A stable implicit nodal integration-based particle finite element method(N-PFEM)for modelling saturated soil dynamics

In this study,we present a novel nodal integration-based particle finite element method(N-PFEM)designed for the dynamic analysis of saturated soils.Our approach incorporates the nodal integration technique into a generalised Hellinger-Reissner(HR)variational principle,creating an implicit PFEM formulation.To mitigate the volumetric locking issue in low-order elements,we employ a node-based strain smoothing technique.By discretising field variables at the centre of smoothing cells,we achieve nodal integration over cells,eliminating the need for sophisticated mapping operations after re-meshing in the PFEM.We express the discretised governing equations as a min-max optimisation problem,which is further reformulated as a standard second-order cone programming(SOCP)problem.Stresses,pore water pressure,and displacements are simultaneously determined using the advanced primal-dual interior point method.Consequently,our numerical model offers improved accuracy for stresses and pore water pressure compared to the displacement-based PFEM formulation.Numerical experiments demonstrate that the N-PFEM efficiently captures both transient and long-term hydro-mechanical behaviour of saturated soils with high accuracy,obviating the need for stabilisation or regularisation techniques commonly employed in other nodal integration-based PFEM approaches.This work holds significant implications for the development of robust and accurate numerical tools for studying saturated soil dynamics.

OPTIMIZATION OF AUTOBODY PANEL STAMPING PROCESS BASED ON DYNAMIC EXPLICIT FINITE ELEMENT METHOD

Taking CPU time cost and analysis accuracy into account, dynamic explicit finite ele- ment method is adopted to optimize the forming process of autobody panels that often have large sizes and complex geometry. In this paper, for the sake of illustrating in detail how dynamic explicit finite element method is applied to the numerical simulation of the autobody panel forming process,an example of optimization of stamping process pain meters of an inner door panel is presented. Using dynamic explicit finite element code Ls-DYNA3D, the inner door panel has been optimized by adapting pa- rameters such as the initial blank geometry and position, blank-holder forces and the location of drawbeads, and satisfied results are obtained.

Transient analysis of 1D inhomogeneous media by dynamic inhomogeneous finite element method

The dynamic inhomogeneous finite element method is studied for use in the transient analysis of one dimensional inhomogeneous media. The general formula of the inhomogeneous consistent mass matrix is established based on the shape function. In order to research the advantages of this method, it is compared with the general finite element method. A linear bar element is chosen for the discretization tests of material parameters with two fictitious distributions. And, a numerical example is solved to observe the differences in the results between these two methods. Some characteristics of the dynamic inhomogeneous finite element method that demonstrate its advantages are obtained through comparison with the general finite element method. It is found that the method can be used to solve elastic wave motion problems with a large element scale and a large number of iteration steps.

Nodeless variable finite element method for heat transfer analysis by means of flux-based formulation and mesh adaptation

Based on flux-based formulation, a nodeless variable element method is developed to analyze two-dimensional steady-state and transient heat transfer problems. The nodeless variable element employs quadratic interpolation functions to provide higher solution accuracy without necessity to actually generate additional nodes. The flux-based formulation is applied to reduce the complexity in deriving the finite element equations as compared to the conventional finite element method, The solution accuracy is further improved by implementing an adaptive meshing technique to generaie finite element mesh that can adapt and move along corresponding to the solution behavior. The technique generates small elements in the regions of steep solution gradients to provide accurate solution, and meanwhile it generates larger elements in the other regions where the solution gradients are slight to reduce the computational time and the computer memory. The effectiveness of the combined procedure is demonstrated by heat transfer problems that have exact solutions. These problems tire： （a） a steady-state heat conduction analysis in a square plate subjected to a highly localized surface heating, and （b） a transient heat conduction analysis in a long plate subjected to moving heat source.

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.

VECTOR BOND GRAPH REPRESENTATION OF FINITE ELEMENT METHOD IN STRUCTURAL DYNAMICS

In this paper we have shown that the invariance of energy(kinetic energy,potential energy)and virtual work is the common feature of vector bond graph and finite element method in struc-tural dynamics.Then we have discussed the vector bond graph representation of finite elementmethod in detail,there are:(1)the transformation of reference systems,(2)the transformation ofinertia matrices,stiffness matrices and vectors of joint force,(3)verctor bond graph representationof Lagrangian dynamic equation of structure.

Discrete formulation of mixed finite element methods for vapor deposition chemical reaction equations

The vapor deposition chemical reaction processes, which are of extremely extensive applications, can be classified as a mathematical model by the following governing nonlinear partial differential equations containing velocity vector, temperature field, pressure field, and gas mass field. The mixed finite element （MFE） method is employed to study the system of equations for the vapor deposition chemical reaction processes. The semidiscrete and fully discrete MFE formulations are derived. And the existence and convergence （error estimate） of the semidiscrete and fully discrete MFE solutions are demonstrated. By employing MFE method to treat the system of equations for the vapor deposition chemical reaction processes, the numerical solutions of the velocity vector, the temperature field, the pressure field, and the gas mass field can be found out simultaneously. Thus, these researches are not only of important theoretical means, but also of extremely extensive applied vistas.

MIXED COMPATIBLE ELEMENT AND MIXED HYBRID INCOMPATIBLE ELEMENT VARIATIONAL METHODS IN DYNAMICS OF VISCOUS BAROTROPIC FLUIDS

This paper presents and proves the mixed compatible finite element variationalprinciples in dynamics of viscous barotropic fluids. When the principles are proved, itis found that the compatibility conditions of stress can be naturally satisfied. The gene-rallzed variational principles with mixed hybrid incompatible finite elements are alsopresented and proved, and they can reduce the computation of incompatible elements indynamics of viscous barotropic flows.

PENALTY FINITE ELEMENT METHOD FOR NONLINEAR DYNAMIC RESPONSE OF VISCOUS FLUID-SATURATED BIPHASE POROUS MEDIA

The governing equations as well as boundary land initial conditions for nonlinear dynamic response problems of viscous fluid-saturated biphase porous medium model, based on mixture theory, are presented. With Galerkin weighted residual method the corresponding nonlinear dynamic penalty finite element equation, in which the dependencies of volume fraction and permeation coefficients an deformation are included, is obtained. The iteration solution method of the nonlinear system equation is also discussed. As a numerical example, the dynamic response of a porous medium column under impulsive loading action is analyzed with the developed finite element program. The numerical results demonstrate the efficiency and correctness of the method.

Virtual Element Formulation for Finite Strain Elastodynamics Dedicated to Professor Karl Stark Pister for his 95th birthday

The virtual element method(VEM)can be seen as an extension of the classical finite element method(FEM)based on Galerkin projection.It allows meshes with highly irregular shaped elements,including concave shapes.So far the virtual element method has been applied to various engineering problems such as elasto-plasticity,multiphysics,damage and fracture mechanics.This work focuses on the extension of the virtual element method to efficient modeling of nonlinear elasto-dynamics undergoing large deformations.Within this framework,we employ low-order ansatz functions in two and three dimensions for elements that can have arbitrary polygonal shape.The formulations considered in this contribution are based on minimization of potential function for both the static and the dynamic behavior.Generally the construction of a virtual element is based on a projection part and a stabilization part.While the stiffness matrix needs a suitable stabilization,the mass matrix can be calculated using only the projection part.For the implicit time integration scheme,Newmark-Method is used.To show the performance of the method,various two-and three-dimensional numerical examples in are presented.

NUMERICAL SIMULATION OF UNSTEADY-STATE UNDEREXPANDED JET USING DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD

A discontinuous Galerkin finite element method （DG-FEM） is developed for solving the axisymmetric Euler equations based on two-dimensional conservation laws. The method is used to simulate the unsteady-state underexpanded axisymmetric jet. Several flow property distributions along the jet axis, including density, pres- sure and Mach number are obtained and the qualitative flowfield structures of interest are well captured using the proposed method, including shock waves, slipstreams, traveling vortex ring and multiple Mach disks. Two Mach disk locations agree well with computational and experimental measurement results. It indicates that the method is robust and efficient for solving the unsteady-state underexpanded axisymmetric jet.

THE APPLICATION OF COMPATIBLE STRESS ITERATIVE METHOD IN DYNAMIC FINITE ELEMENT ANALYSIS OF HIGH VELOCITY IMPACT

There is a common difficulty in elastic-plastic impact codes such as EPIC[2,3] NONSAP[4], etc.. Most of these codes use the simple linear functions usually taken from static problem to represent the displacement components. In such finite element formulation, the stress components are constant in each element and they are discontinuous in any two neighboring elements. Therefore, the bases of using the virtual work principle in such elements are unreliable. In this paper, we introduce a new method, namely, the compatible stress iterative method, to eliminate the above-said difficulty. The calculated examples show that the calculation using the new method in dynamic finite element analysis of high velocity impact is valid and stable, and the element stiffness can be somewhat reduced.

A New Flexible Multibody Dynamics Analysis Methodology of Deployable Structures with Scissor-Like Elements

There are vast constraint equations in conventional dynamics analysis of deployable structures,which lead to differential-algebraic equations(DAEs)solved hard.To reduce the difficulty of solving and the amount of equations,a new flexible multibody dynamics analysis methodology of deployable structures with scissor-like elements(SLEs)is presented.Firstly,a precise model of a flexible bar of SLE is established by the higher order shear deformable beam element based on the absolute nodal coordinate formulation(ANCF),and the master/slave freedom method is used to obtain the dynamics equations of SLEs without constraint equations.Secondly,according to features of deployable structures,the specification matrix method(SMM)is proposed to eliminate the constraint equations among SLEs in the frame of ANCF.With this method,the inner and the boundary nodal coordinates of element characteristic matrices can be separated simply and efficiently,especially on condition that there are vast nodal coordinates.So the element characteristic matrices can be added end to end circularly.Thus,the dynamic model of deployable structure reduces dimension and can be assembled without any constraint equation.Next,a new iteration procedure for the generalized-a algorithm is presented to solve the ordinary differential equations(ODEs)of deployable structure.Finally,the proposed methodology is used to analyze the flexible multi-body dynamics of a planar linear array deployable structure based on three scissor-like elements.The simulation results show that flexibility has a significant influence on the deployment motion of the deployable structure.The proposed methodology indeed reduce the difficulty of solving and the amount of equations by eliminating redundant degrees of freedom and the constraint equations in scissor-like elements and among scissor-like elements.

Nonlinear finite element analysis of effect of seismic waves on dynamic response of Shiziping dam

Many high earth-rockfill dams are constructed in the west of China. The seismic intensity at the dam site is usually very high, thus it is of great importance to ensure the safety of the dam in meizoseismal area. A 3D FEM model is established to analyze the seismic responses of Shiziping earth-rockfill dam. The nonlinear elastic Duncan-Chang constitutive model and the equivalent viscoelastic constitutive model are used to simulate the static and dynamic stress strain relationships of the dam materials, respectively. Four groups of seismic waves are inputted from the top of the bedrock to analyze the dynamic responses of the dam. The numerical results show that the calculated dynamic magnification factors display a good consistency with the specification values. The site spectrum results in larger acceleration response than the specification spectrum. The analysis of relative dynamic displacement indicates that the displacement at the downstream side of the dam is larger than that at the upstream side. The displacement response reduces from the center of river valley to two banks. The displacement responses corresponding to the specification spectrum are a little smaller than those corresponding to the site spectrum. The analysis of shear stress indicates that a large shear stress area appears in the upstream overburden layer, where the shear stress caused by site waves is larger than that caused by specification waves. The analysis of dynamic principal stress indicates that the minimum dynamic stresses in corridor caused by specification and site waves have little difference. The maximum and minimum dynamic stresses are relatively large at two sides. The largest tensile stress occurs at two sides of the floor of grouting corridor, which may result in the crack near the corridor side. The numerical results present good consistency with the observation data of the grouting corridor in Wenchuan earthquake.

Prolonged simulation of near-free surface underwater explosion based on Eulerian finite element method

n the area of naval architecture and ocean engineering,the research about the underwater xplosion problem is of great significance.To achieve prolonged simulation of near-free surface underwater explosion,the underwater explosion transient numerical model is established in this paper based on compressible Eulerian finite element method(EFEM).Compared with Geers Hunter formula,EFEM is availably validated by simulating the free-field underwater xplosion case.Then,the bubble pulsation and flow field dynamic characteristics of the cases with different underwater explosive depth are compared in this work.Lastly,the height of the water hump and the pressure of flow flied are analyzed quantitatively through the simulation results.

Simulation of isothermal precision extrusion of NiTi shape memory alloy pipe coupling by combining finite element method with cellular automaton

In order to present the microstructures of dynamic recrystallization(DRX) in different deformation zones of hot extruded NiTi shape memory alloy(SMA) pipe coupling,a simulation approach combining finite element method(FEM) with cellular automaton(CA) was developed and the relationship between the macroscopic field variables and the microscopic internal variables was established.The results show that there exists a great distinction among the microstructures in different zones of pipe coupling because deformation histories of these regions are diverse.Large plastic deformation may result in fine recrystallized grains,whereas the recrystallized grains may grow very substantially if there is a rigid translation during the deformation,even if the final plastic strain is very large.As a consequence,the deformation history has a significant influence on the evolution path of the DRX as well as the final microstructures of the DRX,including the morphology,the mean grain size and the recrystallization fraction.

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.

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.

Genetic algorithm-finite element method inversion of the factors determining the recent tectonic stress field of part of East Asia area

Genetic algorithm finite element method (GA FEM) is applied to the study of tectonic stress field of part of East Asia area. From the observed stress distribution, 2 D elastic plane stress inversion is made to deduce the boundary forces and investigate controlling factors. It is suggested that the continent continent collision is the dominant factor controlling the Chinese tectonic stress field. The ocean continent convergence along the subduction zone is an important factor. There exists tensile boundary force along the marginal sea.

Analysis on effect of surface fault to site ground motion using finite element method

Dynamic contact theory is applied to simulate the sliding of surface fault. Finite element method is used to analyze the effect of surface fault to site ground motions. Calculated results indicate that amplification effect is obvious in the area near surface fault, especially on the site that is in the downside fault. The results show that the effect of surface fault should be considered when important structure is constructed in the site with surface fault.