An Adaptive Finite Element Approach for Brittle Fracture

The extension of the finite element method to take discrete fracture and failure modes into account is a current field of research. In recent times, first results in terms of cohesive element formulations have been introduced into commercial applications. Such element formulations are able to cover the discrete behaviour of interfaces between different materials or the mechanical processes of thin layers. These approaches are not suitable for simulations with unknown crack paths in homogeneous materials, due to the initial elastic phase of the material formulation and the necessity to define potential crack paths a priori. The presented strategy starts with an unextended model and modifies the structure during the computations in terms of an adaptive procedure. The idea is to generate additional elements, based on the cohesive element formulation, to approximate arbitrary crack paths. For this purpose, a failure criterion is introduced. For nodes where the limiting value is reached, cohesive elements are introduced between the volume element boundaries of accordingly facets and corresponding nodes are duplicated. Necessary modifications for this application on system level as well as the element and the material formulation are introduced. By means of some numerical examples, the functionality of the presented procedure is demonstrated. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Holistic Simulation Approach from a Measured Load to Element Stress Using Combined Multi-body Simulation and Finite Element Modelling

The design of vehicle bodies requires the knowledge of the vehicle's structural response to external loads and disturbances. In rigid multi-body simulation the dynamic behaviour of complex systems is calculated with rigid bodies and neglect of body elasticity. On the other hand, in finite element models large degree of freedom numbers are used to represent the elastic properties of a single body. Both simulation methods can be combined, if the finite element model size is reduced to a degree of freedom number feasible to multi-body simulation. The application to practical purposes requires the use and interconnection of several different software tools. In this contribution a holistic method is presented, which starts with the measurement or synthesis of loads and excitations, continues with the integration of a reduced finite element model into a multi-body system, the dynamic response calculation of this combined model, and concludes with the result expansion to the full finite element model for calculating strain and stress values at any point of the finite element mesh. The applied software tools are Simpack, Nastran, and Matlab. An example is given with a railway vehicle simulated on measured track geometry. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Convergence of Nonlocal Finite Element Energies for Fracture Mechanics

Usually, smeared crack techniques are based on the following features: the fracture is represented by means of a band of finite elements and by a softening constitutive law of damage type. Often, these methods are implemented with nonlocal operators that control the localization effects and reduce the mesh bias. We consider a nonlocal smeared crack energy defined for a finite element space on a structured grid. We characterize the limit energy as the mesh size h tends to zero and we establish a precise link between the discrete and continuum formulations of the fracture energies, showing the correct scaling and the explicit form of the mesh bias.     

A Finite Element Method for Spatially Resolved Simulation of Packed Bed Chromatography

Packed bed chromatography is among the most important unit operations in bio-chemical process engineering for purifying target molecules from contaminants. A liquid solution of different species is pumped through the chromatography column, which is filled with porous particles (beads). Solute molecules can adsorb to the inner surfaces of these beads with different affinities which leads to different retention times in the column and consequently facilitates the desired separation. We present a stabilized space-time finite element scheme to solve for fluid flow and mass transfer in miniaturized chromatography columns, which are used in the design and optimization of industrial-scale applications. Our method can accurately handle realistic size systems with more than 10⁸ degrees of freedom on massively parallel computing facilities. It can also be applied for simulating sections of larger chromatographic beds in lab- and process-scale columns. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A New Finite Element Space for Expanded Mixed Finite Element Method

In this article, we propose a new finite element space Λ$_h$ for the expanded mixed finite element method (EMFEM) for second-order elliptic problems to guarantee its computing capability and reduce the computation cost. The new finite element space Λ$_h$ is designed in such a way that the strong requirement V$_h\subset$Λ$_h$ in [9] is weakened to {v$_h\in$V$_h$; divv$_h$=0}$\subset$Λ$_h$ so that it needs fewer degrees of freedom than its classical counterpart. Furthermore, the new Λ$_h$ coupled with the Raviart-Thomas space satisfies the inf-sup condition, which is crucial to the computation of mixed methods for its close relation to the behavior of the smallest nonzero eigenvalue of the stiff matrix, and thus the existence, uniqueness and optimal approximate capability of the EMFEM solution are proved for rectangular partitions in $\mathbb{R}^d, d=2,3$ and for triangular partitions in $\mathbb{R}^2$. Also, the solvability of the EMFEM for triangular partition in $\mathbb{R}^3$ can be directly proved without the inf-sup condition. Numerical experiments are conducted to confirm these theoretical findings.     

动脉血管流动计算的伽辽金有限元法研究

得到大动脉三维模型的过二重分叉的二维截定常流的NS方程有限元解,采用了物理坐标系统换到曲线边界贴休坐标系的数学技巧,以支流至主动脉流率为参数,计算了雷诺数为1000的壁面切应力,所得结果与前人的工作（包括实验数据）进行了比较,发现与他们的结果非常接近,改进了Sharma和Kapoor(1995)的工作,相比之下,所用的数值方法上更经济,适用的雷诺数更大。     

混凝土断裂力学虚拟裂缝模型的半解析有限元法

利用平面扇形域哈密顿体系的方程,通过分离变量法及共轭辛本征函数向量展开法,以解析的方法推导出基于混凝土断裂力学中虚拟裂缝模型的平面裂纹解析元列式．将该解析元与有限元相结合,构成半解析的有限元法,可求解任意几何形状和荷载混凝土平面裂纹的虚拟裂缝模型计算问题．数值计算结果表明方法对该类问题的求解是十分有效的,并有较高的精度．     

页岩气藏渗流模型的特征混合有限元数值模拟

将特征有限元方法和混合有限元方法进行耦合,对页岩气藏渗流模型进行了数值模拟,给出了详细的误差分析,得到了最优的L~2模误差估计,并用数值实验验证了方法的有效性.     

A Simple Finite Element Method for the Reissner-Mindlin Plate

1.IntroductionTheReissner-MindlinmodeldescribesthedefOrmationofaplatesubjecttoatrans-verseload.Thismodel,aswellasitsgeneralizationtoshells,isfrequentlyusedforp1atesandshellsofsmalltomoderatethickness.Itiswellknownthatmanynumeri-calschemesforthismodelaresatisfactoryonlywhenthethicknessparametertisnottoosmal1.Foraverysmallt,somebadbehaviors(suchaJsthelockingphenomenon)mightoccur.Inl986,F.BrezziandM.Fo.ti.l2]derivedanequivalentformulationoftheReissner-MindlinplateequationsbyusingtheHelmholtz…     

Finite Element Simulation of Frost Wedging in Ice Shelves

Break-up events in ice shelves have been studied extensively during the last years. One popular assumption links disintegration events to surface melting of the ice shelf in conjunction with growing melt-water ponds, leading to hydro-fracture. As this explanation only holds during warm seasons [1], the possibility of frost wedging as forcing mechanism for autumn and winter break-up events is considered. Frost wedging can only occur if a closed ice lid seals the water inside the crack. Hence, the present study of frost wedging in a single crack uses ice lid thicknesses to evaluate the additional pressure on the crack faces. The investigation of the resulting stress intensity factor as a measure of crack criticality follows consequently. The results show that freezing water inside a crack can result in unstable crack growth of an initially stable water filled crack. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

水波的界带有限元

研究了水波计算的位移法.采用物质坐标,以位移为基本未知量,考虑小变形条件,引入流函数满足不可压缩条件.于是,分析力学的变分原理可以运用了,界带有限元、正则变换、保辛积分等有效手段可使数值求解方便得多.     

PROCRACK-A Software Tool for Finite Element Simulation of Three-Dimensional Fatigue Crack Growth

The lifetime of structural components is limited by fatigue cracks. After initiation from an existing defect the crack grows subcritically until it reaches a critical size. At this point it becomes unstable and the structural component fails. PROCRACK is a powerful tool that enables the commercial finite element software Abaqus to calculate the crack propagation in pre-cracked components. The complete capability of Abaqus can be used to simulate nearly arbitrary geometries. Abaqus/CAE is used for the three-dimensional modeling of the initial crack at a geometrical level by means of points, lines and triangles. The numerical analysis is performed by Abaqus/Standard. PROCRACK automatically generates a tube-shaped submodel around the crack front to calculate the stress intensity factors with high accuracy. The Paris law or the NASGRO equation can be used to calculate the incremental crack growth. The shape of the crack and the finite element mesh are updated in every crack growth step. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Phase Field Approach for Dynamic Fracture

In phase field fracture models cracks are indicated by the value of a scalar field variable which interpolates smoothly between broken and undamaged material. The evolution equation for this crack field is coupled to the mechanical field equations in order to model the mutual interaction between the crack evolution and mechanical quantities. In finite element simulations of crack growth at comparatively slow loading velocities, a quasi-static phase field model yields reasonable results. However, the simulation of fast loading or the nucleation of new cracks challenges the limits of such a formulation. Here, the quasi-static phase field model predicts brutal crack extension with an artificially high crack speed. In this work, we analyze to which extend a dynamic formulation of the mechanical part of the phase field model can overcome this paradox created by the quasi-static formulation. In finite element simulations, the impact of the dynamic effects is studied, and differences between the crack propagation behavior of the quasi-static model and the dynamic formulation are highlighted. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

弹性波方程有限元模拟的曲边地表处理

本文对比研究了关于弹性波模拟中的曲边地表形状处理的两种方法,一种是用给定的实际介质数值划定的地表形状,另一种是用样条插值逼近地表形状.本文采用有限元方法进行弹性波数值模拟,给出了基于这两种方法计算的数值例子,并对结果进行了分析比较.结果表明使用后一种方法对地表进行处理时,地表人工离散产生的干扰明显减少,优于前一种方法.     

Simulation of Piezoelectric Smart Lightweight Structures by the Finite Element Method for Acoustic Control

Piezoelectric patches are widely used as distributed actuators and sensors for active vibration control. Active control of sound in this way is mainly interesting in the low frequency range, where passive methods are less effective. To simulate such electromechanical‐acoustical systems a virtual overall model based on the FEM is presented in the paper. Different approaches for model reduction with respect to controller design purposes are discussed. As a simple test example the numerical model of an acoustic box is studied. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

一种高精度的裂纹奇异单元

基于广义伽辽金法的多变量有限元算法,增加了连续体力学有限元模型建立的灵活性.本文利用它,通过数值试验的对比建立了一种高精度的含奇异性的裂纹单元,并对多变量奇异元的构成进行了探讨.