Explicit Dynamic Method Research Articles

Integration process of stamping and welding for DP600 advanced high strength steel sheets

The springback behavior of AHSS (Advanced High Strength Steels) is more serious than ordinary mild steels. Currently, deformations due to springback can be compensated by modifying the tool geometry in the industry, which often consumes for a long time. In addition, the stamping parts usually need welding and assembly, and the welded part also has deformation. Therefore, an integrated process combines stamping and welding is presented in this paper, including stamping, placing welding parts and spot welding a total of 3 processes. This paper takes Ω-shaped parts as the object of study. The dynamic explicit method is adopted in the stamping process, and the static implicit method is used for the analysis of the stress release process. The effect of welding location, thickness of welding plate and width of welding plate on geometrical dimension are considered. Finally, the results of finite element analysis is evaluated by the validation experiment. The result shows that the combination of stamping and welding process can effectively reduce the springback value, and the deformation of the stamping part is less than 1mm. After the stress of the welded part is released, the stress on the inner and outer surface of the Ω-shaped part can be greatly reduced along the thickness direction.

Numerical Investigation of Water Entry Problem of Pounders with Different Geometric Shapes and Drop Heights for Dynamic Compaction of the Seabed

The water entry problem of three-dimensional pounders with different geometric shapes of cube, cylinder, sphere, pyramid, and cone was numerically simulated by the commercial software Abaqus, and the effects of pounder shape and drop height from the free surface of water on deepwater displacement and velocity as well as pinch-off time and depth were investigated. An explicit dynamic analysis method was employed to model fluid-structure interactions using a Coupled Eulerian-Lagrangian (CEL) formulation. The simulation results are verified by showing the computed shape of the air cavity, displacement of sphere, pinch-off time, and depth which all agreed with the experimental results. The results reveal that the drag force of water has the highest and lowest effect on cubical and conical pounders, respectively. Increasing the pounder drop height up to the critical height leads to increased pounder velocity while impacting the model bed and more than the critical drop height has a reverse effect on pounder impact velocity. Pinch-off time is a very weak function of pounder impact velocity; but pinch-off depth increases linearly with increased impact velocity.

Effects of Cell Microtopology on the In-plane Dynamic Crushing Analysis of Re-entrant Square Cellular Material

With the development of three-dimensional printing technologies, so-called cellular materials have achieved increasing attention due to outstanding properties. Unlike pure solid structures, properties of cellular materials are influenced by both utilized material and cell microtopology. The present paper proposes a novel type of re-entrant square cellular material. To explore the relationship between microtopology and macrodynamic responses systematically, an explicit dynamic finite element simulation method is used. This work starts by constructing theoretical models of relative density employing a two-dimensional unit cell. Then, the effects of geometric features and configurations on dynamic properties are explored, and simulations indicate that variations of geometric parameters strongly affect properties and that the staggered re-entrant squares are more stable than the regular re-entrant squares. Subsequently, the effects of the impact velocity on dynamic crushing behaviors are elaborated. On this basis, the relationship of unit mass energy absorption and geometric features is obtained by employing the response surface method. Furthermore, with targets of maximum unit mass energy absorption and minimum relative density, the optimal structural parameters are achieved by using non-dominated sorting genetic algorithm. The study provides a detailed introduction to dynamic behaviors of cellular materials and guidance to design new structures with superior characteristics of energy absorption.

Barlow's method of superconvergence for higher-order finite elements and for transverse stresses in structural elements

In this paper, Barlow's method for determining superconvergent stress/strain points is examined for higher-order finite elements, with particular interest in ones proven in lumped mass explicit dynamic methods, and for transverse stresses in structural elements computed via equilibrium equations. Others have found that for Lagrange polynomial finite elements with equidistant nodes, Barlow and Gauss-Legendre points are coincident for linear and quadratic elements, but are different for cubic and higher order interpolations. The reason for this non-coincidence is identified herein, whereby it is shown to be a result of poor-performing interpolation functions using equal nodal spacing Lagrange polynomials, which results in poor nodal displacement predictions—a violation of a basic premise of Barlow's method. The paradox is shown to be eliminated by using better interpolation functions with “optimal” nodal locations defined by Gauss-Lobatto points. These “optimal” higher-order elements are shown to compute exact superconvergent nodal displacements for one-dimensional bars, and consistent with lower-order elements, the stress/strain superconvergent points predicted by Barlow's method are found to be Gauss-Legendre points of the same precision rule as that of the Gauss-Lobatto rule used for the nodal locations. Barlow's method thus has a sound theoretical foundation for higher-order elements. The coincidence of Barlow with Gauss-Legendre points has been confirmed to be the case for up to 9th order “optimal” nodal location elements in one, two, and three dimensions, which retains the same number of degrees of freedom and also noticeably increases the critical time increment in explicit methods. In addition, calculation of transverse stresses in structural elements, via integration of three-dimensional equilibrium equations, is examined from Barlow's superconvergence viewpoint. Barlow's method provides a distinct means to determine superconvergent points for higher-order derivatives of displacement fields, as necessary for this procedure, and explains the observations of others in computing static transverse stresses from equilibrium equations. A brief catalogue of the newly defined Barlow points for transverse stresses in common element types is provided.

Analysis of the progressive collapse of space truss structures during earthquakes based on a physical theory hysteretic model

This study develops a force–displacement hysteresis model (computer program) for a bar element based on a physical theory model. The model is capable of capturing complex physical phenomena of member, such as yielding under tension, non-elastic buckling under compression, growth effect and degradation of buckling capacity due to the Bauschinger effect. The proposed element model is validated by comparing the simulation results with previous experimental results and is applied to the dynamic analysis of space truss structures. The explicit dynamic analysis method is adopted for solving the nonlinear equations of motion. Furthermore, a case study of a three-layer space truss structure is conducted. The reliability of the proposed algorithm and the need to develop the bar element are verified by comparing the results obtained using the proposed method and the ANSYS finite element analysis software package. Moreover, several fracture criteria for bar elements are defined and are used to analyse the progressive collapse of a space truss structure under seismic loading. The analytical results demonstrate that the selection of the fracture criterion for the bar members significantly affects the calculation of the collapse of the space truss structure under seismic loading. The strut buckling/softening-based fracture criterion can be used to relatively accurately evaluate the collapse resistance of a space truss structure under seismic loading. Finally, the collapse mode of a power transmission tower model under seismic loading is simulated. The simulation results are then compared with the collapse mode of a power transmission tower with a similar structure that collapsed during the Wenchuan earthquake. The simulation results agree closely with the observations, thereby verifying the reliability of the proposed algorithm.

Investigation on erosion mechanism in ultrasonic assisted abrasive waterjet machining

The abrasive erosion mechanism in ultrasonic assisted abrasive waterjet machining is investigated in the present study. The process was theoretically analyzed and a numerical model for the abrasive particle impact process considering the target workpiece vibration was developed. A time-dependent load was imposed on the model boundary to apply the vibration. The model was utilized to investigate the response of target material with explicit dynamic method. Effects of ultrasonic vibration and other process parameters on the material removal and response such as residual stress were investigated. Analysis on erosion process by multiple particles in ultrasonic vibration assisted AWJ was also carried out. The model was finally verified by experiments. The results indicate that the application of ultrasonic vibration can enhance the material removal capacity of the abrasive particle and intensify the material deformation.

Residual ultimate strength assessment of double hull oil tanker after collision

The aim of the present study is the assessment of a residual ultimate strength of an Aframax-class double hull oil tanker damaged in collision. A contribution to the research of the problem is given in a systematic investigation of the influence of the rotation of neutral axis (NA), which is performed by imposing appropriate boundary conditions. Nonlinear finite element method (NFEM), using explicit dynamic integration method implemented in LS-Dyna, is employed. NFEM results are compared with the IACS CSR progressive collapse analysis (PCA) method. Residual strength diagrams are developed for a rapid residual ultimate longitudinal strength assessment in both sagging and hogging and accounting for correction factor because of the rotation of NA. Following this, developed diagrams are compared with previously published researches. The results of this study may be used by classification societies in a Rules development process, in the risk assessment studies of the maritime transportation and for a quick calculation of the hull girder residual strength of a damaged ship in the situation requiring emergency response action.

Study on Surface Roughness of Al2024 Alloy during Shot Peening Process Based on Finite Element Method

Based on the explicit dynamic analysis method, the finite element models of successive shots and multiple shots for shot peening process are established by using LS-DYNA software.The simulations of the elastic-plastic dynamic process of shots impacting on a metallic target during shot peening process were accomplished. For Al2024-T3 alloy plate, the surface roughness induced by shot peening is studied and the effect of overlapping on the general trend is evaluated.The analysis results show that the surface roughness increases rapidly at the initial stage of shot peening and forms micro-scale pits. With the increase of the coverage, the surface deformation increased slowly when the surface coverage reached 100%.

Study on influence of nonlinear finite element method models on ultimate bending moment for hull girder

The various assessment methods of ultimate strength for hull girder of ships or offshore structures might lead to different results and computation time. The nonlinear finite element (FE) analyses include the implicit static analysis and explicit dynamic analysis, which both can consider the large deflection and material nonlinearity during the process of progressive collapse. Comparing with the implicit static analysis, the explicit dynamic analysis can consider the transient influence of time and avoid the convergence issue in iterative procedure. The object of the present paper is to figure out a reliable and suitable FE modelling in the explicit dynamic method, which could keep the balance of the acceptable accurate results and computation resources. Several influential factors on the collapse behaviours of hull girder are discussed including boundary conditions, geometric ranges of finite element model, element types, loading methods and loading time. The results of a Suezmax oil tanker and Reckling models assessed by the explicit dynamic method are compared with that by the other analytical methods or in the experiment.

Finite element modeling and pyroshock response analysis of separation nuts

Separation nuts are widely used as release devices to fasten and separate substructures of launching systems in aerospace applications. High shock transient response is generated during the separation of release devices, which tends to cause damage to the nearby micro mechanism and hardware. The purpose of this article is to predict the shock response of separation nut and find out the sensitive parameters for shock response. In this article, the explicit dynamics method hydrocodes is adopted to model the separation nuts, upon which the pyroshock response is investigated. Firstly, the separation mechanism of the nuts is introduced. Then, a FE model for the separation nuts is developed using hydrocodes software ANSYS/Autodyn, which is validated by comparing the simulation results with the pyroshock test data in shock response spectrum (SRS). Finally, the effects of the preload level and the amount of explosive on the pyroshock response are discussed. The simulation results demonstrate that decreasing the preload level is a more efficient way to reduce the pyroshock received by the spacecraft.

Analysis of the seismic collapse of a high-rise power transmission tower structure

In this paper, an explicit dynamic analysis method is proposed to calculate the progressive collapse of a high-rise power transmission tower structure subjected to earthquake; the failure rule for member elements and the effect of different ground motion inputs and tower heights on the tower's collapse pattern in an earthquake are investigated. The study results show that explicit dynamic analysis can be easily applied to member fractures and that this method is suitable for calculating the seismic collapse of a power transmission tower. The selection of the member element failure rule has a significant impact on the forecast collapse pattern of a power transmission tower in an earthquake. The compression member buckling and softening failure rule, coupling the material nonlinearity with elastic buckling phenomenon, can stave off the effort in modeling the constructional eccentricities, which result in Euler buckling. For different earthquake waves, the high-rise power transmission tower demonstrates different collapse failure modes. The static collapse pattern from a pushover analysis and the dynamic collapse pattern are very different. The actual collapse pattern of a power transmission tower during the Wenchuan earthquake and the computer simulated collapse pattern are compared to validate the algorithm proposed in this paper. Finally, the seismic collapse vulnerability of a high-rise power transmission tower is evaluated based on probability estimate method.

Analysis on Aircraft Brake Squeal Problem Based on Finite Element Method

Brake squeal phenomenon is a problem that has been long studied using multiple methods and theories. Finite Element Method (FEM) has been applied to the study of brake squeal problem. First, a disc brake model has been established. Complex mode theory has been applied to the mode analysis and unstable vibration modes can be extracted subsequently. The form of unstable vibration mode has been studied. Then, transient dynamic simulation using explicit dynamic method has been performed. Response in both time and frequency domain has been analyzed. Two methods have been compared, considering accuracy and calculation consumption. Then, the effect of different parameters such as coefficient of friction, stiffness, and brake force fluctuation frequency on squeal phenomenon has been analyzed. It can be found that coefficient of friction and the brake stiffness have a positive correlation with the extent of brake squeal phenomenon, while the frequency of brake force fluctuation should remain as low as possible. Afterwards, a ring-shaped layer of viscoelastic damping material is constrained to outer margin of the stator to restrain the unstable modal. This method can change the vibration nature and improve the brake squeal problem.

Seismic Response Analysis of Concrete Lining Structure in Large Underground Powerhouse

Based on the dynamic damage constitutive model of concrete material and seismic rock‐lining structure interaction analysis method, the seismic response of lining structure in large underground powerhouse is studied in this paper. In order to describe strain rate dependence and fatigue damage of concrete material under cyclic loading, a dynamic constitutive model for concrete lining considering tension and shear anisotropic damage is presented, and the evolution equations of damage variables are derived. The proposed model is of simple form and can be programmed into finite element procedure easily. In order to describe seismic interaction characteristics of the surrounding rock and lining, an explicit dynamic contact analysis method considering bond and damage characteristics of contact face between the surrounding rock and lining is proposed, and this method can integrate directly without iteration. The proposed method is applied to seismic stability calculation of Yingxiuwan Underground Powerhouse, results reveal that the amplitude and duration of input seismic wave determine the damage degree of lining structure, the damage zone of lining structure is mainly distributed in its arch, and the contact face damage has great influence on the stability of the lining structure.

Local stress analysis of a defective rolling bearing using an explicit dynamic method

This article provides insights into the localized stress in a defect zone of the rolling bearings when the rolling elements pass through the defect. A dynamic finite element model of a rolling bearing with an artificial round defect in its outer raceway is solved numerically using the explicit dynamic finite element software package, ABAQUS. The maximum Mises stress and maximum contact pressure in the defect zone are obtained in the simulation. The effects of radial load, rotation speed, and initial defect size on the stress level are investigated. The results show that higher stresses are generated during the rolling balls passing through the defect. The radial load and defect size have significant effects on the stress level of defect, while low-level rotation speed has neglected effects.

Dynamic programming for discrete-time finite-horizon optimal switching problems with negative switching costs

Abstract In this paper we study a discrete-time optimal switching problem on a finite horizon. The underlying model has a running reward, terminal reward, and signed (positive and negative) switching costs. Using optimal stopping theory for discrete-parameter stochastic processes, we extend a well-known explicit dynamic programming method for computing the value function and the optimal strategy to the case of signed switching costs.

Numerical Analysis of Influence of Cutting Edge Radius on the Minimum Thickness of the Machined Layer

Possibilities of miniaturization of products are constantly increasing and create numerous technological challenges at the same time. One of the important aspects of the machining process, which is the essence of this work, is the geometry of the cutting tool. This work aims to investigate the influence of three different radius of cutting edge on the minimum thickness of machined layer. The phenomena on a typical incremental step were described using a step-by-step incremental procedure, with an updated Lagrangian formulation. The machining process is considered as geometrical and physical non-linear initial and boundary problem. The finite element method (FEM) and the dynamic explicit method (DEM) were used to obtain the solution. The application was developed in the ANSYS/LS-DYNA system which makes possible a complex time analysis of the physical phenomena: states of displacements, strains and stresses. Numerical computations of the strain have been conducted with the use of methodology which requires a proper definition of the contact zone, without the necessity to introduce boundary conditions. Examples of calculations are presented and show what the depth of cut at a given radius of cutting edge allows achieving a minimum thickness of cutting.

A comparison between dynamic implicit and explicit finite element simulations of the native knee joint

The finite element (FE) method has been widely used to investigate knee biomechanics. Time integration algorithms for dynamic problems in finite element analysis can be classified as either implicit or explicit. Although previously both static/dynamic implicit and dynamic explicit method have been used, a comparative study on the outcomes of both methods is of high interest for the knee modeling community. The aim of this study is to compare static, dynamic implicit and dynamic explicit solutions in analyses of the knee joint to assess the prediction of dynamic effects, potential convergence problems, the accuracy and stability of the calculations, the difference in computational time, and the influence of mass-scaling in the explicit formulation. The heel-strike phase of fast, normal and slow gait was simulated for two different body masses in a model of the native knee. Our results indicate that ignoring the dynamic effect can alter joint motion. Explicit analyses are suitable to simulate dynamic loading of the knee joint in high-speed simulations, as this method offers a substantial reduction of the computational time with a similar prediction of cartilage stresses and meniscus strains. Although mass-scaling can provide even more gain in computational time, it is not recommended for high-speed activities, in which inertial forces play a significant role.

An accelerated explicit method with GPU parallel computing for thermal stress and welding deformation of large structure models

To simulate welding induced transient thermal stress and deformation of large scale FE models, an accelerated explicit method (ACEXP) and graphical processing units (GPU) parallel computing program of the finite element method (FEM) were developed. In the accelerated explicit method, a two-stage computation scheme is employed. The first computation stage is based on a dynamic explicit method considering the characteristics of the welding mechanical process by controlling both the temperature increment and time scaling parameter. In the second computation stage, a static equilibrium computation scheme is implemented after dynamic thermal loading to obtain a static solution of transient thermal stress and welding deformation. It has been demonstrated that the developed GPU parallel computing program has a good scalability for large-scale models of more than 20 million degrees of freedom. The validity of the accelerated explicit method is verified by comparing the transient thermal stress and deformation with those computed by an implicit FEM. Finally, welding deformation and residual stress in a structure model assembled from nine high-strength steel plates and 26 weld lines were efficiently analyzed by ACEXP and GPU parallel computing within 45 h. The computed welding deformation agreed well with measured results, and a good accuracy was obtained.

An Accelerated Explicit Method and GPU Parallel Computing for Thermal Stress and Welding Deformation of Automotive Parts

An accelerated explicit method and GPU parallel computing program of finite element method (FEM) are developed for simulating transient thermal stress and welding deformation in large scale models. In the accelerated explicit method, a two-stage computation scheme is employed. The first computation stage is based on a dynamic explicit method considering the characteristics of the welding mechanical process by controlling both the temperature increment and time scaling parameter. In the second computation stage, a static equilibrium computation scheme is implemented after thermal loading to obtain a static solution of transient thermal stress and welding deformation. It has been demonstrated that the developed GPU parallel computing program has a good scalability for large scale models of more than 20 million degrees of freedom (DOFs). The validity of the accelerated explicit method is verified by comparing the transient thermal deformation and residual stresses with those computed by the implicit FEM and experimental measurements. Finally, the thermal stress and strain in an automotive engine cradle model with more than 12 million DOFs were efficiently computed and the results are discussed.

Explicit Dynamic DDA Method considering Dynamic Contact Force

This paper proposes an explicit dynamic DDA method considering dynamic contact force, which aims at solving the problems of low efficiency of dynamic contact detection and the simulation of dynamic contact force in the conventional DDA method. The mutual contact between blocks can be regarded as the application of point loading on a single block, and the corresponding contact submatrix can be calculated and the simultaneous equations of the block system can be integrated. The central difference method is adopted to deduce the explicit expression of block displacement containing dynamic contact force. With the relationship between displacement and dynamic contact force, contact constraint equations of a block system are obtained to calculate the dynamic contact force and the corresponding block displacement. The accuracy of the explicit dynamic DDA method is verified using two numerical cases. The calculation results show that the new DDA method can be applied in large-scale geotechnical engineering.