Explicit Finite Element Method Research Articles

Stress Wave Attenuation in Noncollinear Structures Subjected to Impulsive Transient Loadings

AbstractThis paper presents an exploration of noncollinear Timoshenko beam structures for attenuating the stress waves generated from impulsive transient loadings. Due to the existence of the noncollinear segments, flexural waves are generated in addition to the longitudinal waves. Furthermore, the resulting waves are dispersive and thus provide higher potential for the attenuation of the stress waves. Symmetric patterns are found to be more appropriate for increasing the stress-wave attenuation capacity, as these patterns can eliminate bending stress effects at the boundary of the structures. More generally, an adaptive optimization methodology is developed to find the most efficient layout of the noncollinear stress-wave attenuators (NSWAs). This methodology uses genetic algorithms (GA), coupled with an explicit finite-element (FE) method for analyzing the wave-propagation behavior of the structures. The developed methodology is capable of updating the FE model of each trial solution, as the geometric c...

Parametric Study of Hydroforming of Paper Materials Using the Explicit Finite Element Method with a Moisture‐dependent and Temperature‐dependent Constitutive Model

A moisture‐dependent and temperature‐dependent constitutive model for paper materials was proposed and implemented into a finite element model of the paper hydroforming process. Experimental hydroforming was conducted at temperatures of 23°C and 110 °C and moisture contents of 6.9 and 10.6 (respectively corresponding to 50 and 80% relative humidity). The proposed model, which also included the effects of drying, captured the extent of forming of all experimental results within reasonable accuracy. For the moisture content and temperature conditions in this study, the phenomenon of drying was found to be the reason why the application of temperature had a much greater effect on the degree of forming than hydroforming at various moisture contents. A simulation‐based parametric study was conducted in order to identify the importance of various process and material parameters. This parametric study confirmed many previous empirical findings and was capable of quantifying the extent to which these process and material parameters affect the three‐dimensional formability of paper. The coefficient of friction was identified as one of the most important factors when determining the extent of forming. Copyright © 2016 John Wiley & Sons, Ltd.

Punchless Drawing of Magnesium Alloy Sheet Under Cold Condition and its Computation

Shallow cup drawing of magnesium alloy AZ31-O sheet was performed under cold condition using the Maslennikov’s technique. A deformable rubber pad was used, instead of the “hard” punch, in this technique. A small die profile radius was adopted, which was twice or four-times the sheet thickness. A semisolid lubricant was used for lubrication of the blank-die interface. On the other hand, the rubber-blank interface was degreased to increase friction. A limiting drawing ratio of 1.31 was obtained in the circular cup drawing. A peculiar fracture mode appeared in which the material suddenly fractured with the crack evolution emanating from the flange periphery. In the square cup drawing, an adequate blank shape was found to be circular compared with the other ones. Numerical simulation was also conducted using dynamic explicit finite element method. Adequate setting including speed scaling enabled us to predict the accurate deformation pattern and the forming force.

A modified integration rule for an explicit time-domain finite element method using rectangular elements for room acoustics simulations

A modified integration rule for an explicit time-domain finite element method using rectangular elements for room acoustics simulations

動的陽解法による樹脂ペレットの流動性向上のためのペレット形状最適化

動的陽解法による樹脂ペレットの流動性向上のためのペレット形状最適化

Prediction of residual stress using explicit finite element method

This paper presents the residual stress behaviour under various values of friction coefficients and scratching displacement amplitudes. The investigation is based on numerical solution using explicit finite element method in quasi-static condition. Two different aeroengine materials, i.e. Super CMV (Cr-Mo-V) and Titanium alloys (Ti-6Al- 4V), are examined. The usage of FEM analysis in plate under normal contact is validated with Hertzian theoretical solution in terms of contact pressure distributions. The residual stress distributions along with normal and shear stresses on elastic and plastic regimes of the materials are studied for a simple cylinder-on-flat contact configuration model subjected to normal loading, scratching and followed by unloading. The investigated friction coefficients are 0.3, 0.6 and 0.9, while scratching displacement amplitudes are 0.05 mm, 0.10 mm and 0.20 mm respectively. It is found that friction coefficient of 0.6 results in higher residual stress for both materials. Meanwhile, the predicted residual stress is proportional to the scratching displacement amplitude, higher displacement amplitude, resulting in higher residual stress. It is found that less residual stress is predicted on Super CMV material compared to Ti-6Al-4V material because of its high yield stress and ultimate strength. Super CMV material with friction coefficient of 0.3 and scratching displacement amplitude of 0.10 mm is recommended to be used in contact engineering applications due to its minimum possibility of fatigue.

An Explicit Quadrilateral Shell Element

The present study introduces a 4-node quadrilateral shell element (which is called EQ7) for the analysis of plates and shells. The element is a flat element with 6 degrees of freedom at each node; three displacements and three rotations. It is based on the Explicit Finite Element Method. All quantities, matrices, etc., are explicitly derived. We apply to the shell element a number of modes and besides the Modal Stiffness Matrix we introduce the Modal Mass Matrix and the Modal Geometric Matrix. We employ also an iterative scheme for the solution of the linear system of equations. Numerical simulations are provided. Stress Wave Patterns are found in deforming plates and shells. Because all quantities are explicitly derived, the theory and method is suited for efficient computer implementation.

An explicit time-domain finite element method for room acoustics simulations: Comparison of the performance with implicit methods

This paper presents the applicability of an explicit time-domain finite element method (TD-FEM) using a dispersion reduction technique called modified integration rules (MIR) on room acoustics simulations with a frequency-independent finite impedance boundary. First, a dispersion error analysis and a stability analysis are performed to derive the dispersion relation and the stability condition of the present explicit TD-FEM for three-dimensional room acoustics simulations with an infinite impedance boundary. Secondly, the accuracy and efficiency of the explicit TD-FEM are presented by comparing with implicit TD-FEM using MIR through room acoustics simulations in a rectangular room with infinite impedance boundaries. Thirdly, the stability condition of the explicit TD-FEM is investigated numerically in the case with finite impedance boundaries. Finally, the performance of the explicit TD-FEM in room acoustics simulations with finite impedance boundaries is demonstrated in a comparison with the implicit TD-FEM. Although the stability of the present explicit TD-FEM is dependent on the impedance values given at boundaries, the explicit TD-FEM is computationally more efficient than the implicit method from the perspective of computational time for acoustics simulations of a room with larger impedance values at boundaries.

The influence of metallic shell deformation on the contact mechanics of a ceramic-on-ceramic total hip arthroplasty.

Total hip arthroplasty of ceramic-on-ceramic bearing combinations is increasingly used clinically. The majority of these implants are used with cementless fixation that a metal-backing shell is press-fitted into the pelvic bone. This usually results in the deformation of the metallic shell, which may also influence the ceramic liner deformation and consequently the contact mechanics between the liner and the femoral head under loading. The explicit dynamic finite element method was applied to model the implantation of a cementless ceramic-on-ceramic with a titanium shell and subsequently to investigate the effect of the metallic shell deformation on the contact mechanics. A total of three impacts were found to be necessary to seat the titanium alloy shell into the pelvic bone cavity with a 1 mm diameter interference and a 1.3 kg impactor at 4500 mm s(-1) velocity. The maximum deformation of the metallic shell was found to be 160 µm in the antero-superior and postero-inferior direction and 97 µm in the antero-inferior and postero-superior direction after the press-fit. The corresponding values were slightly reduced to 67 and 45 µm after the ceramic liner was inserted and then modified to 74 and 43 µm under loading, respectively. The maximum deformation and the maximum principal stress of the ceramic liner were 31 µm and 144 MPa (tensile stress), respectively, after it was inserted into the shell and further increased to 52 µm and 245 MPa under loading. This research highlights the importance of the press-fit of the metallic shell on the contact mechanics of the ceramic liner for ceramic-on-ceramic total hip arthroplasties and potential clinical performances.

Interlaminar Stresses Calculation Using a Stacked-Shell Finite Element Modeling Approach

The innovative stacked-shell modeling approach is investigated in the frame of an explicit finite element method for the prediction of laminated structural elements' static response, focusing on the interlaminar stress calculation. The main advantage of the investigated stacked-shell modeling technique is the lower computational cost compared to conventional methods, for the same accuracy in displacement and stress results. A laminated plate under sinusoidally distributed transverse loading, a laminated strip under three-point bending and a laminated cylindrical shell under cylindrical bending have been used in the assessment of the developed methodology; static results referring to displacement and both in-plane and out-of-plane stresses of the investigated cases have shown that the proposed technique is highly efficient in the calculation of interlaminar stresses of composite structures, which provides the background for an accurate and efficient delamination prediction.

Effect of Housing Support on Bearing Dynamics

The objective of this investigation was to determine the effect of housing support on bearing performance and dynamics. In order to achieve the objective, an existing dynamic bearing model (DBM) was coupled with flexible housing model to include the effect of support structure on bearing dynamics and performance. The DBM is based on the discrete element method, in which the bearing components are assumed to be rigid. To achieve the coupling, a novel algorithm was developed to detect contact conditions between the housing support and bearing outer race and then calculate contact forces based on the penalty method. It should be noted that although commercial finite element (FE) software such as abaqus is available to model flexible housings, combining these codes with a bearing model is quite difficult since the data transfer between the two model packages is time-consuming. So, a three-dimensional (3D) explicit finite element method (EFEM) was developed to model the bearing support structure for both linear elastic and nonlinear inelastic elastomeric materials. The constitutive relationship for elastomeric material is based on an eight chain model, which captures hyperelastic behavior of rubber for large strains. The viscoelastic property is modeled by using the generalized Maxwell-element rheological model to exhibit rate-dependent behaviors, such as creep and hysteresis on cyclic loading. The results of this investigation illustrate that elastomeric material as expected has large damping to reduce vibration and absorb energy, which leads to a reduction in ball–race contact forces and friction. A parametric study confirmed that the viscoelastic stress (VS) contributes significantly to the performance of the material, and without proper amount of viscoelasticity it loses its advantage in vibration reduction and exhibits linear elastic material characteristics. As expected, it is also demonstrated that housing supports made of linear elastic material provide minimal damping and rely on the bearing friction to dissipate energy. A study of housing support geometry demonstrates that bearing support plays a large role on the dynamic performance of the bearing. Motion of bearing outer race is closely related to the geometry and symmetry of the housing.

Parametric analysis of a highly dynamical phenomena caused by a propeller blade loss

Dynamic phenomena can jeopardize the structural integrity of aerospace structures and engineers have developed different strategies to analyze them. One of the most highly dynamical and severe failures in an aircraft provided with turboprops is an airscrew blade loss. This article analyzes this event using implicit and explicit finite element methods including non-linear behaviors, damages, and several types of failures trying to identify the key parameters in the failure sequence. The model includes non-deterministic variables and studies its stochastic behavior through series of Monte Carlo simulations. The influence of lost blade size is studied in detail as well as the effect of stiffness and strength variations on the engine mounting system through elastomeric devices. In the paper, different parameters that can influence the phenomenon are studied, including propeller rotational frequency, structural damping, and angular position where the blade is lost.

Analysis method of ultimate hull girder strength under combined loads

The objective of this study is to propose an analysis method of ultimate hull girder strength under combined bending and torsion. The hull girder is modelled by a series of thin-walled beam elements and the average stress–average strain relationship of plate and stiffened panel elements under axial loads considering the effect of shear stress is implemented in the beam elements. First, a torsional moment is applied to the beam model for a whole model within the elastic range. Then, the ultimate bending strength of cross-sections is calculated applying Smith's method to beam elements considering the warping and shear stresses. The proposed simplified method is applied to the progressive collapse tests of scale models under combined loads. On the other hand, nonlinear explicit finite element method (FEM) is adopted for the analysis of the test models. The effectiveness of the simplified method is discussed comparing with the results of experiments and FEM analysis.

Analysis on the Rock–Cutter Interaction Mechanism During the TBM Tunneling Process

The accurate prediction of rock cutting forces of disc cutters is crucial for tunnel boring machine (TBM) design and construction. Disc cutter wear, which affects TBM penetration performance, has frequently been found at TBM sites. By considering the operating path and wear of the disc cutter, a new model is proposed for evaluating the cutting force and wear of the disc cutter in the tunneling process. The circular path adopted herein, which is the actual running path of the TBM disc cutter, shows that the lateral force of the disc cutter is asymmetric. The lateral forces on the sides of the disc cutter are clearly different. However, traditional solutions are obtained by assuming a linear path, where the later forces are viewed as equal. To simulate the interaction between the rock and disc cutter, a simple brittle damage model for rock mass is introduced here. Based on the explicit dynamic finite element method, the cutting force acting on the rock generated by a single disc cutter is simulated. It is shown that the lateral cutting force of the disc cutter strongly affects the wear extent of disc cutter. The wear mechanism is thus underestimated by the classical model, which was obtained by linear cutting tests. The simulation results are discussed and compared with other models, and these simulation results agree well with the results of present ones.

Computational method of large deformation and its application in deep mining tunnel

The characteristics of deep rock mass, such as the elastic resilience, creep, stress release, expansion, dilation and the long-term strength, are of great importance to the rock mass deformation and failure mechanism. However, there is not yet a constitutive model which can describe all these properties of the deep rock mass. The proposed dynamic failure constitutive model in this paper analyzes the elastic resilience and the dilation deformation of the surrounding rock mass during the unloading process, and the pre-peak (elastic and internal frictional hardening stages) and the post-peak(softening and residual failure stages) stages are also taken into account. A computational software has been coded based on the dynamic explicit finite element method. The constitutive model has also been implemented into this software. The complete stress–strain relation using the new model in numerical unloading test was obtained. The sensitivity of the parameters of the dynamic failure constitutive model has also been analyzed. Based on the long-term monitored data for Zhuji coal mine, the parameter inversion of the two different sections of the piebald mudstone has been conducted with the nonlinear least square method. Further, the whole process simulation of the deformation of Zhuji coal mine has been performed with the inversed parameters. A high degree of agreement on the deformation has been achieved by the comparison between the calculated and the measured data in actual engineering project.

유한요소해석을 이용한 차대차 측면충돌에 대한 연구

The deformed degree of car body varies largely with the collision part from side collision of car-to-car. In case of deformation of car body caused by collision, the movement is different as speed energy changes to strain energy. Generally, in the analysis of traffic accident, the movement of car after the collision is analyzed by law of conservation of motion and the error of energy absorption rate along the deformation of car body can be calibrated by inputting coefficient of restitution, but it is current situation that coefficient of restitution applied by referring to the research results of forward collision and backward collision because the research results of side collision is rare. Vehicle model of finite element method applied by structure of car body and materials of each component was analyzed by explicit finite element method, and coefficient of restitution and collision detection time along contact part of side collision was drawn by analyzing the results. Analysis result acquired through the law of conservation momentum by applying finally-computed coefficient of restitution and crash detection time compared to collision result of actual vehicle. As a result, the reliability of analysis was higher than the existing analysis method were acquired when applying the drawn initial input value that used finite element method analysis model.

An Energy-Based Approach in Predicting Failure of the Glazing Systems Subjected to Blast Loads

In an air blast, building windows break into high-velocity flying shards (annealed glass windows) or fragments (fully tempered windows) that are a primary source of injury to the buildings occupants. In order to successfully design these glazing systems against air blast loading, there should be a balance between the safety and security of the window panel and considerations for the physical appearance and cost-effectiveness, based on the proposed level of security and previous lessons learned. Better understanding of the glazing systems' failure due to the blast load characteristics is an important step forward in mitigating injuries. In this paper, glass failure dynamics is studied using energy methods and brittle failure theories combined with finite element simulations and techniques. Because both methods take into account glass panel characteristics and blast load intensities, employing explicit nonlinear finite element methods with analytical energy methods to model the brittle failure of the conventional building glazing systems is the superior strategy. The results of this study will be beneficial in development of more comprehensive blast- resistance design guidelines and a glazing injury model that will enhance the security of the buildings and improve the safety of the occupants during an air blast.

Finite element analysis of sliding distance and contact mechanics of hip implant under dynamic walking conditions.

An explicit finite element method was developed to predict the dynamic behavior of the contact mechanics for a hip implant under normal walking conditions. Two key parameters of mesh sensitivity and time steps were examined to balance the accuracy and computational cost. Both the maximum contact pressure and accumulated sliding distance showed good agreement with those in the previous studies using the implicit finite element analysis and analytical methods. Therefore, the explicit finite element method could be used to predict the contact pressure and accumulated sliding distance for an artificial hip joint simultaneously in dynamic manner.

A high performance crashworthiness simulation system based on GPU

Crashworthiness simulation system is one of the key computer-aided engineering (CAE) tools for the automobile industry and implies two potential conflicting requirements: accuracy and efficiency. A parallel crashworthiness simulation system based on graphics processing unit (GPU) architecture and the explicit finite element (FE) method is developed in this work. Implementation details with compute unified device architecture (CUDA) are considered. The entire parallel simulation system involves a parallel hierarchy-territory contact-searching algorithm (HITA) and a parallel penalty contact force calculation algorithm. Three basic GPU-based parallel strategies are suggested to meet the natural parallelism of the explicit FE algorithm. Two free GPU-based numerical calculation libraries, cuBLAS and Thrust, are introduced to decrease the difficulty of programming. Furthermore, a mixed array and a thread map to element strategy are proposed to improve the performance of the test pairs searching. The outer loop of the nested loop through the mixed array is unrolled to realize parallel searching. An efficient storage strategy based on data sorting is presented to realize data transfer between different hierarchies with coalesced access during the contact pairs searching. A thread map to element pattern is implemented to calculate the penetrations and the penetration forces; a double float atomic operation is used to scatter contact forces. The simulation results of the three different models based on the Intel Core i7-930 and the NVIDIA GeForce GTX 580 demonstrate the precision and efficiency of this developed parallel crashworthiness simulation system.

A scalable coupled surface–subsurface flow model

The coupling of physically-based models for surface and subsurface water flows is a recent concern. The study of their interactions is important both for water resource management and environmental studies. However, despite constant innovation, physically-based simulations of water flows are still time consuming. That is especially problematic for large and/or long-term studies, or to test a large range of parametrizations with an adjoint model. As the current trend in computing sciences is to increase the computational power with additional computational units, new model developments are expected to scale efficiently on parallel infrastructures. This paper describes a coupled surface–subsurface flow model that combines implicit and explicit time discretizations for the surface and subsurface dynamics, respectively. Despite that the surface flow has a faster dynamics than the subsurface flow, we are able to use a unique nearly-optimal time step for each submodel, hence improving the resources use. The surface model is discretized with an implicit control volume finite element method while the subsurface model is solved by means of an explicit discontinuous Galerkin finite element method. The surface and subsurface models are coupled by weakly imposing the continuity of water pressure. By imposing a threshold on the influence coefficients of the control volume finite element method, we can prevent the occurrence of unphysical fluxes in anisotropic elements. The proposed coupling is shown to produce results similar to state-of-the-art models for four different test cases while achieving better strong and weak scalings on up to 192 processors.