Computing of the Anchor by the Method of Three-Dimension Point-Radiate Infinite Elements

On the basis of the one-dimension infinite element theory, the coordinate translation and shape function of 3D point-radiate 8-node and 4-node infinite elements are derived. They are coupled with 20-node and 8-node finite elements to compute the compression distortion of the prestressed anchorage segment. The results indicate that when the prestressed force acts on the anchorage head and segment, the stresses and the displacements in the rock around the anchorage head and segment concentrate on the zone center with the anchor axis, and they decrease with exponential forms. Therefore,the stresses and the displacement spindles are formed. The calculating results of the infinite element are close to the theoretical results. This indicates the method is right. This article introduces a new way to study the mechanism of prestressed anchors. The obtained results have an important role in the research of the anchor mechanism and engineering application.

Elastodynamic Infinite Elements with Modified Bessel Shape Functions for Dynamic Soil-Structure Interaction

The paper is devoted to formulations of decay and mapped elastodynamic infinite elements, based on modified Bessel shape functions. These elements are appropriate for Soil-Structure Interaction （SSI） problems, solved in time or frequency domain and can be treated as a new form of the recently proposed Elastodynamic Infinite Elements with United Shape Functions （EIEUSF） infinite elements. The formulation of 2D Horizontal type Infinite Elements （HIE） is demonstrated here, but by similar techniques 2D Vertical （VIE） and 2D Comer （CIE） Infinite Elements can also be formulated. Using elastodynamic infinite elements is the easier and appropriate way to achieve an adequate simulation including basic aspects of Soil-Structure Interaction. Continuity along the artificial boundary （the line between finite and infinite elements） is discussed as well and the application of the proposed elastodynamic infinite elements in the Finite Element Method （FEM） is explained in brief. Finally, a numerical example shows the computational efficiency of the proposed infinite elements.

THE h-p VERSION OF THE INFINITE ELEMENT METHOD AND ITS APPLICATION

The paper investigates the h-p version of the infinite element method. An exponential conver gence can be abtained by a small amount of computing work.

On the Total Dynamic Response of Soil-Structure Interaction System in Time Domain Using Elastodynamic Infinite Elements with Scaling Modified Bessel Shape Functions

This paper is devoted to a new approach—the dynamic response of Soil-Structure System (SSS), the far field of which is discretized by decay or mapped elastodynamic infinite elements, based on scaling modified Bessel shape functions are to be calculated. These elements are appropriate for Soil-Structure Interaction problems, solved in time or frequency domain and can be treated as a new form of the recently proposed elastodynamic infinite elements with united shape functions (EIEUSF) infinite elements. Here the time domain form of the equations of motion is demonstrated and used in the numerical example. In the paper only the formulation of 2D horizontal type infinite elements (HIE) is used, but by similar techniques 2D vertical (VIE) and 2D corner (CIE) infinite elements can also be added. Continuity along the artificial boundary (the line between finite and infinite elements) is discussed as well and the application of the proposed elastodynamical infinite elements in the Finite element method is explained in brief. A numerical example shows the computational efficiency and accuracy of the proposed infinite elements, based on scaling Bessel shape functions.

Vehicle–track–tunnel dynamic interaction:a finite/infinite element modelling method

The aim of this study is to develop coupled matrix formulations to characterize the dynamic interaction between the vehicle,track,and tunnel.The vehicle–track coupled system is established in light of vehicle–track coupled dynamics theory.The physical characteristics and mechanical behavior of tunnel segments and rings are modeled by the finite element method,while the soil layers of the vehicle–track–tunnel(VTT)system are modeled as an assemblage of 3-D mapping infinite elements by satisfying the boundary conditions at the infinite area.With novelty,the tunnel components,such as rings and segments,have been coupled to the vehicle–track systems using a matrix coupling method for finite elements.The responses of sub-systems included in the VTT interaction are obtained simultaneously to guarantee the solution accuracy.To relieve the computer storage and save the CPU time for the large-scale VTT dynamics system with high degrees of freedoms,a cyclic calculation method is introduced.Apart from model validations,the necessity of considering the tunnel substructures such as rings and segments is demonstrated.In addition,the maximum number of elements in the tunnel segment is confirmed by numerical simulations.

INFINITE ELEMENT METHOD FOR PROBLEMS ON UNBOUNDED AND MULTIPLY CONNECTED DOMAINS

The author studies the infinite element method for the boundary value problems of second order elliptic equations on unbounded and multiply connected domains. The author makes a partition of the domain into infinite number of elements. Without dividing the domain, as usual, into a bounded one and an exterior one, he derives an initial value problem of an ordinary differential equation for the combined stiffness matrix, then obtains the approximate solution with a small amount of computer work. Numerical examples are given.

Analysis of ground vibrations due to underground trains by 2.5D finite/infinite element approach

The 2.5D finite/infinite element approach is adopted to study wave propagation problems caused by underground moving trains. The irregularities of the near field, including the tunnel structure and parts of the soil, are modeled by the finite elements, and the wave propagation properties of the far field extending to infinity are modeled by the infinite elements. One particular feature of the 2.5D approach is that it enables the computation of the three-dimensional response of the half-space, taking into account the load-moving effect, using only a two-dimensional profile. Although the 2.5D finite/infinite element approach shows a great advantage in studying the wave propagation caused by moving trains, attention should be given to the calculation aspects, such as the rules for mesh establishment, in order to avoid producing inaccurate or erroneous results. In this paper, some essential points for consideration in analysis are highlighted, along with techniques to enhance the speed of the calculations. All these observations should prove useful in making the 2.5D finite/infinite element approach an effective one.

Mapping-Based 3D Hexahedral Finite Element Mesh Generation Method

Mapping mesh generation is widely applied in pre-processes of Finite Element Method （FEM）. In this study, the basic 3D mapping equations by Lagrange interpolating function are founded. Based these equations, a mapping pattern library, which maps essential configurations e.g. line, circle, rotary body, sphere etc. to hexahedral FEM mesh, has been built. Then available FEM mesh will be generated by clipping and assembling the mapped essential objects. Study case illustrates that the proposed method is simple and efficient to generate valid FEM mesh for complex 3D engineering structure.

Mapping relationship analysis of welding assembly properties for thin-walled parts with finite element and machine learning algorithm

The finite element(FE)-based simulation of welding characteristics was carried out to explore the relationship among welding assembly properties for the parallel T-shaped thin-walled parts of an antenna structure.The effects of welding direction,clamping,fixture release time,fixed constraints,and welding sequences on these properties were analyzed,and the mapping relationship among welding characteristics was thoroughly examined.Different machine learning algorithms,including the generalized regression neural network(GRNN),wavelet neural network(WNN),and fuzzy neural network(FNN),are used to predict the multiple welding properties of thin-walled parts to mirror their variation trend and verify the correctness of the mapping relationship.Compared with those from GRNN and WNN,the maximum mean relative errors for the predicted values of deformation,temperature,and residual stress with FNN were less than 4.8%,1.4%,and 4.4%,respectively.These results indicate that FNN generated the best predicted welding characteristics.Analysis under various welding conditions also shows a mapping relationship among welding deformation,temperature,and residual stress over a period of time.This finding further provides a paramount basis for the control of welding assembly errors of an antenna structure in the future.

Application of semi-analytical finite element method coupled with infinite element for analysis of asphalt pavement structural response

A specific computational program SAFEM was developed based on semi-analytical finite element （FE） method for analysis of asphalt pavement structural responses under static loads. The reliability and efficiency of this FE program was proved by comparison with the general commercial FE software ABAQUS. In order to further reduce the computational time without decrease of the accuracy, the infinite element was added to this program. The results of the finite-infinite element coupling analysis were compared with those of finite element analysis derived from the verified FE program, The study shows that finite-infinite element coupling analysis has higher reliability and efficiency.

Calculation of prestressed anchor segment by 3D infinite element

Based on 1D infinite element theory,the coordinate transformation and shape function of 3D point-radiation 4-node infinite elements were derived.They were coupled with 8-node finite elements to compute the compressive deformation of the prestressed anchor segment.The results indicate that when the prestressed force acts on the anchor segment,the stresses and displacements in the rock around the anchor segment are concentrated in the zone center with the anchor axis and are subjected to exponential decay.Therefore,the stresses and the displacement spindles are formed.The calculation results of the infinite element are close to the theoretical results.

Coupled method of finite and dynamic infinite elements for simulating wave propagation in elastic solids involving infinite domains

This paper deals with the coupled method of finite and dynamic infinite elements for simulating wave propagation in elastic and viscoelastic solids involving infinite domains.This method can be used to simultaneously simulate material complexities in the near field and the infinite extent of the far field.Based on the governing equations of wave motion in two-dimensional and three-dimensional elastic/viscoelastic solids,the mass and stiffness matrices of the dynamic infinite element have been derived.The proposed two-dimensional dynamic infinite element can be used to simulate both the P-wave and the SV-wave propagation within the element,while the proposed three-dimensional dynamic infinite element can be used to simultaneously simulate the Rayleigh wave,P-wave and S-wave propagation within the element.The related simulation results have demonstrated that the coupled method of finite and dynamic infinite elements can be accurately used to simulate,both physically and computationally,wave propagation in elastic/viscoelastic solids involving infinite domains.Thus,this method provides an advanced scientific tool for dealing with both scientific and engineering problems involving infinite domains.

PHYSICAL VALUE MAPPING ALGORITHM OF MESH IN FINE CAE ANALYSIS OF AUTOMOBILE BODY STRUCTURE

A physical value mapping （PVM） algorithm based on finite element mesh from the stamped part in stamping process to the product is presented, In order to improve the efficiency of the PVM algorithm, a search way from the mesh of the product to the mesh of the stamped part will be adopted. At the same time, the search process is divided into two steps： entire search （ES） and local search （LS）, which improve the searching efficiency. The searching area is enlarged to avoid missing projection elements in ES process. An arc-length method is introduced in LS process. The validity is confirmed by the results of the complex industry-forming product.

Soil seismic analysis for 2D oblique incident waves using exact free-field responses by frequency-based finite/infinite element method

The seismic analysis of a viscoelastic half-space under two-dimensional(2D)oblique incident waves is carried out by the finite/infinite element method(FIEM).First,the frequency-domain exact solutions for the displacements and stresses of the free field are derived in general form for arbitrary incident P and SV waves.With the present formulation,no distinction needs to be made for SV waves with over-critical incident angles that make the reflected P waves disappear,while no critical angle exists for P waves.Next,the equivalent seismic forces of the earthquake(Taft Earthquake 1952)imposed on the near-field boundary are generated by combining the solutions for unit ground accelerations with the earthquake spectrum.Based on the asymmetric finite/infinite element model,the frequency-domain motion equations for seismic analysis are presented with the key parameters selected.The results obtained in frequency and time domain are verified against those of Wolf’s,Luco and de Barros’and for inversely computed ground motions.The parametric study indicated that distinct phase difference exists between the horizontal and vertical responses for SV waves with over-critical incident angles,but not for under-critical incident angles.Other observations were also made for the numerical results inside the text.

Hot deformation behavior and finite element simulation of Mg-8.3Gd-4.4Y-1.5Zn-0.8Mn alloy

To study the hot deformation behavior of Mg-8.3 Gd-4.4 Y-1.5 Zn-0.8 Mn(wt%) alloy,hot compression tests were conducted using a Gleeble-3500 thermal simulator at temperatures ranging from 653 to773 K,true strain rates of 0.001-1 s^(-1),and a deformation degree of 60%.Results of hot compression experiments show that the flow stress of the alloy increases with the strain rate.The true stress-true strain curves are corrected by correcting the effect of temperature rise in the deformation process.Activation energy,Q,equal to 287380 J/mol and material constant,n,equal to 4.59 were calculated by fitting the true stress-true strain curves.Then,the constitutive equation was established and verified via finite element simulation.Results of the hot processing map show that the probability of material instability increases with the degree of deformation,which indicates that the material is not suitable for large deformation in a single pass.On the whole,the alloy is appropriate for multipass processing with small deformation and a suitable processing temperature and strain rate are 733 K and 0.01 s-1,respectively.

Multiscale Finite ElementMethods for Flows on Rough Surfaces

In this paper,we present the Multiscale Finite Element Method(MsFEM)for problems on rough heterogeneous surfaces.We consider the diffusion equation on oscillatory surfaces.Our objective is to represent small-scale features of the solution via multiscale basis functions described on a coarse grid.This problem arises in many applications where processes occur on surfaces or thin layers.We present a unified multiscale finite element framework that entails the use of transformations that map the reference surface to the deformed surface.The main ingredients of MsFEM are(1)the construction of multiscale basis functions and(2)a global coupling of these basis functions.For the construction of multiscale basis functions,our approach uses the transformation of the reference surface to a deformed surface.On the deformed surface,multiscale basis functions are defined where reduced(1D)problems are solved along the edges of coarse-grid blocks to calculate nodalmultiscale basis functions.Furthermore,these basis functions are transformed back to the reference configuration.We discuss the use of appropriate transformation operators that improve the accuracy of the method.The method has an optimal convergence if the transformed surface is smooth and the image of the coarse partition in the reference configuration forms a quasiuniform partition.In this paper,we consider such transformations based on harmonic coordinates(following H.Owhadi and L.Zhang[Comm.Pure and Applied Math.,LX(2007),pp.675-723])and discuss gridding issues in the reference configuration.Numerical results are presented where we compare the MsFEM when two types of deformations are used formultiscale basis construction.The first deformation employs local information and the second deformation employs a global information.Our numerical results showthat one can improve the accuracy of the simulations when a global information is used.

An adaptive scaled boundary finite element method by subdividing subdomains for elastodynamic problems

The scaled boundary finite element method(SBFEM) is a semi-analytical numerical method,which models an analysis domain by a small number of large-sized subdomains and discretises subdomain boundaries only.In a subdomain,all fields of state variables including displacement,stress,velocity and acceleration are semi-analytical,and the kinetic energy,strain energy and energy error are all integrated semi-analytically.These advantages are taken in this study to develop a posteriori h-hierarchical adaptive SBFEM for transient elastodynamic problems using a mesh refinement procedure which subdivides subdomains.Because only a small number of subdomains are subdivided,mesh refinement is very simple and efficient,and mesh mapping to transfer state variables from an old mesh to a new one is also very simple but accurate.Two 2D examples with stress wave propagation were modelled.The results show that the developed method is capable of capturing propagation of steep stress regions and calculating accurate dynamic responses,using only a fraction of degrees of freedom required by adaptive finite element method.

High resolution strain mapping of a single axially heterostructured nanowire using scanning X-ray diffraction

Axially heterostructured nanowires are a promising platform for next generation electronic and optoelectronic devices.Reports based on theoretical modeling have predicted more complex strain distributions and increased critical layer thicknesses than in thin films,due to lateral strain relaxation at the surface,but the understanding of the growth and strain distributions in these complex structures is hampered by the lack of high-resolution characterization techniques.Here,we demonstrate strain mapping of an axially segmented GalnP-lnP 190 nm diameter nanowire heterostructure using scanning X-ray diffraction.We systematically investigate the strain distribution and lattice tilt in three different segment lengths from 45 to 170 nm,obtaining strain maps with about 10^-4 relative strain sensitivity.The experiments were performed using the 90 nm diameter nanofocus at the NanoMAX beamline,taking advantage of the high coherent flux from the first diffraction limited storage ring MAX IV.The experimental results are in good agreement with a full simulation of the experiment based on a three-dimensional(3D)finite element model.The largest segments show a complex profile,where the lateral strain relaxation at the surface leads to a dome-shaped strain distribution from the mismatched interfaces,and a change from tensile to compressive strain within a single segment.The lattice tilt maps show a cross-shaped profile with excellent qualitative and quantitative agreement with the simulations.In contrast,the shortest measured InP segment is almost fully adapted to the surrounding GalnP segments.

基于BIM技术的浅埋隧道无限元法数值研究

近年来,BIM技术在交通运输基础工程领域的应用日益广泛,如地铁、高铁、公路、隧道等项目全生命周期的管理都有BIM技术的参与。本研究通过BIM软件–Revit建立浅埋隧道的信息模型,基于BIM信息模型,导入ABAQUS有限元分析软件,对越秀公园站浅埋暗挖多孔隧道进行有限元与无限元耦合模拟,验证了无限元在隧道数值模拟中的可行性。其次通过设置不同的工况,验证了无限元与有限元耦合模拟的准确性,并且研究了隧道的开挖对不同工况下,地表沉降和衬砌内力的影响,得出最优的开挖工序,为后续浅埋隧道的力学行为的研究提供借鉴。

基于BIM技术的浅埋双孔隧道地震响应规律研究

通过BIM软件Revit建立浅埋双孔隧道的信息模型,基于BIM信息模型,导入ABAQUS结构分析软件,基于无限元-有限元方法应用于浅埋双孔隧道进行力学行为分析的可行性和准确性,分析隧道衬砌的刚度和设置减震层对浅埋双孔隧道在典型地震波作用下的响应规律,找到适合该浅埋双孔隧道的减震层材料和厚度,为后续浅埋隧道地震响应规律的研究提供借鉴。