finite element method solver is extended with the surface tension effect. The evaluation of surface tension takes the notion of pressure boundary method, while a simple and systematic scheme is proposed to fit the finite element method solver for the Laplacian operator. Because of the difference in dimension for filling function and velocity function, the integration of filling function in second derivative is not suitable to be transformed into the boundary integration and the integration of function in lower order derivative. To evaluate conveniently the curvature of filling front, hence the force of surface tension, a simple and systematic scheme is suggested and implemented into the finite element method solver. This specific scheme includes only the vectorial operations in low cost, and is completely systematic without piecemeal operations. Fitness of the proposed method is proved by the numerical examples of filling flow in a small-scaled channel. It shows the considerable effect of surface tension for the problems in micro-scale of sub-millimeter sizes, in which the boundary conditions at front surface are not negligible in powder injection moulding process. The surface tension effect becomes the dominating role for governing the trace and shape of filling front, which can no longer be neglected.

A new criterion for loading time determination with minimum dynamic effects in quasi-static contact modeling

PurposeThe explicit finite element method (FEM) is one of the most popular approaches in quasi-static contact analysis which involves highly nonlinear friction and large deformation. Usually, a high loading rate is expected to improve computation efficiency in FEM. However, a higher loading rate often results in significant dynamic effects in the simulations. This study aims to propose a new criterion to achieve a good balance between a high loading rate and minimal dynamic effects.Design/methodology/approachThe proposed criterion is based on the fluctuation of total strain energy as well as the smoothness of its first derivative to determine the proper loading time with an acceptable level of dynamic effect.FindingsAsperities’ sliding contact and Hertz contact problems have been solved with the proposed criterion to verify its validity. The simulations show that the computation efficiency with the proposed criterion can be improved by up to 80 per cent compared to the regular energy ratio criterion.Originality/valueThis criterion will provide a valuable tool in determining the proper loading time to improve the computation efficiency for quasi-static analysis of asperities’ contacts.

Modelling of strain softening materials based on equivalent damage force

The main aim of the work presented in this paper was treatment of damage and deformation localisation observed in the finite element method (FEM) analysis of strain softening materials combined with local constitutive models where damage is represented using continuum damage mechanics (CDM). The CDM/FEM approach typically suffers from a number of shortcomings, including mathematical (change of the type of partial differential equations leading to ill-posed boundary value problem), numerical (pronounced mesh dependency) and physical (infinitely small softening zone with the zero dissipated energy). The approach proposed here is still based on the local constitutive model including damage, but introduces an alternative representation of damage effects in the system of linear momentum balance equations. The damage effects are included through equivalent damage force (EDF), which contributes to the right-hand side of the momentum balance equations. The main advantages of this approach are that the problem remains well posed, as the type of partial differential equations remains unchanged when the material enters softening; numerical stability is preserved without a need for regularisation measures; and significantly reduced mesh dependency. In addition, the EDF approach can be used in combination with existing local CDM damage models and does not violate symmetry of the material stiffness tensor.The EDF approach is applicable to modelling of strain softening typically observed in damaged quasi brittle materials such as fibre reinforced composites and concrete.The EDF model was implemented in the in-house developed coupled FEM-SPH code, where an explicit FEM code is coupled with a stable Total-Lagrange form of SPH. Its performance is demonstrated in the analysis of a dynamic one dimensional (1D) stress wave propagation problem, which was analytically solved by Bazant and Belytschko in 1985. For a range of loading rates that correspond to the material softening regime, the numerical results shown nonlocal character with a finite size of the damaged zone, controlled with the damage characteristic length, which can be experimentally determined and is an input parameter independent of the discretisation density.

Spring-back analysis in the cold-forming process of ship hull plates

Hull structures and offshore structures are composed of curved thick plates. Line heating method has traditionally been used to produce such curved plates. However, it is recognized that the hot-forming process causes a variety of issues on doubly or multiple curved plates. A multi-point forming mechanism with square press heads is a new forming process for 3D ship hull plate. Cold working has a high dimensional accuracy but results in spring-back. In this paper, the cold-forming process using explicit dynamic finite element method (FEM) and its spring-back process using implicit FEM were analyzed, and the impact of curvature and thickness on spring-back of hull plates was discussed. Moreover, the validity of the numerical method was confirmed by comparison with experimental results.

Dynamic axial crush analysis and design optimization of a square multi-cell thin-walled tube with lateral variable thickness

In this paper, we proposed a strategy to improve the energy absorption efficiency of a square multi-cell tube by designing the lateral wall thickness distribution. We uniformly arranged the walls so that we could vary the thickness of the walls while forming a square multi-cell tube. Explicit formulations for predicting the mean crushing force of the multi-cell tube under axial compression were derived based upon the Super Folding Element method. The energy absorption capacities of a variety of typical square multi-cell tubes with different lateral thickness distribution were obtained by theoretical and numerical analysis. The predicting results of the formulations have good agreement with the numerical simulation performed by explicit non-linear finite element method. The theoretical and numerical results showed that the energy absorption capacities could be improved by modifying the lateral thicknesses of the multi-cell tube. The optimization based on a surrogate model and the explicit prediction formulations was carried out to find the optimal lateral thickness distribution of 3 × 3 square multi-cell tube. We found that the tube has better energy absorption properties when the material is concentrated in the center of the cross-section. Based on the optimization results, a non-convex multi-corner multi-cell square tube with lateral variable thickness was proposed that resulted in a 48.3% improvement in energy absorption capacity compared with traditional uniform thickness multi-cell tube.

Explicit finite element analysis of failure behaviors of thermoplastic composites under transverse tension and shear

This paper studies failure behaviors of glass fiber/PC resin thermoplastic composites under transverse tension and shear loads using explicit finite element method. Microscopic long fiber/matrix composite representative volume elements with randomly distributed fibers and periodic boundary conditions are established by ABAQUS-PYTHON script language. The finite-deformation viscoplastic Gurson model is used for predicting the plastic deformation and void growth of thermoplastic glassy polymer matrix, which is implemented using ABAQUS-VUMAT explicit subroutine. The bilinear cohesive model with finite-thickness interface element is used to simulate the fiber/matrix debonding. Three important issues are explored: first, effects of the cohesive interface strength on the plastic deformation and void growth of composites are studied using three mesh models and three fiber distributions. Second, failure surface under different tensile and shear displacement ratios is obtained, compared with the predictions using the Hashin and Puck failure criteria developed mainly for thermoset composites. Finally, the influence of the plastic softening effect of matrix on the strain concentration or localization behaviors is discussed. Results show the tension/shear load ratio and the cohesive interface strength produce large effects on the void growth and failure surface of composites, but fiber distribution shows a small effect on transverse load-bearing ability of composites.

Research on the Vibration Insulation of High‐Speed Train Bogies in Mid and High Frequency

According to a large amount of the test data, the mid and high frequency vibrations of high‐speed bogies are very notable, especially in the 565~616 Hz range, which are just the passing frequencies corresponding to the 22nd to 24th polygonal wear of the wheel. In order to investigate the main cause of wheel higher‐order polygon formation, a 3D flexible model of a Chinese high‐speed train bogie is developed using the explicit finite element method. The results show that the couple vibration of bogie and wheelset may lead to the high‐order wears of wheel. In order to reduce the coupled resonance of the wheelset and the bogie frame, the effects of the stiffness and damping of the primary suspensions, wheelset axle radius, and bogie frame strength on the vibration transmissibility are discussed carefully. The numerical results show that the resonance peaks in high frequency range can be reduced by reducing the stiffness of axle box rotary arm joint, reducing the wheelset axle radius or strengthening the bogie frame location. The related results may provide a reference for structure improvement of the existing bogies and structure design of the new high‐speed bogies.

Numerical modeling of ultrasonic wave propagation - by using of explicit FEM in ABAQUS

Monitoring of structures implies integration of sensors and actuators, smart materials, data transfer as well as computer analyses and simulations with the purpose of damage detection, localization, assessment and prediction of the state of damage at the certain moment and in time. This paper presents the application of the explicit finite element method for modeling of the wave propagation. The examples of concrete plates and thin steel plates in which the propagation of the Lamb waves occur were analyzed. Explicit finite element method was shown to be very efficient even for the waves in ultrasound range. Efficiency, ease of the use and reliability of the wave propagation modeling by the explicit finite element method can contribute to the development of a new and the improvement of the existing methods for the monitoring of structures. The main purpose of this paper is to demonstrate a waveform propagation model using an explicit FEM in ABAQUS software.

Comparison between numerical analysis and the levitation mass method measurement test of a spherical structure early impacting water

In order to precisely measure water impact loads of a spherical structure vertically dropping onto a calm water surface, a new validity check of the analysis using the levitation mass method experiment is proposed. The main feature of levitation mass method experiment is to obtain a better estimation of early water impact loads through the application of Doppler effect. Experimental results of different heights are verified based on the Assessment Index and are in comparison with the classical experimental data for validation purpose. It shows that the levitation mass method measurement is useful and effective to obtain the water impact loads for the crashworthiness analysis. Besides, early water impact hydrodynamic behaviors are simulated based on the nonlinear explicit finite element method, together with application of a multi-material arbitrary Lagrangian–Eulerian solver. A penalty coupling algorithm is utilized to realize fluid–structure interaction between the spherical body and fluids. Convergence studies are performed to construct the proper finite element model by the comparison with experimental results, where mesh sensitivity, contact stiffness, and time-step size parametric studies are thoroughly investigated. The comparisons between experimental and numerical results show good consistency by the prediction of the water impact coefficients on the structure.

Parallelized implementation of an explicit finite element method in many integrated core (MIC) architecture

Hardware accelerators are becoming increasingly important in boosting high performance computing systems. In this study, we develop a parallel explicit finite element (FE) analysis system based on a many integrated core (MIC) architecture for fast simulation of nonlinear dynamic problems of plate and shell structures. To minimize data transfer between heterogeneous architectures, parallel computation of the all explicit FE calculation is realized by developing a vectorized thread-level parallelism algorithm. The parallelism includes a novel dependency relationship link based method for efficiently solving parallel explicit shell element equations. A heterogeneous model is established to overlap data transfer and offloaded computation, and thus reduce the time required for large intermediate data storage in the actual engineering nonlinear problem simulation. Finally, a high performance nonlinear dynamic simulation system is developed. The simulations of benchmarks and engineering problems show that the parallel computing method proposed in this paper can give full play to the hardware performance of MIC architecture and effectively improve the computation efficiency of an explicit FE solution. For a bus body model containing approximately 3.8 million degrees of freedom, the computational speed is improved 17 times over CPU sequential computation, and the relative speedup grows with the increasing number of threads, the highest relative speedup exceeds 80.

Implicit–explicit multistep finite-element methods for nonlinear convection-diffusion-reaction equations with time delay

ABSTRACTIn this paper, two classes of implicit–explicit (IMEX) multistep finite-element methods are constructed to solve the nonlinear delay convection-diffusion-reaction equations. This equations are discretized with finite-element method in space and IMEX multistep methods (including IMEX one-leg methods and IMEX linear multistep methods) in time. The resulting schemes are efficient because it can reduce the coupling degree, and avoid solving the large-scale systems of nonlinear algebraic equations. The -norm error estimates with handling the breaking point and stability results for the proposed methods are obtained. Numerical results demonstrate the efficiency and accuracy of the approaches.

Asynchronous parallel algorithm for three-dimensional soil-structure interaction analysis based on explicit-implicit integration scheme

A computationally efficient explicit-implicit FEM in parallel manner to analyze the response of three-dimensional soil-structure system subjected to seismic wave is presented. The unbounded soil is modelled by lumped-mass explicit finite element method and viscoelastic artificial boundary, the structure is analysed through implicit finite element method, and response of the rigid foundation is calculated through explicit time integration scheme. The different time steps can be chosen for the explicit and implicit integration scheme, which can greatly improve the efficiency. The synchronous and asynchronous parallel algorithms using MPI are proposed for the soil-structure interaction analysis. The codes for this method are programmed. Example for seismic response analysis of a nuclear plant is given, which validates the feasibilty and efficiency of the proposed method.

Lode dependent plasticity coupled with nonlinear damage accumulation for ductile fracture of aluminium alloy

The experimental program was designed and proportional tests carried out at a room temperature on aluminium alloy 2024-T351. These concerned tension, torsion and compression, in order to investigate the damage accumulation nonlinearity and to reliably calibrate new phenomenological ductile fracture criterion. This fracture model, KHPS2, expressed through the fracture strain, was dependent on the stress triaxiality and normalized third invariant of deviatoric stress tensor. The ductile fracture model was then coupled with the yield criterion, as in the continuum damage mechanics, using the material softening. The plasticity model was considered in the form of taking into account the Lode dependence for investigated material, through normalized third invariant of deviatoric stress tensor. The whole approach, fully applicable to multiaxial ductile fracture related problems, was implemented using the user subroutine into the commercial software, based on the explicit finite element method. In the end, the proposed approach was verified using chosen realized fracture tests, which were used in the calibration, and newly designed KHPS2 criterion along with an existing one—modified Hosford–Coulomb model. The latter model showed better performance in simulations despite worse approximation ability, which can be attributed to its micromechanically-motivated formulation.

Numerical Evaluation of Dynamic Response for Flexible Composite Structures under Slamming Impact for Naval Applications

The deformable composite structures subjected to water-entry impact can be caused a phenomenon called hydroelastic effect, which can modified the fluid flow and estimated hydrodynamic loads comparing with rigid body. This is considered very important for ship design engineers to predict the global and the local hydrodynamic loads. This paper presents a numerical model to simulate the slamming water impact of flexible composite panels using an explicit finite element method. In order to better describe the hydroelastic influence and mechanical properties, composite materials panels with different stiffness and under different impact velocities with deadrise angle of 100 have been studied. In the other hand, the inertia effect was observed in the early stage of the impact that relative to the loading rate. Simulation results have been indicated that the lower stiffness panel has a higher hydroelastic effect and becomes more important when decreasing of the deadrise angle and increasing the impact velocity. Finally, the simulation results were compared with the experimental data and the analytical approaches of the rigid body to describe the behavior of the hydroelastic influence.

Three-dimensional metal particle flow simulation during the whole rolling process for 60 kg/m heavy rail

Three-dimensional metal particle flow simulation during the whole rolling process for 60 kg/m heavy rail was accomplished by explicit dynamic finite element method and modified updating geometric m...

Hybrid approach for two dimensional damage localization using piezoelectric smart aggregates

In the paper, a novel approach for damage localization in reinforced concrete plates, based on the computational analysis of piezoelectric smart aggregates, has been presented. The hybrid approach for damage localization is based on two criteria: wave propagation energy and time of flight. The comprehensive numerical analysis using standard and explicit finite element method has been conducted. In addition, the proposed algorithm of the hybrid method has been coded in MATLAB. The approach has been verified numerically using different square reinforced concrete plate models, considering different number, position and size of damage, as well as different number and position of the piezoelectric smart aggregates. Obtained results confirm the successful application of the novel approach to the damage localization.

A partitioned fully explicit Lagrangian finite element method for highly nonlinear fluid‐structure interaction problems

SummaryIn this work, a fully explicit partitioned method for the simulation of Fluid Structure Interaction (FSI) problems is presented. The fluid domain is modelled with an explicit Particle Finite Element Method (PFEM) based on the hypothesis of weak compressibility. The Lagrangian description of the fluid is particularly effective in the simulation of FSI problems with free surface flows and large structural displacements, since the fluid boundaries are automatically defined by the position of the mesh nodes. A distinctive feature of the proposed FSI strategy is that the solid domain is modelled using the explicit integration FEM in an off‐the‐shelf commercial software (Abaqus/Explicit). This allows to perform simulations with a complete and advanced description on the structural domain, including advanced structural material models and contact. The structure‐to‐fluid coupling algorithm is based on a technique derived from the Domain Decomposition Methods, namely, the Gravouil and Combescure algorithm. The method allows for arbitrarily large interface displacements using different time incrementation and nonconforming meshes in the different domains, which is an essential feature for the efficiency of an explicit solver involving different materials. The resulting fully explicit and fully lagrangian finite element approach is particularly appealing for the possibility of its efficient application in a large variety of highly non‐linear engineering problems.

Nonlinear interaction between underwater explosion bubble and structure based on fully coupled model

The interaction between an underwater explosion bubble and an elastic-plastic structure is a complex transient process, accompanying violent bubble collapsing, jet impact, penetration through the bubble, and large structural deformation. In the present study, the bubble dynamics are modeled using the boundary element method and the nonlinear transient structural response is modeled using the explicit finite element method. A new fully coupled 3D model is established through coupling the equations for the state variables of the fluid and structure and solving them as a set of coupled linear algebra equations. Based on the acceleration potential theory, the mutual dependence between the hydrodynamic load and the structural motion is decoupled. The pressure distribution in the flow field is calculated with the Bernoulli equation, where the partial derivative of the velocity potential in time is calculated using the boundary integral method to avoid numerical instabilities. To validate the present fully coupled model, the experiments of small-scale underwater explosion near a stiffened plate are carried out. High-speed imaging is used to capture the bubble behaviors and strain gauges are used to measure the strain response. The numerical results correspond well with the experimental data, in terms of bubble shapes and structural strain response. By both the loosely coupled model and the fully coupled model, the interaction between a bubble and a hollow spherical shell is studied. The bubble patterns vary with different parameters. When the fully coupled model and the loosely coupled model are advanced with the same time step, the error caused by the loosely coupled model becomes larger with the coupling effect becoming stronger. The fully coupled model is more stable than the loosely coupled model. Besides, the influences of the internal fluid on the dynamic response of the spherical shell are studied. At last, the case that the bubble interacts with an air-backed stiffened plate is simulated. The associated interesting physical phenomenon is obtained and expounded.

Finite element analysis of damage and failure of reinforced concrete members under earthquake loading

SummaryThis paper presents a three‐dimensional analysis framework, based on the explicit finite element method, for the simulation of reinforced concrete components under cyclic static and dynamic loading. A recently developed triaxial constitutive model for concrete is combined with a material model for reinforcing steel which can account for rupture due to low‐cycle fatigue. The reinforcing bars are represented with geometrically nonlinear beam elements to account for buckling of the reinforcement. The strain penetration effect is also accounted for in the models. The modeling scheme is used in a commercial finite element program and validated with the results of experimental static and dynamic tests on reinforced concrete columns and walls. The analyses are supplemented with a parametric study to investigate the impact of several modeling assumptions on the obtained results.