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.     

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.     

Dual BEM for crack growth analysis on distributed-memory multiprocessors

The Dual Boundary Element Method (DBEM) has been presented as an effective numerical technique for the analysis of linear elastic crack problems [Portela A, Aliabadi MH. The dual boundary element method: effective implementation for crack problems. Int J Num Meth Engng 1992;33:1269–1287]. Analysis of large structural integrity problems may need the use of large computational resources, both in terms of CPU time and memory requirements. This paper reports a message-passing implementation of the DBEM formulation dealing with the analysis of crack growth in structures. We have analyzed the construction of the system and its resolution. Different data distribution techniques have been studied with several problems. Results in terms of scalability and load balance for these two stages are presented in this paper.     

A two-parameter model for crack growth simulation by combined FEM–DBEM approach

This paper describes the application of a two-parameters crack growth model, based on the usage of two threshold material parameters (ΔK_th and K_max,th) and on the allowance for residual stresses, introduced at the crack tip by a fatigue load spectrum or by material plastic deformations. The coupled usage of finite element method (FEM) and dual boundary element method (DBEM) is proposed in order to take advantage of the main capabilities of the two methods.The procedure is validated by comparison with available experimental results, in order to assess its capability to predict the retardation phenomena, introduced by a variable load spectrum or by a plastic deformation introduced with a tool on the panel (indentation).In particular two different tests are made: the first test involve a CT specimen undergoing a load spectrum and the second one involve a dented panel undergoing a constant amplitude fatigue load. In both cases a satisfactory numerical–experimental correlation will be proved.The main advantages of the aforementioned procedure are: the simplicity of the crack growth law calibration (few constant amplitude tests are sufficient without the need for any non-physical calibration parameters), and the possibility to simulate residual stress effects on crack propagation with a simplified approach, based on linear elastic fracture mechanics.     

Finite element analysis of crack closure in plate bending

The effect of crack closure in plate bending is studied using the finite element method. Elastic plates containing through-wall-thickness stationary cracks under transverse pressure loading are considered with different plate thicknesses and boundary conditions, respectively. Crack closure on the compression side is modeled two different ways: line closure and surface closure models. A plate bending element degenerated from a three-dimensional solid element is used to model such crack closure. Effects of crack closure are compared using the line or surface closure model for different plate thicknesses and boundary conditions, respectively.     

Boundary element analysis of three-dimensional mixed-mode cracks via the interaction integral

A three-dimensional boundary element method (BEM) implementation of the interaction integral methodology for the numerical analysis of mixed-mode three-dimensional cracks is presented in this paper. The interaction integral is evaluated from a domain representation naturally compatible with the BEM, since stresses, strains and derivatives of displacements at internal points can be evaluated using their appropriate boundary integral equations. Special emphasis is put in the selection of the auxiliary function that represents the virtual crack advance in the domain integral. This is found to be a key feature to obtain reliable results at the intersection of crack fronts with free surfaces. Several examples are analysed to demonstrate the efficiency and accuracy of the implementation.     

Fracture resistance via topology optimization

The fracture resistance of structures is optimized using the level-set method. Fracture resistance is assumed to be related to the elastic energy released by a crack propagating in a normal direction from parts of the boundary that are in tension, and is calculated using the virtual crack extension technique. The shape derivative of the fracture-resistance objective function is derived. Two illustrative two-dimensional case studies are presented: a hole in a plate subjected to biaxial strain; and a bridge fixed at both ends subjected to a single load in which the compliance and fracture resistance are jointly optimized. The structures obtained have rounded corners and more material at places where they are in tension. Based on the results, we propose that fracture resistance may be modeled more easily but less directly by including a term proportional to surface area in the objective function, in conjunction with nonlinear elasticity where the Young’s modulus in tension is lower than in compression.     

带边角裂纹悬臂Mindlin 板的振动特性研究

本文基于Mindlin板理论,应用Ritz法研究带边角裂纹Mindlin板的振动特性,分析了不同裂纹参数如裂纹位置,裂纹长度,裂纹角度对悬臂Mindlin板的固有频率和模态的影响.利用Ritz法求解固有频率和模态函数,本文构造了一个特殊的模态函数,其模态函数由两部分构成,一部分是用梁函数组合法得到的无裂纹理想完整矩形板的振型,另一部分是利用裂纹尖端奇异性理论,构造描述裂纹附近位移和转角不连续的角函数.通过高精度的数值计算软件Maple得出结果,并与有限元软件ANSYS分析的结果进行对比,验证本文计算结果的准确性.     

Virtual trackballs revisited

Rotation of three-dimensional objects by a two-dimensional mouse is a typical task in computer-aided design, operation simulations, and desktop virtual reality. The most commonly used rotation technique is a virtual trackball surrounding the object and operated by the mouse pointer. We review and provide a mathematical foundation for virtual trackballs. The first, but still popular, virtual trackball was described by Chen et al. (1998). We show that the virtual trackball by Chen et al. does not rotate the object along the intended great circular arc on the virtual trackball and we give a correction. Another popular virtual trackball is Shoemake's quaternion implementation (1992), which we show to be a special case of the virtual trackball by Chen et al.. Shoemake extends the scope of the virtual trackball to the full screen. Unfortunately, Shoemake's virtual trackball is inhomogeneous and discontinuous with consequences for usability. Finally, we review Bell's virtual trackball (1998) and discuss studies of the usability of virtual trackballs.     

A doubly iterative BEM for solving crack closing in an elastic body

An algorithm for the two-dimensional elastic bodies with closed crack and defects loaded by a moving contact elastic body is proposed using a sub-regional boundary element method. Since the extent and status of the contact surface of two elastic bodies and the crack within the body are all not known in advance, a doubly iterative contact algorithm has been presented. The BEM program for solving the closed crack cases has been developed, some numerical examples have been calculated, and the results of the center crack cases are in good agreement with the analytical solution in classical fracture mechanics. In the condition of friction and non-friction, some coupling computational results of the SIF for the closed crack cases, which have different angles and loaded by a moving contact elastic body, have also been obtained by numerical computation. The cracked plate subjected to the moving contact elastic body has been analyzed under the conditions of drilling hole near the crack.     

Accurate evaluation of support reactions in finite element plate-bending analysis

Two simple approaches are presented which allow the distribution of support reactions to be predicted with as high degree of accuracy as the displacements. In the first approach the plate element assembly is completed with special one-dimensional elastic support elements. If their Winkler coefficient is suitably tuned, an accurate prediction of reactions is obtained as a part of the finite element analysis without unduly affecting the displacements and moments of the plate. In the second approach, a standard finite element calculation (without elastic support elements) is performed first and the distribution of reactions is then evaluated based on the known nodal forces at boundary nodes of the plate.

The two approaches are indiscriminately applicable with Kirchhoff and Reissner-Mindlin plate bending elements. Their practical efficiency is illustrated by numerical examples.     

Starting jet flows in a three-dimensional channel with larynx-shaped constriction

A numerical model for the three-dimensional starting jet flow in a channel with a static larynx-shaped constriction is presented. Detailed resolution of this kind of jet flow is necessary in order to understand the complex coupling between flow and acoustics in the process of human phonation. The numerical model is based on the equation of continuity and the Navier–Stokes equations. The investigations are done with the open source CFD package OpenFOAM. Numerical simulations are performed for a square-sectioned channel geometry, which is constricted with a fixed shape conforming to the fully opened human glottis. Time-dependent inflow boundary conditions are applied in order to model transient glottal flow rates. The setup of the numerical simulations corresponds to the configuration of a model experiment in order to allow detailed validation. The numerical results are in good agreement with the experimental data, when the near-wall region in the glottal gap is adequately resolved by the numerical grid. The results illustrate the complex interactions between the jet flow and the surrounding vortices.     

求解应力强度因子的样条虚边界元交替法

为求解平面裂纹问题的应力强度因子,提出基于Muskhelishvili基本解和样条虚边界元法的样条虚边界元交替法.该方法将平面内带裂纹有限域问题分解成带裂纹无限域问题与不带裂纹有限域问题的叠加.带裂纹无限域问题利用Muskhelishvili基本解法直接得出,不带裂纹有限域问题采用样条虚边界元法求解.利用该方法对复合型中心裂纹方板和I型偏心裂纹矩形板进行分析.数值结果表明该方法精度高且适用性强.     

Topology optimization of three-dimensional structures using optimum microstructures

In this paper, optimum three-dimensional microstructures derived in explicit analytical form by Gibianski and Cherkaev (1987) are used for topology optimization of linearly elastic three-dimensional continuum structures subjected to a single case of static loading. For prescribed loading and boundary conditions, and subject to a specified amount of structural material within a given three-dimensional design domain, the optimum structural topology is determined from the condition of maximum integral stiffness, which is equivalent to minimum elastic complicance or minimum total elastic energy at equilibrium.The use of optimum microstructures in the present work renders the local topology optimization problem convex, and the fact that local optima are avoided implies that we can develop and present a simple sensitivity based numerical method of mathematical programming for solution of the complete optimization problem.Several examples of optimum topology designs of three-dimensional structures are presented at the end of the paper. These examples include some illustrative full three-dimensional layout and topology optimization problems for plate-like structures. The solutions to these problems are compared to results obtained earlier in the literature by application of usual two-dimensional plate theories, and clearly illustrate the advantage of the full three-dimensional approach.     

A novel perturbation expansion method for coupled system of acoustics and structures

We formulate a coupled vibration problem between a structure and an acoustic field in a mathematically rigorous fashion. A typical example of the structure is a car body that can be modeled by a cluster of thin plates. The problem leads to a nonstandard eigenvalue problem in a function space. Furthermore, we introduce a coupling strength parameter ε as a multiplier applied to the nondiagonal coupling terms. A natural interpretation of this parameter is given. We represent an eigenpair for the coupled system by a perturbation series with respect to ε which enable us to express the eigenpair for the coupled case by those for the decoupled case. We prove that the series consists only of even order terms of ε. In some practical applications, by using this perturbation series, it would become unnecessary to perform time consuming computations to get coupled eigenvalues, and hence the present results obtained by the perturbation analysis might have considerable engineering importance. We confirm the adequacy of this perturbation analysis by investigating some numerical examples. The results are given for a two-dimensional coupled problem. Without loss of generality, the same operator theoretical approach applies to the eigenvalue problems of the coupled vibration problem in a more general three-dimensional acoustic region with a plate for a part of its boundary.     

二维多域弹性问题虚边界无网格伽辽金法分析

针对复杂的不同材料属性的多域组合问题（比如复合材料交界面上接触应力的计算）,虚边界无网格伽辽金法被进一步研究,提出了二维多域弹性问题虚边界无网格伽辽金法。简要介绍了多域组合思想、子域虚边界元法,详细推导了二维多域弹性问题分析的虚边界无网格伽辽金法,得到具体的离散格式,便于编程,推广研究。方程的加权系数为位移、面力、连续边界上的位移与面力关系式偏导,数值意义明确,公式具体。最后通过计算数值实例为复合材料交界面上接触应力的计算,给出了复合圆盘接触面上的法向、径向应力,分多种方案调整每个子域的虚边界半径值,所得结果与解析解、其他数值方法进行比较。结论是二维多域弹性问题虚边界无网格伽辽金法的方法计算可行、精确性与稳定性好。     

虚拟服装展示系统的比较研究

虚拟服装展示是借助立体全息技术、互联网或数字互动大屏幕来展示人体或数字角色“穿上”虚拟服装后的动态视觉效果。随着数字媒体艺术、交互技术和立体显示技术的发展,虚拟服装展示系统被广泛用于立体时装设计、服装表演、娱乐秀、商场试衣以及电视广告等领域。本文分析比较了近年来国内外虚拟服装展示领域的技术发展,并归纳总结出当前虚拟服装展示的5种人机交互模式。作者认为：随着全息技术、体感交互、立体视觉和增强现实等智能环境技术的发展,以“私人订制”为代表的个性化、时尚化和智能化的虚拟试衣体验将成为未来人们服装购买体验中不可或缺的重要环节之一。     

Solid modeling aspects of three-dimensional fragmentation

The ways in which the topology and geometry of a three-dimensional finite-element model may evolve as a consequence of fracture and fragmentation are enumerated, and the actions which may be taken in order to update the boundary representation of the solid so as to faithfully reflect that evolution are described. Arbitrary topological and geometrical evolution of a three-dimensional solid, not necessarily restricted to an evolution of its surface, are addressed. Solids are described by their boundary representation (BRep) and a surface and volume triangulation. Fracture processes are modeled by the introduction of cohesive elements at element interfaces. Simple rules are shown to enable the simulation of strikingly complex crack patterns. The scope and versatility of the approach is illustrated with the aid of selected examples of application.     

Laminar boundary layer on a flat plate with rotating cylinder

In the preseparation region a problem on the incompressible three-dimensional boundary layer development on a flat plate with an obstacle is posed. The uniqueness of the problem for a model equation is proved. It is shown that the outflow surface in the boundary layer on the plate is absent at the cylinder rotation. In this case there exists the special cylindrical surfaces (V-surfaces) whose rulings are orthogonal to the plate surface. The velocity vectors on each such ruling lie in the same plane, however this plane does not touch the V-surface. An absolute stable two-layer implicit difference weighted scheme of the second order approximation in all the variables is suggested which requires no fitting of the outflow surface. The comparison of the computational results with ones obtained by other authors and experiment is carried out. It is shown that besides the case of the cylinder rotation the V-surface takes place also in the case of the swept leading edge without rotation.