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.

A dynamic large-deformation particle finite element method for geotechnical applications based on Abaqus

In this paper,the application of Abaqus-based particle finite element method(PFEM)is extended from static to dynamic large deformation.The PFEM is based on periodic mesh regeneration with Delaunay triangulation to avoid mesh distortion.Additional mesh smoothing and boundary node smoothing techniques are incorporated to improve the mesh quality and solution accuracy.The field variables are mapped from the old to the new mesh using the closest point projection method to minimize the mapping error.The procedures of the proposed Abaqus-based dynamic PFEM(Abaqus-DPFEM)analysis and its implementation in Abaqus are detailed.The accuracy and robustness of the proposed approach are examined via four illustrative numerical examples.The numerical results show a satisfactory agreement with published results and further confirm the applicability of the Abaqus-DPFEM to solving dynamic large-deformation problems in geotechnical engineering.

A symplectic finite element method based on Galerkin discretization for solving linear systems

We propose a novel symplectic finite element method to solve the structural dynamic responses of linear elastic systems.For the dynamic responses of continuous medium structures,the traditional numerical algorithm is the dissipative algorithm and cannot maintain long-term energy conservation.Thus,a symplectic finite element method with energy conservation is constructed in this paper.A linear elastic system can be discretized into multiple elements,and a Hamiltonian system of each element can be constructed.The single element is discretized by the Galerkin method,and then the Hamiltonian system is constructed into the Birkhoffian system.Finally,all the elements are combined to obtain the vibration equation of the continuous system and solved by the symplectic difference scheme.Through the numerical experiments of the vibration response of the Bernoulli-Euler beam and composite plate,it is found that the vibration response solution and energy obtained with the algorithm are superior to those of the Runge-Kutta algorithm.The results show that the symplectic finite element method can keep energy conservation for a long time and has higher stability in solving the dynamic responses of linear elastic systems.

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.

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.

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.

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.

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.

An explicit finite element method for dynamic analysis in three-medium coupling system and its application

In this paper, an explicit finite element method to analyze the dynamic responses of three-medium coupled systems with any terrain is developed on the basis of the numerical simulation of the continuous conditions on the bounda-ries among fluid saturated porous medium, elastic single-phase medium and ideal fluid medium. This method is a very effective one with the characteristic of high calculating speed and small memory needed because the formulae for this explicit finite element method have the characteristic of decoupling, and which does not need to solve sys-tem of linear equations. The method is applied to analyze the dynamic response of a reservoir with considering the dynamic interactions among water, dam, sediment and basement rock. The vertical displacement at the top point of the dam is calculated and some conclusions are given.

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.

FINITE ELEMENT METHOD COMBINED WITH DYNAMIC PHOTOELASTIC ANALYSIS TO DETERMINE DYNAMIC STRESS-INTENSITY FACTORS

The present paper is addressed to the finite element method combined with dynamic photoelastic analysis of propagating cracks, that is, on the basis of [1] by Chien Wei-zang, finite elements which incorporate the propagating crack-tip singularity intrinsic to two-dimensional elasticity are employed. THe relation between crack opening length and time step obtained from dynamic photoelaslie analysis is used as a definite condition for solving the dynamic equations and simulating the crack propagations as well As an example, the impact response of dynamie-bending-test specimen is investigated and the dynamic stress-intensity factor obtained from the mentioned finite element analysis and dynamic photoelasticity is in reasonable agreement with each other.

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.

Dynamic Analysis of A Deepwater Drilling Riser with A New Hang-off System

The safety of risers in hang-off states is a vital challenge in offshore oil and gas engineering.A new hang-off system installed on top of risers is proposed for improving the security of risers.This approach leads to a challenging problem:coupling the dynamics of risers with a new hang-off system combined with multiple structures and complex constraints.To accurately analyze the dynamic responses of the coupled system,a coupled dynamic model is established based on the Euler-Bernoulli beam-column theory and penalty function method.A comprehensive analysis method is proposed for coupled dynamic analysis by combining the finite element method and the Newmarkβmethod.An analysis program is also developed in MATLAB for dynamic simulation.The simulation results show that the dynamic performances of the risers at the top part are significantly improved by the new hang-off system,especially the novel design,which includes the centralizer and articulation joint.The bending moment and lateral deformation of the risers at the top part decrease,while the hang-off joint experiences a great bending moment at the bottom of the lateral restraint area which requires particular attention in design and application.The platform navigation speed range under the safety limits of risers expands with the new hang-off system in use.

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.

3D magnetotelluric inversions with unstructured finite-element and limited-memory quasi-Newton methods

Traditional 3D Magnetotelluric(MT) forward modeling and inversions are mostly based on structured meshes that have limited accuracy when modeling undulating surfaces and arbitrary structures. By contrast, unstructured-grid-based methods can model complex underground structures with high accuracy and overcome the defects of traditional methods, such as the high computational cost for improving model accuracy and the difficulty of inverting with topography. In this paper, we used the limited-memory quasi-Newton(L-BFGS) method with an unstructured finite-element grid to perform 3D MT inversions. This method avoids explicitly calculating Hessian matrices, which greatly reduces the memory requirements. After the first iteration, the approximate inverse Hessian matrix well approximates the true one, and the Newton step(set to 1) can meet the sufficient descent condition. Only one calculation of the objective function and its gradient are needed for each iteration, which greatly improves its computational efficiency. This approach is well-suited for large-scale 3D MT inversions. We have tested our algorithm on data with and without topography, and the results matched the real models well. We can recommend performing inversions based on an unstructured finite-element method and the L-BFGS method for situations with topography and complex underground structures.

Superconvergence of nonconforming finite element penalty scheme for Stokes problem using L^2 projection method

A modified penalty scheme is discussed for solving the Stokes problem with the Crouzeix-Raviart type nonconforming linear triangular finite element. By the L^2 projection method, the superconvergence results for the velocity and pressure are obtained with a penalty parameter larger than that of the classical penalty scheme. The numerical experiments are carried out to confirm the theoretical results.