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.

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.

Eigenvalue Analysis of Thin Plate with Complicated Shapes By a Novel Infinite Element Method

A novel infinite element method(IEM)is presented for solving plate vibration problems in this paper.In the proposed IEM,the substructure domain is partitioned into multiple layers of geometrically similar finite elements which use only the data of the boundary nodes.A convergence criterion based on the trace of the mass matrix is used to determine the number of layers in the IE model partitioning process.Furthermore,in implementing the Craig-Bampton(CB)reduction method,the inversion of the global stiffness matrix is calculated using only the stiffness matrix of the first element layer.The validity and performance of the proposed method are investigated by means of four illustrative problems.The first example considers the case of a simple clamped rectangular plate.It is observed that the IEM results are consistent with the theoretical results for first six natural frequencies.The second example considers the frequency response of a clamped rectangular plate with a crack.The main feature of IEM is that a very fine and good quality virtual mesh can be created around the crack tip.The third and fourth examples consider the natural frequency of a multiple point supported plate and a perforated plate,respectively.The results are obtained just need to adjust the reference point or boundary nodes.The parametric analyses for various geometric profiles are easy to be conducted using these numerical techniques.In general,the results presented in this study have shown that the proposed method provides a direct,convenient and accurate tool for eigenvalue analysis of thin plate structure with complicated shapes.

INFINITE ELEMENT METHOD FOR THE EXTERIOR PROBLEMS OF THE HELMHOLTZ EQUATIONS

There are two cases of the exterior problems of the Helmholtz equation. If λ ≥ 0 the bilinear form is coercive, and if λ < 0 it is the scattering problem. We give a new approach of the infinite element method, which enables us to solve these exterior problems as well as corner problems. A numerical example of the scattering problem is given. [ABSTRACT FROM AUTHOR]

INFINITE ELEMENT METHOD FOR ELLIPTIC PROBLEMS

An infinite element method for solving elliptic equations with variable coefficients ispresented in this paper. For those solutions which possess singularities,very accurate singu-lar numerical solutions can be obtained with a small scale of computation; besides, it isunnecessary to know the order of singularity of the solutions or the analytic expressionsof particular solutions in advance. A numerical example is given in contrast with the finiteelement method.

A General Boundary Solution Method for Potential Flow around a 2D Semi-infinite Body

By using Cauchy's integral formula of analytical complex function and the third order complex spline function, a general boundary solution method for solving the complex potential field of the flow field around a 2D semi infinite body is presented in this paper. The pressure coefficients obtained by the present method agree well with those given by Acrivous, showing the validity of our method.

ADAPTIVE ELLIPSOIDAL ACOUSTIC INFINITE ELEMENT

It is shown that the basis of the ellipsoidal acoustic infinite elementBurnett method, the multipole expansion, cannot represent real ellipsoidal acoustic field exactly.To solve the problem, a weight of angular direction is added to the multipole expansion. Thecomparison of the modified method and the prime method shows that the modified method can describeand solve the ellipsoidal acoustic field more accurately than ever. A dilating sphere is used totest the new method further. Unlike other infinite element methods, varied ratio of the ellipsoidalartificial boundary instead of sphere is used. The pressure value of the artificial boundary isutilized as the initial value of the new method. Then the radiating phenomena of the ellipsoidalacoustic field can be researched using the new method. These examples show the feasibility of theadaptive method.

A NOVEL ELLIPSOIDAL ACOUSTIC INFINITE ELEMENT

A novel ellipsoidal acoustic infinite element is proposed. It is based a new pressure representation, which can describe and solve the ellipsoidal acoustic field more exactly. The shape functions of this novel acoustic infinite element are similar to the (Burnett's) method, while the weight functions are defined as the product of the complex conjugates of the shaped functions and an additional weighting factor. The code of this method is cheap to generate as for 1-D element because only 1-D integral needs to be numerical. Coupling with the standard finite element, this method provides a capability for very efficiently modeling acoustic fields surrounding structures of virtually any practical shape. This novel method was deduced in brief and the conclusion was kept in detail. To test the feasibility of this novel method efficiently,in the examples the infinite elements were considered,excluding the finite elements relative. This novel ellipsoidal acoustic infinite element can deduce the analytic solution of an oscillating sphere. The example of a prolate spheroid shows that the novel infinite element is superior to the boundary element and other acoustic infinite elements. Analytical and numerical results of these examples show that this novel method is feasible.

PLANE INFINITE ANALYTICAL ELEMENT AND HAMILTONIAN SYSTEM

It is not convenient to solve those engineering problems defined in an infinite field by using FEM. An infinite area can be divided into a regular infinite external area and a finite internal area. The finite internal area was dealt with by the FEM and the regular infinite external area was settled in a polar coordinate. All governing equations were transformed into the Hamiltonian system. The methods of variable separation and eigenfunction expansion were used to derive the stiffness matrix of a new infinite analytical element.This new element, like a super finite element, can be combined with commonly used finite elements. The proposed method was verified by numerical case studies. The results show that the preparation work is very simple, the infinite analytical element has a high precision, and it can be used conveniently. The method can also be easily extended to a three-dimensional problem.

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.

Numerical Simulation of Geotechnical Problems by Coupled Finite and Infinite Elements

in geotechnical engineering, numerical simulation of problems is of great importance. This work proposes a new formulation of coupled finite-infinite elements which can be used in numerical simulation ofgeotechnical problems in both static and dynamic conditions. Formulation and various implementation aspects of the proposed coupled finite-infinite elements are carefully discussed. To the authors＇ knowledge, this approach that considers coupled finite-infinite elements is more efficient in the sense that appropriate and accurate results are obtained by using less elements. The accuracy and efficiency of the proposed approach is considered by comparing the obtained results with analytical and numerical results. In a static case, the problem of circular domain ol infinite length is considered. In a dynamic case, one dimensional wave propagation problems arising from the Heaviside step fimction and impulse functions are considered. In order to get a more complete picture, two dimensional wave propagation in a circular qtmrter space is considered and the results are presented. Finally, a soil-structure interaction system subjected to seismic excitation is analyzed. In the analysis of soil-structure interaction phenomenon, frames with different number of storeys and soil media with various stiffness characteristics have been taken into consideration. In the analysis, the finite element software ANSYS has been used. For the newly developed infinite element, the programming has been done by the help of the User Programmable Features of the ANSYS software, which enable creating new elements in the ANSYS software.

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.

3D Diffraction of obliquely incident SH waves by twin infinitely long cylindrical cavities in layered poroelastic half-space

Abstract This paper studies three-dimensional diffraction of obliquely incident plane SH waves by twin infinitely long cylindrical cavities in layered poroelastic half-space using indirect boundary element method. The approach is validated by comparison with the literature, and the effects of cavity interval, incident frequency, and boundary drainage condition on the diffraction are studied through numerical examples. It is shown that, the interaction between two cavities is significant and surface displacement peaks become large when two cavities are close, and the surface displacement may be significantly amplified by twin cavities, and the influence range with large amplification can be as wide as 40 times of the cavity radius. Surface displacements in dry poroelastic case and saturated poroelastic cases with drained and undrained boundaries are evidently different under certain circumstances, and the differences may be much larger than those in the free-field response.

An Efficient Model for Transient Surface Waves in Both Finite and Infinite Water Depths

A numerical model is developed to simulate fully nonlinear extreme waves in finite and infinite water-depth wave tanks. A semi-mixed Enlerian-Lagrangian formulation is adopted and a higher-order boundary element method in conjunction with an image Green function is used for the fluid domain. The botmdary values on the free surface are updated at each time step by a fourth-order Runga-Kutta time-marching scheme at each time step. Input wave characteristics are specified at the upstream boundary by an appropriate wave theory. At the downstream boundary, an artificial damping zone is used to prevent wave reflection back into the computational domain. Using the image Green function in the whole fluid domain, the integrations on the two lateral walls and bottom are excluded. The simulation results on extreme wave elevations in finite and infinite water-depths are compared with experimental results and second-order analytical solutions respectively. The wave kinematics is also discussed in the present study.

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.

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.

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。

齿轮箱内部激励下振动噪声仿真研究

目的研究齿轮箱体在内部激励下的传动稳定性和振动噪声的产生、传播和辐射规律。方法考虑时变刚度、误差激励等因素对齿轮系统的影响,利用集中参数法建立齿轮传动纯扭转动力学模型。结合MATLAB数值计算,从动态啮合力入手,分析振动噪声在内部动态激励作用下的时域和频域特征。建立齿轮箱体有限元模型,进行模态分析和频率响应分析。以动力学分析结果为边界条件,分别利用声学无限元法和无反射边界法进行齿轮箱振动噪声仿真。结果获得了2000Hz内的固有频率、振型和频率响应曲线,结合振动峰值频率,对齿轮箱的振动情况进行了预测。得到了齿轮箱在无界声场中的辐射声功率级曲线、场点声压级曲线、声指向性和声压级云图,并对声学无限元法和无反射边界法的计算结果进行了对比,得到了二者的最佳适用条件。结论齿轮箱内部动态激励具有明显的周期性和冲击性,齿轮传动过程中含有较多的啮合频率和二倍频成分。齿轮箱上下表面为薄壁结构,振动比较明显,是各阶振型发生振动的主要部位。箱体在低阶模态下为单一振型,在高阶模态下出现多种振型耦合的现象。无限元法计算时间较长,但在近场分析时精度较高,适用于近场声学问题分析。无反射边界相比于无限元法耗费更少的计算时间,远场分析的精度更高,适用于高频、远场声学问题分析。

以创新能力为导向的研究性教学模式改革与实践——以高等数学为例

本文将对分课堂和五星教学模式的优势相结合,以一流课程建设为切入点,借助现代信息技术,提出了以创新能力培养为导向的研究性教学方法.并以高等数学中微元法和无穷限积分教学为例,展示了问题驱动+同伴讨论的研究性教学设计.

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。