Multi-scale Simulation Method with Coupled Finite/Discrete Element Model and Its Application

The existing research on continuous structure is usually analyzed with finite element method (FEM) and granular medium with discrete element method (DEM), but there are few researches on the coupling interaction between continuous structure and discrete medium. To the issue of this coupling interaction, a multi-scale simulation method with coupled finite/discrete element model is put forward, in their respective domains of discrete and finite elements, the nodes follow force law and motion law of their own method, and on the their interaction interface, the touch type between discrete and finite elements is distinguished as two types: full touch and partial touch, the interaction force between them is calculated with linear elastic model. For full touch, the contact force is proportional to the overlap distance between discrete element and finite element patch. For partial touch, first the finite element patch is extended on all sides indefinitely to be a complete plane, the full contact force can be obtained with the touch type between discrete element and plane being viewed as full touch, then the full overlap area between them and the actual overlap area between discrete element and finite element patch are computed, the actual contact force is obtained by scaling the full contact force with a factor which is determined by the ratio of the actual overlap area to the full overlap area. The contact force is equivalent to the finite element nodes and the force and displacement on the nodes can be computed, so the ideal simulation results can be got. This method has been used to simulate the cutter disk of the earth pressure balance shield machine (EPBSM) made in North Heavy Industry (NHI) with its excavation diameter of 6.28 m cutting and digging the sandy clay layer. The simulation results show that as the gradual increase of excavating depth of the cutter head, the maximum stress occurs at the roots of cutters on the cutter head, while for the soil, the largest stress is distributed at the region which directly contacted with the cutters. The proposed research can provide good solutions for correct design and installation of cutters, and it is necessary to design mounting bracket to fix cutters on cutter head.

Study on spline wavelet finite-element method in multi-scale analysis for foundation

A new finite element method （FEM） of B-spline wavelet on the interval （BSWI） is proposed. Through analyzing the scaling functions of BSWI in one dimension, the basic formula for 2D FEM of BSWI is deduced. The 2D FEM of 7 nodes and 10 nodes are constructed based on the basic formula. Using these proposed elements, the multiscale numerical model for foundation subjected to harmonic periodic load, the foundation model excited by external and internal dynamic load are studied. The results show the pro- posed finite elements have higher precision than the tradi- tional elements with 4 nodes. The proposed finite elements can describe the propagation of stress waves well whenever the foundation model excited by extemal or intemal dynamic load. The proposed finite elements can be also used to con- nect the multi-scale elements. And the proposed finite elements also have high precision to make multi-scale analysis for structure.

Prediction of grain scale plasticity of NiTi shape memory alloy based on crystal plasticity finite element method

Grain scale plasticity of NiTi shape memory alloy(SMA)during uniaxial compression deformation at 400℃was investigated through two-dimensional crystal plasticity finite element simulation and corresponding analysis based on the obtained orientation data.Stress and strain distributions of the deformed NiTi SMA samples confirm that there exhibits a heterogeneous plastic deformation at grain scale.Statistically stored dislocation(SSD)density and geometrically necessary dislocation(GND)density were further used in order to illuminate the microstructure evolution during uniaxial compression.SSD is responsible for sustaining plastic deformation and it increases along with the increase of plastic strain.GND plays an important role in accommodating compatible deformation between individual grains and thus it is correlated with the misorientation between neighboring grains,namely,a high GND density corresponds to large misorientation between grains and a low GND density corresponds to small misorientation between grains.

Increment-Dimensional Scaled Boundary Finite Element Method for Solving Transient Heat Conduction Problem

An increment-dimensional scaled boundary finite element method (ID-SBFEM) is developed to solve the transient temperature field.To improve the accuracy of SBFEM,the effect of high frequency factor on dynamic stiffness is considered,and the first-order continued fraction technique is used.After the derivation,the SBFE equations are obtained,and the dimensions of thermal conduction,the thermal capacity matrix and the vector of the right side term in the equations are doubled.An example is presented to illustrate the feasibility and good accuracy of the proposed method.

Application of scaled boundary finite element method in static and dynamic fracture problems

The scaled boundary finite element method （SBFEM） is a recently developed numerical method combining advantages of both finite element methods （FEM） and boundary element methods （BEM） and with its own special features as well. One of the most prominent advantages is its capability of calculating stress intensity factors （SIFs） directly from the stress solutions whose singularities at crack tips are analytically represented. This advantage is taken in this study to model static and dynamic fracture problems. For static problems, a remeshing algorithm as simple as used in the BEM is developed while retaining the generality and flexibility of the FEM. Fully-automatic modelling of the mixed-mode crack propagation is then realised by combining the remeshing algorithm with a propagation criterion. For dynamic fracture problems, a newly developed series-increasing solution to the SBFEM governing equations in the frequency domain is applied to calculate dynamic SIFs. Three plane problems are modelled. The numerical results show that the SBFEM can accurately predict static and dynamic SIFs, cracking paths and load-displacement curves, using only a fraction of degrees of freedom generally needed by the traditional finite element methods.

Dynamic Crack Propagation Analysis Using Scaled Boundary Finite Element Method

The prediction of dynamic crack propagation in brittle materials is still an important issue in many engineering fields. The remeshing technique based on scaled boundary finite element method(SBFEM) is extended to predict the dynamic crack propagation in brittle materials. The structure is firstly divided into a number of superelements, only the boundaries of which need to be discretized with line elements. In the SBFEM formulation, the stiffness and mass matrices of the super-elements can be coupled seamlessly with standard finite elements, thus the advantages of versatility and flexibility of the FEM are well maintained. The transient response of the structure can be calculated directly in the time domain using a standard time-integration scheme. Then the dynamic stress intensity factor(DSIF) during crack propagation can be solved analytically due to the semi-analytical nature of SBFEM. Only the fine mesh discretization for the crack-tip super-element is needed to ensure the required accuracy for the determination of stress intensity factor(SIF). According to the predicted crack-tip position, a simple remeshing algorithm with the minimum mesh changes is suggested to simulate the dynamic crack propagation. Numerical examples indicate that the proposed method can be effectively used to deal with the dynamic crack propagation in a finite sized rectangular plate including a central crack. Comparison is made with the results available in the literature, which shows good agreement between each other.

Two-scale finite element method for piezoelectric problem in periodic structure

The prediction of the mechanical and electric properties of piezoelectric fibre composites has become an active research area in recent years. By means of introducing a boundary layer problem, some new kinds of two-scale finite element methods for solutions to the electric potential and the displacement for composite material in periodic struc- ture under the coupled piezoelectricity are derived. The coupled two-scale relation of the electric potential and the displacement is set up, and some finite element approximate estimates and numerical examples which show the effectiveness of the method are presented.

High-efciency improved symmetric successive over-relaxation preconditioned conjugate gradient method for solving large-scale finite element linear equations

Fast solving large-scale linear equations in the finite element analysis is a classical subject in computational mechanics. It is a key technique in computer aided engineering （CAE） and computer aided manufacturing （CAM）. This paper presents a high-efficiency improved symmetric successive over-relaxation （ISSOR） preconditioned conjugate gradient （PCG） method, which maintains lelism consistent with the original form. Ideally, the by 50% as compared with the original algorithm. the convergence and inherent paralcomputation can It is suitable for be reduced nearly high-performance computing with its inherent basic high-efficiency operations. By comparing with the numerical results, it is shown that the proposed method has the best performance.

Thermo-hydro-mechanical-air coupling finite element method and its application to multi-phase problems

In this paper, a finite element method （FEM）-based multi-phase problem based on a newly proposed thermal elastoplastic constitutive model for saturated/unsaturated geomaterial is discussed. A program of FEM named as SOFT, adopting unified field equations for thermo-hydro-mechanical-air （THMA） behavior of geomaterial and using finite element-finite difference （FE-FD） scheme for so/l-water-air three-phase coupling problem, is used in the numerical simulation. As an application of the newly proposed numerical method, two engineering problems, one for slope failure in unsaturated model ground and another for in situ heating test related to deep geological repository of high-level radioactive waste （HLRW）, are simulated. The model tests on slope failure in unsaturated Shirasu ground, carried out by Kitamura et al. （2007）, is simulated in the framework of soil-water-air three-phase coupling under the condition of constant temperature. While the in situ heating test reported by Munoz （2006） is simulated in the same framework under the conditions of variable temperature hut constant air pressure.

Surrounding rock deformation analysis of underground caverns with multi-body finite element method

Discontinuous deformation problems are common in rock engineering. Numerical analysis methods based on system models of the discrete body can better solve these problems. One of the most effective solutions is discontinuous deformation analysis （DDA） method, but the DDA method brings about rock embedding problems when it uses the strain assumption in elastic deformation and adopts virtual springs to simulate the contact problems. The multi-body finite element method （FEM） proposed in this paper can solve the problems of contact and deformation of blocks very well because it integrates the FEM and multi-body system dynamics theory. It is therefore a complete method for solving discontinuous deformation problems through balance equations of the contact surface and for simulating the displacement of whole blocks. In this study, this method was successfully used for deformation analysis of underground caverns in stratified rock. The simulation results indicate that the multi-body FEM can show contact forces and the stress states on contact surfaces better than DDA, and that the results calculated with the multi-body FEM are more consistent with engineering practice than those calculated with DDA method.

Scaled Boundary Finite Element Analysis of Wave Passing A Submerged Breakwater

The scaled boundary finite element method （SBFEM） is a novel semi-analytical technique combining the advantage of the finite element method （FEM） and the boundary element method （BEM） with its unique properties. In this paper, the SBFEM is used for computing wave passing submerged breakwaters, and the reflection coeffcient and transmission coefficient are given for the case of wave passing by a rectangular submerged breakwater, a rigid submerged barrier breakwater and a trapezium submerged breakwater in a constant water depth. The results are compared with the analytical solution and experimental results. Good agreement is obtained. Through comparison with the results using the dual boundary element method （DBEM）, it is found that the SBFEM can obtain higher accuracy with fewer elements. Many submerged breakwaters with different dimensions are computed by the SBFEM, and the changing character of the reflection coeffcient and the transmission coefficient are given in the current study.

Three-Dimensional Thermo-Elastic-Plastic Finite Element Method Modeling for Predicting Weld-Induced Residual Stresses and Distortions in Steel Stiffened-Plate Structures

The objective of the present paper is to develop nonlinear finite element method models for predicting the weld-induced initial deflection and residual stress of plating in steel stiffened-plate structures. For this purpose, three-dimensional thermo-elastic-plastic finite element method computations are performed with varying plate thickness and weld bead length (leg length) in welded plate panels, the latter being associated with weld heat input. The finite element models are verified by a comparison with experimental database which was obtained by the authors in separate studies with full scale measurements. It is concluded that the nonlinear finite element method models developed in the present paper are very accurate in terms of predicting the weld-induced initial imperfections of steel stiffened plate structures. Details of the numerical computations together with test database are documented.

FINITE ELEMENT METHOD ON NUMERICAL SIMULATION OF STRATUM CORNEUM'S PENETRATION PROPERTY

How the outer substance could penetrate through the skin lies in the stratum corneum, because it is the main barrier in the multi-layers of the skin. Supposing the keratin cell with a special geometry as tetrakaidecahedron, the penetration property of stratum corneum was the key problem which was numerically simulated with finite element method. At first the discretization of the stratum corneum region was given in two steps： first, the discretization of the keratin cell; second, the discretization of fattiness that surrounds the keratin. Then there was the work of numerical simulation. In this procedure, the finite element method and the multi-grid method were used. The former was to obtain the discretization of basic elements; the latter was to decrease the high frequency error. At last the visualization of the numerical simulation was shown.

An RKDG finite element method for the one-dimensional inviscid compressible gas dynamics equations in a Lagrangian coordinate

In this paper,Runge-Kutta Discontinuous Galerkin（RKDG） finite element method is presented to solve the onedimensional inviscid compressible gas dynamic equations in a Lagrangian coordinate.The equations are discretized by the DG method in space and the temporal discretization is accomplished by the total variation diminishing Runge-Kutta method.A limiter based on the characteristic field decomposition is applied to maintain stability and non-oscillatory property of the RKDG method.For multi-medium fluid simulation,the two cells adjacent to the interface are treated differently from other cells.At first,a linear Riemann solver is applied to calculate the numerical ？ux at the interface.Numerical examples show that there is some oscillation in the vicinity of the interface.Then a nonlinear Riemann solver based on the characteristic formulation of the equation and the discontinuity relations is adopted to calculate the numerical ？ux at the interface,which suppresses the oscillation successfully.Several single-medium and multi-medium fluid examples are given to demonstrate the reliability and efficiency of the algorithm.

STRAIGHTFORWARD MULTI-SCALE BOUNDARY ELEMENT METHOD FOR GLOBAL/LOCAL MECHANICAL ANALYSIS OF ELASTIC HETEROGENEOUS MATERIAL

A straightforward multi-scale boundary element method is proposed for global and local mechanical analysis of heterogeneous material.The method is more accurate and convenient than finite element based multi-scale method.The formulations of this method are derived by combining the homogenization approach and the fundamental equations of boundary element method.The solution gives the convenient formulations to compute global elastic constants and the local stress field.Finally,two numerical examples of porous material are presented to prove the accuracy and the efficiency of the proposed method.The results show that the method does not require the iteration to obtain the solution of the displacement in micro level.

A New Formulation of the Scaled Boundary Finite Element Method for Heterogeneous Media:Application to Heat Transfer Problems

The solution to heat transfer problems in two-dimensional heterogeneous media is attended based on the scaled boundary finite element method(SBFEM)coupled with equilibrated basis functions(EqBFs).The SBFEM reduces the model order by scaling the boundary solution onto the inner element.To this end,tri-lateral elements are emanated from a scaling center,followed by the development of a semi-analytical solution along the radial direction and a finite element solution along the circumferential/boundary direction.The discretization is thus limited to the boundaries of the model,and the semi-analytical radial solution is found through the solution of an eigenvalue problem,which restricts the methods’applicability to heterogeneous media.In this research,we first extracted the SBFEM formulation considering the heterogeneity of the media.Then,we replaced the semi-analytical radial solution with the EqBFs and removed the eigenvalue solution step from the SBFEM.The varying coefficients of the partial differential equation(PDE)resulting from the heterogeneity of the media are replaced by a finite series in the radial and circumferential directions of the element.A weighted residual approach is applied to the radial equation.The equilibrated radial solution series is used in the new formulation of the SBFEM.

Modeling Technology in Finite Element Analysis of Electrostatic Proximity Fuze Problem

In order to analyze the electrostatic field concerned with electrostatic proximity fuze problem using the available finite analysis software package, the technology to model the problem with a scale reduction object and boundary was presented. The boundary is determined by the maximum distance the sensor can detect. The object model is obtained by multiplying the terms in Poisson's equation with a scale reduction factor and the real value can be reconstructed with the same reverse process after software calculation. Using the finite element analysis program, the simulation value is close to the theoretical value with a little error. The boundary determination and scale reduction method is suitable to modeling the irregular electrostatic field around air targets, such as airplane, missile and so on, which is based on commonly used personal computer (PC). The technology reduces the calculation and storage cost greatly.

Towards a Micromechanical Understanding of Landslides—Aiming at a Combination of Finite and Discrete Elements with Minimal Number of Degrees of Freedom

In this paper, we propose a combination of discrete elements for the soil and finite elements for the fluid flow field inside the pore space to simulate the triggering of landslides. We give the details for the implementation of third order finite elements (“P2 with bubble”) together with polygonal discrete elements, which allows the formulation with a minimal number of degrees of freedom to save computer time and memory. We verify the implementation with several standard problems from computational fluid dynamics, as well as the decay of a granular step in a fluid as test case for complex flow.

Optimal design of automotive body B-pillar using simplified finite element model of body-in-prime combined with an optimization procedure

Optimization of an automotive body structure faces the difficulty of having too many design variables and a too large design search space. A simplified model of body-in-prime(BIP) can solve this difficulty by reducing the number of design variables. In this study, to achieve lighter weight and higher stiffness, the simplified model of BIP was developed and combined with an optimization procedure;consequently, optimal designs of automotive body B-pillar were produced. B-pillar was divided into four quarters and each quarter was modelled by one simplified beam. In the optimization procedure, depth, width, and thickness of the simplified beams were considered as the design variables.Weight, bending and torsional stiffness were also considered as objective functions. The optimization procedure is composed of six stages: designing the experiments, calculating grey relational grade, calculating signal-to noise ratio,finding an optimum design using Taguchi grey relational analysis, performing sensitivity analysis using analysis of variance(ANOVA) and performing non-dominated sorting and multi-criteria decision making. The results show that the width of lower B-pillar has the highest effect(about 55%) and the obtained optimum design point could reduce the weight of B-pillar by about 40% without reducing the BIP stiffness by more than 1.47%.

An Effective Numerical Calculation Method for Multi-Time-Scale Mathematical Models in Systems Biology

The improvements of high-throughput experimental devices such as microarray and mass spectrometry have allowed an effective acquisition of biological comprehensive data which include genome, transcriptome, proteome, and metabolome (multi-layered omics data). In Systems Biology, we try to elucidate various dynamical characteristics of biological functions with applying the omics data to detailed mathematical model based on the central dogma. However, such mathematical models possess multi-time-scale properties which are often accompanied by time-scale differences seen among biological layers. The differences cause time stiff problem, and have a grave influence on numerical calculation stability. In the present conventional method, the time stiff problem remained because the calculation of all layers was implemented by adaptive time step sizes of the smallest time-scale layer to ensure stability and maintain calculation accuracy. In this paper, we designed and developed an effective numerical calculation method to improve the time stiff problem. This method consisted of ahead, backward, and cumulative algorithms. Both ahead and cumulative algorithms enhanced calculation efficiency of numerical calculations via adjustments of step sizes of each layer, and reduced the number of numerical calculations required for multi-time-scale models with the time stiff problem. Backward algorithm ensured calculation accuracy in the multi-time-scale models. In case studies which were focused on three layers system with 60 times difference in time-scale order in between layers, a proposed method had almost the same calculation accuracy compared with the conventional method in spite of a reduction of the total amount of the number of numerical calculations. Accordingly, the proposed method is useful in a numerical analysis of multi-time-scale models with time stiff problem.