基于边界元素法的柔软物体变形模拟

在计算机动画和虚拟现实技术中，基于物理的建模方法是高真实感地模拟物体受力变形和运动的有效途径．近年来基于边界元的物理模型方法因其简捷的计算模式而受到关注，该文针对当前边界元模型在视觉效果和计算量上的一些缺陷，分别提出了两方面的改进方法，基于LOD的动态自适应多分辨率网格边界元模型和近似的非线性边界元的物理模型，分别用于在不损失视觉效果的前提下减少计算量以及模拟物体大变形，并提出了相应的加速算法，取得了较好的效果．     

The development of the Trefftzian methodology for engineering design analysis

This paper reviews the developments in the Trefftzian Methodology, which have been undertaken by the authors at the University of Sheffield during the past fifteen years and the application of these developments to engineering design analysis. Initially, in the late 1970s, this work concentrated on the Direct Boundary Element Method (DBEM) and the Indirect Boundary Element Method (IBEM). Unfortunately these methods, as they are normally formulated, give rise to singular integrals, which require special mathematical treatment, when the source and field points coincide on the boundary of the component being analysed. These singular integrals can however be eliminated by placing the source boundary outside the domain of the problem being analysed so that the field and source points never coincide. This technique is known as either the Regular Direct Boundary Element Method (RDBEM) or the Regular Indirect Boundary Element Method (RIBEM) In a further development of the RIBEM, based on the Trefftz Method, the continuous distribution of sources is replaced with sources distributed at discrete points on the source boundary. This modified Trefftz Method eliminates the integrations in the solution procedure, it provides a series solution in terms of the fundamental solution of the problem being analysed and is referred to as the Indirect Discrete Boundary Method (IDBM). The emergence of the IDBM provided the opportunity to develop a combined Boundary Element Finite Element technique which enables these methods to be used simultaneously in a single calculation, thereby exploiting their strengths and minimising their weaknesses. A number of case studies will be discussed in the paper to illustrate the developments in the Trefftzian Methodology and its application to engineering design analysis.     

Prediction of geometric uncertainty effects on Fluid Dynamics by Polynomial Chaos and Fictitious Domain method

In this paper the Tensorial-expanded Chaos Collocation method has been used to solve Fluid Dynamic problems with geometric uncertainties. The main advantage of the Tensorial-expanded Chaos Collocation method is its non-intrusive formulation, so existing deterministic solvers can be used. A Least-Squares Spectral Element Method has been employed for the analysis of the deterministic differential problems obtained by Tensorial-expanded Chaos Collocation. This algorithm exploits a Fictitious Domain approach, so it is particularly suitable to solve differential problems defined on stochastic domains. The great capabilities of the Tensorial-expanded Chaos Collocation method combined to the Fictitious Domain-Least-Squares Spectral Element Method are demonstrated by numerical experiments.     

A partition of unity enriched dual boundary element method for accurate computations in fracture mechanics

We introduce a novel enriched Boundary Element Method (BEM) and Dual Boundary Element Method (DBEM) approach for accurate evaluation of Stress Intensity Factors (SIFs) in crack problems. The formulation makes use of the Partition of Unity Method (PUM) such that functions obtained from a priori knowledge of the solution space can be incorporated in the element formulation. An enrichment strategy is described, in which boundary integral equations formed at additional collocation points are used to provide auxiliary equations in order to accommodate the extra introduced unknowns. In addition, an efficient numerical quadrature method is outlined for the evaluation of strongly singular and hypersingular enriched boundary integrals. Finally, results are shown for mixed mode crack problems; these illustrate that the introduction of PUM enrichment provides for an improvement in accuracy of approximately one order of magnitude in comparison to the conventional unenriched DBEM.     

Relations between FEM and FVM applied to the poisson equation

The Finite Volume Method (FVM) with Voronoi bosex for discretizing elliptic boundary value problems is discussed. For this method the matrix of the linear system of equations is shown to be equal to the matrix for the Finite Element Method (FEM) iff a Delaunay triangulation is used.     

An object-oriented approach to the Generalized Finite Element Method

The Generalized Finite Element Method (GFEM) is a meshbased approach that can be considered as one instance of the Partition of Unity Method (PUM). The partition of unity is provided by conventional interpolations used in the Finite Element Method (FEM) which are extrinsically enriched by other functions specially chosen for the analyzed problem. The similarities and differences between GFEM and FEM are pointed out here to expand a FEM computational environment. Such environment is an object-oriented system that allows linear and non-linear, static and dynamic structural analysis and has an extense finite element library. The aiming is to enclose the GFEM formulation with a minimum impact in the code structure and meet requirements for extensibility and robustness. The implementation proposed here make it possible to combine different kinds of elements and analysis models with the GFEM enrichment strategies. Numerical examples, for linear analysis, are presented in order to demonstrate the code expansion and to illustrate some of the above mentioned combinations.     

A direct hybrid finite element – Wave based modelling technique for efficient coupled vibro-acoustic analysis

This paper presents a newly developed hybrid simulation technique for coupled structural–acoustic analysis, which applies a wave based model for the acoustic cavity and a direct or modally reduced Finite Element model for the structural part. The resulting hybrid model benefits from the computational efficiency of the wave based method, while retaining the Finite Element Method’s ability to model the structural part of the problem in great detail. Application of this approach to the analysis of three fully coupled vibro-acoustic problems with an increasing modelling complexity shows the improved computational efficiency as compared to classical Finite Element procedures and illustrates the potential of the hybrid method as a powerful tool for the analysis of coupled structural–acoustic systems in the low- and mid-frequency range.     

A boundary element formulation for the substation grounding design

A Boundary Element approach for the numerical computation of substation grounding systems is presented. In this general formulation, several widespread intuitive methods (such as Average Potential Method (APM)) can be identified as the result of specific choices for the test and trial functions and suitable assumptions introduced in the Boundary Element Method (BEM) formulation to reduce computational cost. While linear and parabolic leakage current elements allow to increase accuracy, computing time is drastically reduced by means of new completely analytical integration techniques and semi-iterative methods for solving linear equations systems. This BEM formulation has been implemented in a specific Computer Aided Design system for grounding analysis developed in the last years. The feasibility of this new approach is demonstrated with its application to a real problem.     

A combined DEM–FEM numerical method for Shot Peening parameter optimisation

A numerical modelling approach capable of simulating Shot Peening (SP) processes of industrial interest was developed by combining the Discrete Element Method (DEM) with the Finite Element Method (FEM).In this approach, shot–shot and shot–target interactions as well as the overall shot flow were simulated efficiently using rigid body dynamics. A new algorithm to dynamically adapt the coefficient of restitution (CoR) for repeated impacts of shots on the same spot was implemented in the DEM code to take into account the effect of material hardening. Then, a parametric study was conducted using the Finite Element Method (FEM) to investigate the influence of the SP parameters on the development of residual stresses.Finally, a two-step coupling method is presented to combine the output of DEM simulation with FEM analyses to retrieve the Compressive Residual Stresses (CRS) after multiple impacts with the aim to evaluate the minimum area required to be modelled to realistically capture the field of residual stresses. A series of such coupled analyses were performed to determine the effect of peening angle and the combination of initial velocity and mass flow rate on CRS.     

元素判别值分配法用于求解Hamilton圈问题的算法设计

Hamilton问题有最小Hamilton圈(H-圈)及Hamilton通路问题。H-圈问题可用于求解货郎担问题。但尚没有一种有效的求解方法。作者研究的‘元素判别值分配法’可以用于求解H-圈问题。该文介绍该方法用于求解最小H-圈的表上求解及程序求解的算法设计。     

Development of an RVE using a DEM–FEM scheme under modified approximate periodic boundary condition to estimate the elastic mechanical properties of open foams

Engineering with Computers - In this article, a methodology based on Discrete Element Method (DEM) and Finite Elements Method (FEM) combined with modified Approximate Periodic Boundary Condition...     

A simplified finite element solution for the plates on elastic foundation

The simplified Finite Element Method is used to analyze plates supported on an elastic continuum. The method assembles the stiffness matrix of the foundation into a banded, diagonal matrix and, therefore, can be solved by using the tridiagonal technique. This process reduces the computer storage dramatically. Various problems of plates on elastic continua have been solved and the results are compared with those obtained using the conventional Finite Element Methods. Good agreements are obtained.     

基于边界面法的完整实体应力分析理论与应用

提出基于边界面法（Boundary Face Method,BFM）的完整实体应力分析方法.在该分析中,避免对结构作几何上的简化,结构的所有局部细节都按实际形状尺寸作为三维实体处理.以边界积分方程为理论基础的BFM是完整实体应力分析的自然选择.在该方法中,边界积分和场变量插值都在实体边界曲面的参数空间里实现.高斯积分点的几何数据,如坐标、雅可比和外法向量都直接由曲面算得,而不是通过单元插值近似获得,从而避免几何误差.该方法的实现直接基于边界表征的CAD模型,可做到与CAD软件的无缝连接.线弹性问题的应用实例表明,该方法可以简单有效地模拟具有细小特征的复杂结构,并且计算结果的应力精度比边界元法（Boundary Element Method,BEM）和有限元法（Finite Element Method,FEM）高.     

Surface Representation with Closest Point Projection in the X-FEM

Mathematical Models and Computer Simulations - At present, the eXtended Finite Element Method (X-FEM) is a common generalization of the classical finite element method for solving problems of...     

三维离散单元法数值模拟中查找邻居元的一种新算法

将三维离散单元法(DEM)运用到模拟泥石流运动的计算中时，发现查找邻居元耗费大量时间和空间。为了克服缺点，文中提出了一种新的算法——链树图法，并对其原理、算法、运行时间和空间进行分析。通过与原算法盒子空间法的比较表明，新算法在运行时间和空间都明显优于原算法。     

Thick shells of revolution: Derivation of the dynamic stiffness matrix of continuous elements and application to a tested cylinder

This paper describes a procedure for calculating the dynamic stiffness matrix of tubular shells with free edge boundary conditions. Such an analysis forms the basis for the Continuous Element Method. The method is used to formulate a thick axisymmetric shell element which takes into account rotatory inertia, transverse shear deformation and non-axisymmetric loadings.     

Numerical–experimental crack growth analysis in AA2024-T3 FSWed butt joints

This paper deals with a numerical and experimental investigation on the influence of residual stresses on fatigue crack growth in AA2024-T3 friction stir welded butt joints. The computational approach is based on the sequential usage of the Finite Element Method (FEM) and the Dual Boundary Element Method (DBEM). Linear elastic FE simulations are performed to evaluate the process induced residual stresses, by means of the contour method. The computed stress field is transferred to a DBEM environment and superimposed to the stress field produced by a remote fatigue traction load applied on a friction stir welded cracked specimen; the crack propagation is then simulated according to a two-parameter growth model. Numerical results have been compared with experimental data showing good agreement and evidencing the predictive capability of the proposed method. The obtained results highlight the influence of the residual stress distribution on crack growth.     

A new family of exponential infinite elements for the analysis of lossless electromagnetic waveguides

In this paper the Finite Element Method is employed for the analysis of electromagnetic lossless waveguides. The curl-curl equation, deduced from Maxwell's equations, is solved for the electric field. We have studied the appearance of parasitic solutions and formulated a sufficient condition for their elimination which puts a contraint on the Finite Element spaces for the approximation of the field components. A new family of discontinuous exponential infinite elements is proposed for the analysis of open waveguides: they are employed together with edge elements and a non-linear eigenvalue problem is deduced. We have presented numerical results in order to prove the validity of such infinite elements versus the Virtual Boundary Technique.     

An enriched finite element method for efficient solutions of transient heat diffusion problems with multiple heat sources

Engineering with Computers - We propose an efficient formulation using the framework of Generalized Finite Element Method (GFEM) for the solutions of transient heat diffusion problems having...     

Maintaining large time steps in explicit finite element simulations using shape matching

We present a novel hybrid method to allow large time steps in explicit integrations for the simulation of deformable objects. In explicit integration schemes, the time step is typically limited by the size and the shape of the discretization elements as well as by the material parameters. We propose a two-step strategy to enable large time steps for meshes with elements potentially destabilizing the integration. First, the necessary time step for a stable computation is identified per element using modal analysis. This allows determining which elements have to be handled specially given a desired simulation time step. The identified critical elements are treated by a geometric deformation model, while the remaining ones are simulated with a standard deformation model (in our case, a corotational linear Finite Element Method). In order to achieve a valid deformation behavior, we propose a strategy to determine appropriate parameters for the geometric model. Our hybrid method allows taking much larger time steps than using an explicit Finite Element Method alone. The total computational costs per second are significantly lowered. The proposed scheme is especially useful for simulations requiring interactive mesh updates, such as for instance cutting in surgical simulations.