Intelligent finite element mesh generation

A knowledge-based and automatic finite element mesh generator (INTELMESH) for two-dimensional linear elasticity problems is presented. Unlike other approaches, the proposed technique incorporates the information about the object geometry as well as the boundary and loading conditions to generate an a priori finite element mesh which is more refined around the critical regions of the problem domain. INTELMESH uses a blackboard architecture expert system and the new concept of substracting to locate the critical regions in the domain and to assign priority and mesh size to them. This involves the decomposition of the original structure into substructures (or primitives) for which an initial and approximate analysis can be performed by using analytical solutions and heuristics. It then uses the concept of wave propagation to generate graded nodes in the whole domain with proper density distribution. INTELMESH is fully automatic and allows the user to define the problem domain with minimum amount of input such as object geometry and boundary and loading conditions. Once nodes have been generated for the entire domain, they are automatically connected to form well-shaped triangular elements ensuring the Delaunay property. Several examples are presented and discussed. When incorporated into and compared with the traditional approach to the adaptive finite element analysis, it is expected that the proposed approach, which starts the process with near optimal initial meshes, will be more accurate and efficient.     

Reduction of train-induced building vibrations by using open and filled trenches

A numerical investigation on the effectiveness of open and in-filled trenches in reducing the building vibrations due to passing trains is presented. Particularly, a two-dimensional soil-structure system containing the cross-section of a railway embankment, the underlying soil, a trench barrier and a nearby six-storey building is considered. For the analysis, a time domain coupled boundary element-finite element algorithm is employed. Unlike most of the previous formulations, this model completely considers the soil-structure interaction effects and directly determines the effect of the wave barrier on the structural response. The effects of geometrical and material properties of the trench and its backfill material on the structural response are investigated. The results point out that using a trench barrier, a reduction level up to 80% of the building vibrations and internal forces can be achieved. Increasing the depth or the width of a trench may improve its reduction effect and a softer backfill material results in a better isolation effect.     

Analysis and design of acoustic transition sections for impedance matching and mode conversion

This work considers the problem of designing passive transition sections to provide impedance matching and mode conversion for acoustic wave propagation. The base configuration consists of two waveguides connected by a transition section. The objective is to find a placement of material inside this section to make it function as an impedance matcher or a mode converter with minimal losses. A finite element approximation of the Helmholtz equation in a truncated domain together with Dirichlet-to-Neumann type non-reflecting boundary conditions models the wave propagation. Material distribution techniques solve the resulting topology optimization problem and the resulting interfacial devices show good transmission properties.     

基于分层模型的复合材料耦合Lamb波频率—波数域特性研究

针对复合材料层合板中耦合Lamb波的传播问题,基于分层模型提出解析建模与有限元数值模拟相结合的方法对其进行预测和评估。利用Legendre正交多项式展开法推导多层各向异性复合材料层合板中耦合Lamb波的控制方程,并对频率-波数域频散特性曲线实现数值求解。基于平面壳单元构建复合材料层合板的有限元模型,采用波结构加载法生成单一Lamb波基本模态,设计复合材料层合板的不同纤维取向、边界和界面约束条件,并经二维傅里叶变换获得有限元模拟数据的频率-波数域频散特性曲线。通过对比验证,结果表明两种方法均有较好的吻合性。     

基于动力学仿真的系留气球鼻锥有限元分析

针对系留气球进行了动力学仿真分析,在此基础上对一种用于固定球体的新型鼻锥结构进行了结构有限元分析,以确定其强度与刚度.首先采用计算流体力学CFD求得特定风速下系留气球所受的气动力,随后通过多体动力学软件Adams进行动力学仿真分析,确定作用在鼻锥上载荷的大小,并以此作为有限元分析的载荷边界条件;然后采用有限元分析的方法对鼻锥结构进行静力学和动力学分析;最后确定极限风速下艇首与鼻锥连接处的变形、载荷及应力情况.通过分析,为新型鼻锥结构进一步的设计改进与优化提供了参考依据.     

The FEM optimization of active vibration control in structures by solving the corresponding two-point-boundary-value problem

An algorithm for solving optimal active vibration control problems by the finite element method (FEM) is presented. The optimality equations for the problem are derived from Pontryagin’s principle in the form of a set of the fourth order ordinary differential equations that, together with the initial and final boundary conditions, constitute the boundary value problem in the time domain, which in control is referred to as a two-point-boundary-value problem. These equations decouple in the modal space and can be solved by the FEM technique. An analogy between the optimality equations and the governing equations for a set of certain static beams permits obtaining numerical solutions to the optimal control problem with the help of standard ‘structural’ FEM software. The optimal action of actuators is automatically calculated by applying the independent modal space control concept. The structure’s response to actuation forces is also determined and can independently be verified for spillover effects. As an illustration, the algorithm is used for the analysis of optimal action of actuators to attenuate vibrations of an elastic fin.     

Lagrangian finite element modelling of dam–fluid interaction: Accurate absorbing boundary conditions

The dynamic dam–fluid interaction is considered via a Lagrangian approach, based on a fluid finite element (FE) model under the assumption of small displacement and inviscid fluid. The fluid domain is discretized by enhanced displacement-based finite elements, which can be considered an evolution of those derived from the pioneering works of Bathe and Hahn [Bathe KJ, Hahn WF. On transient analysis of fluid–structure system. Comp Struct 1979;10:383–93] and of Wilson and Khalvati [Wilson EL, Khalvati M. Finite element for the dynamic analysis of fluid–solid system. Int J Numer Methods Eng 1983;19:1657–68]. The irrotational condition for inviscid fluids is imposed by the penalty method and consequentially leads to a type of micropolar media. The model is implemented using a FE code, and the numerical results of a rectangular bidimensional basin (subjected to horizontal sinusoidal acceleration) are compared with the analytical solution. It is demonstrated that the Lagrangian model is able to perform pressure and gravity wave propagation analysis, even if the gravity (or surface) waves are dispersive. The dispersion nature of surface waves indicates that the wave propagation velocity is dependent on the wave frequency.For the practical analysis of the coupled dam–fluid problem the analysed region of the basin must be reduced and the use of suitable asymptotic boundary conditions must be investigated. The classical Sommerfeld condition is implemented by means of a boundary layer of dampers and the analysis results are shown for the cases of sinusoidal forcing.The classical Sommerfeld condition is highly efficient for pressure-based FE modelling, but may not be considered fully adequate for the displacement-based FE approach. In the present paper a high-order boundary condition proposed by Higdom [Higdom RL. Radiation boundary condition for dispersive waves. SIAM J Numer Anal 1994;31:64–100] is considered. Its implementation requires the resolution of a multifreedom constraint problem, defined in terms of incremental displacements, in the ambit of dynamic time integration problems. The first- and second-order Higdon conditions are developed and implemented. The results are compared with the Sommerfeld condition results, and with the analytical unbounded problem results.Finally, a number of finite element results are presented and their related features are discussed and critically compared.     

Finite Element Simulation of Three-Dimensional Free-Surface Flow Problems

An adaptive finite element algorithm is described for the stable solution of three-dimensional free-surface-flow problems based primarily on the use of node movement. The algorithm also includes a discrete remeshing procedure which enhances its accuracy and robustness. The spatial discretisation allows an isoparametric piecewise-quadratic approximation of the domain geometry for accurate resolution of the curved free surface. The technique is illustrated through an implementation for surface-tension-dominated viscous flows modelled in terms of the Stokes equations with suitable boundary conditions on the deforming free surface. Two three-dimensional test problems are used to demonstrate the performance of the method: a liquid bridge problem and the formation of a fluid droplet.     

Numerical study of dynamic processes in a continuous medium with a crack initiated by a near-surface disturbance by means of the grid-characteristic method

The purpose of this work is to study the problem of the near-surface disturbance propagation in a massive rock containing various heterogeneities, i.e., empty or filled cracks. Numerical solutions have been obtained for problems of wave propagation in such highly heterogeneous media, including those taking into account the plastic properties of the rock that can be manifested in the vicinity of a seismic gap or a well bore. All kinds of elastic and elastoplastic waves are analyzed resulting from the propagation of the initial disturbance and the waves arising from the reflection from the cracks and from the boundaries of the integration domain. An investigation was carried out of wave identification by means of seismograms obtained at the receiver located near the ground surface. In this study, the grid-characteristic method is employed using computational grids with triangular meshes and boundary conditions formulated at the interface between the rock and the crack, and on free surfaces in an explicit form. The proposed numerical method is extremely general and is suitable for investigations of the processes of seismic waves’ interaction with heterogeneous inclusions because it ensures the construction of the most correct computational algorithms at the boundaries of the integration domain and at the medium’s interface.     

High-order FEM domain decomposition models for high-frequency wave propagation in heterogeneous media

Large scale scientific computing models, requiring iterative algebraic solvers, are needed to simulate high-frequency wave propagation because large degrees of freedom are needed to avoid the Helmholtz computer model pollution effects. In this work, we investigate the use of multiple additive Schwarz type domain decomposition (DD) approximations to efficiently simulate two- and three-dimensional high-frequency wave propagation with high-order FEM. We compare our DD based results with those obtained using a standard geometric multigrid approach for up to 1,000 and $300$ wavelength models in two- and three-dimensions, respectively.     

Detection of cavities in Helmholtz-type equations using the boundary element method

Helmholtz-type equations arise naturally in many physical applications related to wave propagation, vibration phenomena and heat transfer. These equations are often used to describe the vibration of a structure, the acoustic cavity problem, the radiation wave, the scattering of a wave and heat conduction in fins. In this paper, the numerical recovery of a single and two circular cavities in Helmholtz-type equations from boundary data is investigated. The boundary element method (BEM), in conjunction with a constrained least-squares minimisation, is used to solve this inverse geometric problem. The accuracy and stability of the proposed numerical method with respect to the distance between the cavities and the outer boundary of the solution domain, the location and size of the cavities, and the distance between the cavities are also analysed. Unique and stable numerical solutions are obtained.     

Finite element methods for the Stokes problem on complicated domains

It is a standard assumption in the error analysis of finite element methods that the underlying finite element mesh has to resolve the physical domain of the modeled process. In case of complicated domains which appear in many applications such as ground water flows this requirement sometimes becomes a bottleneck. The resolution condition links the computational complexity to the number (and size) of geometric details although the accuracy requirements, possibly, are moderate and would allow a (locally) coarse mesh width. Therefore even the coarsest available discretization can lead to a huge number of unknowns. The composite mini element is a remedy to this dilemma because the degrees of freedom are not linked to the number of geometric details. The basic concept for the Stokes problem with uniform no-slip boundary conditions has been introduced and analyzed in [D. Peterseim, S. Sauter, The composite mini element – coarse mesh computation of Stokes flows on complicated domains, SINUM, 46(6) (2008) 3181–3206]. Here, we generalize the composite mini element to slip, leak and Neumann boundary conditions so that it becomes applicable to this much larger and more important problem class. The main results are (a) the algorithmic concept remains unchanged and the new boundary conditions can be implemented as a weighted quadrature rule, (b) the stability and convergence can be proved under very mild assumption on the domain geometries, (c) the analysis is far from trivial and requires the development of substantially new tools compared to the simple case of uniform no-slip boundary conditions.     

Benchmarking two simulation models for underwater and atmospheric sound propagation

Computational wave propagation models are widely used in underwater and atmospheric sound propagation simulation. In most realistic cases the physical domains involved are irregular. We have developed finite element techniques, applied to general irregular meshes and coupled with discrete, artificial absorbing boundary conditions of nonlocal type, for the Helmholtz equation and its ‘standard’ parabolic approximation. The physical domain is axially symmetric, with several fluid layers of variable acoustic properties. Boundaries and interfaces of general topography are allowed. The resulting models are referred to as the FENL and CNP1-NL models, respectively. We present results of the FENL model for underwater acoustic applications related to object identification and of the CNP1-NL for atmospheric sound propagation over an irregular terrain.     

3-D Rail-Wheel contact analysis using FEA

Mechanics of the Rail-Wheel contact is one of the fundamental areas of the study in Railway Engineering, requiring both vast application expertise and dependable analysis approaches. Analytical formulations describing the physics of this phenomenon are only defined for certain type of simple contact geometries, therefore for more complicated geometries the analytical models utilizing closed formulations remain elusive. Remaining option is to utilize numerical computation methods. Railway engineers are, to the certain extent, successfully applied one of the numerical computation techniques known as Finite Element Analysis (FEA) into Rail-Wheel contact problems to validate their results by comparing them to their real life data obtained over the years. In the literature, most of the work on the Rail-Wheel contact FEA is either 2-dimensional axi-symmetric or simple 3D Rail-Wheel models with poor mesh count/quality or undesired Tet-mesh, latter known to exhibit stiff deformation characteristics during the deformation. Also, in majority of the FEA studies, boundary conditions and/or total load are applied with some approximations. This study focuses more on the fundamental way of handling Rail-Wheel contact problems from the FEA standpoint, and highlights required steps for more realistic 3D solutions to these types of problems. 3D FE analysis results obtained show good agreement with real life problems experienced at both railway Wheel and Rail.     

超声波在各向同性固体中传播的数值模拟

介绍以应用动量守恒和应力-应变关系为各向同性弹性介质进行微变形建立超声波传播方程,并利用一种有限元方法和差分法,分析超声波(P波)在各向问性介质中传播,及在裂缝上的散射结果.并且通过计算机程序模拟二维超声波的传播,散射的数值模拟与几何理论结果是相符合的.因此超声检测仿真软件是可以预测超卢检测过程中的波形.超声探头的建模发展趋势是利用FDM和FEM方法研究超声检测的仿真软件,分析结果将广泛应用到检测过程中.     

Influence of natural disasters on ground facilities

The purpose of this article is to study the problem of the propagation of waves that result in earthquakes in different geological media: homogeneous, multilayer, gradient, with fractured layer, and karst cavern. The authors pose the problem of analyzing the impact of waves on ground structures: buildings and dams. Numerical solutions of problems of wave propagation in heterogeneous media are obtained. On the basis of the analysis of wave patterns, the types of waves propagated from the focus of the earthquake are qualified. The comparison of the impact of elastic waves on the day surface for the cases of different geological media is done. Synthetic seismograms for these media are obtained. The influence of elastic waves on the stability of ground structures is qualitatively examined. The grid-characteristic method for triangle meshes with the formulation of boundary conditions on interfaces of rock-crack, building-rock, rock-water, and dam-water, as well as free surfaces in an explicit form, is used in this paper.     

Numerical solution of the ‘classical’ Boussinesq system

We consider the ‘classical’ Boussinesq system of water wave theory, which belongs to the class of Boussinesq systems modelling two-way propagation of long waves of small amplitude on the surface of water in a horizontal channel. (We also consider its completely symmetric analog.) We discretize the initial-boundary-value problem for these systems, corresponding to homogeneous Dirichlet boundary conditions on the velocity variable at the endpoints of a finite interval, using fully discrete Galerkin-finite element methods of high accuracy. We use the numerical schemes as exploratory tools to study the propagation and interactions of solitary-wave solutions of these systems, as well as other properties of their solutions.     

The simulation of 3D elastic scattering produced by thin rigid inclusions using the traction boundary element method

A mixed formulation that uses both the traction boundary element method (TBEM) and the boundary element method (BEM) is proposed to compute the three-dimensional (3D) propagation of elastic waves scattered by two-dimensional (2D) thin rigid inclusions. Although the conventional direct BEM has limitations when dealing with thin-body problems, this model overcomes that difficulty. It is formulated in the frequency domain and, taking into account the 2-1/2D configuration of the problem, can be expressed in terms of waves with varying wavenumbers in the zdirection, k_z. The elastic medium is homogeneous and unbounded and it should be noted that no restrictions are imposed on the geometry and orientation of the internal crack.     

Schwarz iterations for the efficient solution of screen problems with boundary elements

This paper investigates two domain decomposition algorithms for the numerical solution of boundary integral equations of the first kind. The schemes are based on theh-type boundary element Galerkin method to which the multiplicative and the additive Schwarz methods are applied. As for twodimensional problems, the rates of convergence of both methods are shown to be independent of the number of unknowns. Numerical results for standard model problems arising from Laplaces' equation with Dirichlet or Neumann boundary conditions in both two and three dimensions are discussed. A multidomain decomposition strategy is indicated by means of a screen problem in three dimensions, so as to obtain satisfactory experimental convergence rates.     

Multi-scale boundary element modelling of material degradation and fracture

In the present paper a multi-scale boundary element method for modelling damage is proposed. The constitutive behaviour of a polycrystalline macro-continuum is described by micromechanics simulations using averaging theorems. An integral non-local approach is employed to avoid the pathological localization of micro-damage at the macro-scale. At the micro-scale, multiple intergranular crack initiation and propagation under mixed mode failure conditions is considered. Moreover, a non-linear frictional contact analysis is employed for modelling the cohesive-frictional grain boundary interfaces. Both micro- and macro-scales are being modelled with the boundary element method. Additionally, a scheme for coupling the micro-BEM with a macro-FEM is also proposed. To demonstrate the accuracy of the proposed method, the mesh independency is investigated and comparisons with two macro-FEM models are made to validate the different modelling approaches. Finally, microstructural variability of the macro-continuum is considered to investigate possible applications to heterogeneous materials.