Two-Scale Simulation of a Disc With a Crack by X-FEM and Cell Model

The two-scale simulation of a linear-elastic orthotropic disc with a central crack under mode-I loading may be used to verify the extended finite element method implementation of orthotropic enrichment functions into finite element codes such as FEAP. The stress distribution on the finer scale is simultaneously resolved by the high fidelity generalized method of cells called at each integration point of the macro elements. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

正交异性复合材料板复合型裂纹尖端的J积分

本文采用复变函数和微积分理论两种途径探讨线弹性正交异性复合材料板复合型裂纹尖端的Ｊ积分，得到了该Ｊ积分在△＞０和△＜０两种情况下的表示式，证明了它们的路径无关性，推出了它们的计算公式。     

Mixed FEM of higher-order for a frictional contact problem

This paper presents mixed finite element methods of higher-order for an idealized frictional contact problem in linear elasticity. The approach relies on a saddle point formulation where the frictional contact condition is captured by a Lagrange multiplier. The convergence of the mixed scheme is proven and some a priori estimates for the h- and p-method are derived. Furthermore, a posteriori error estimates are presented which rely on the estimation of the discretization error of an auxiliary problem and some further terms capturing the error in the friction and complementary conditions. Numerical results confirm the applicability of the a posteriori error estimates within h- and hp-adaptive schemes. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

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)     

柱塞泵油膜压力分析的高效有限单元法

利用有限单元法,数值分析轴向柱塞泵缝隙高度可变时阀门板上油膜的压力分布.缝隙中油压变化的确定,通常是应用Pasynkow 润滑理论中的Reynolds方程.使用基于有限单元法的自编程序,数值地求解该方程.为了提高结果的精度,基于解的残差估计,应用了加密的自适应网格.给出了依赖于泵的几何条件和工作参数的计算结果.     

Mixed FEM and BEM coupling for the three‐dimensional magnetostatic problem

We present two new mixed finite element methods coupled with a boundary method for the three dimensional magnetostatic problem. Such formulations are obtained by coupling a finite element method inside a bounded domain with a boundary integral method involving either the Calderon equations or the inverse of Dirichlet Neumann operator to treat the exterior domain. First, we present the formulations and then prove that our mixed formulations are well posed and that they lead to a convergent Galerkin method. Finally, we give numerical results for a sphere immersed in a homogeneous (source) field in the two formulations. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 443–462, 2003     

Adaptive Fuzzy Sliding Mode Controller and Observer for a Dive Cell

We present an adaptive fuzzy sliding mode control strategy in combination with a sliding mode observer for a dive cell. Numerical results demonstrate the outperformance of the presented controller compared to a conventional sliding mode approach. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Crack Arrest Model for a Plate Weakened by Internal and External Cracks - a Modified Dugdale Approach

A modified Dugdale model solution is obtained for an elastic-perfectly-plastic plate weakened by one internal and two external straight collinear hairline cracks. The tension applied to the infinite boundary of the plate opens the rims of cracks with forming a plastic zone ahead of each tip of the internal crack and also at each finitely distant tip of the two external cracks. The developed plastic zones are closed by normal cohesive linearly varying yield-point stress distributions applied to their rims. The problem is solved using the complex-variable technique. A case study is carried out to find the load required to prevent the cracks from further growing with respect to affecting parameters. The results obtained are reported graphically and analyzed.     

A Bayesian Approach to Estimating Decision Parameters in a Replacement Inventory System

This paper deals with the estimation of decision parameters in a special class of inventory systems in which the rate of stock depletion depends on the internal operations of the parent organization instead of market demands. Stocking decisions for this type of inventory systems are unique in that demands for the stocked items are internal demands, sporadic in some instances, infrequent in others, and almost never the direct results of conscious economic decisions. To cope with the peculiar situation, Bayesian point and interval estimation procedures are used. The estimated probability measures provide a basis on which stocking decisions pertinent to this type of inventory systems can be made or evaluated. Specific statistical postulates are made, and a numerical example is given for illustration. The possibility of applying the estimated results to one of the existing inventory models is briefly discussed at the end.     

High Performance Computing Techniques for the FEM Simulation in Structural Mechanics

For the solution of large scale simulations in structural mechanics iterative solving methods are mandatory. The efficiency of such methods can crucially depend on different factors: choice of material parameters, quality of the underlying computational mesh and number of processors in a parallel computing system. We distinguish between three aspects of ‘efficiency’: processor efficiency (degree to which the solving algorithm is able to exploit the processor's computational power), parallel efficiency (ratio between computation and communication times) and numerical efficiency (convergence behaviour). With the new FEM software package Feast we pursue the aim to develop a solver mechanism which at the same time gains high efficiencies in all three aspects, while trying to minimise the mentioned dependencies. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Biphasic Approach for the Simulation of Growth Processes in Soft Biological Tissues Incorporating Damage-Induced Stress Softening

In this contribution a coupled material framework is presented, which considers the effects of damage and growth in soft biological tissues. The tissue is described as a porous medium by taking into account a solid and a fluid phase. The fluid phase is assumed to carry nutrients supplying growth of the solid phase. The latter one is described as a fiber-reinforced material, where a damage variable is introduced for the fiber part of the associated free energy function. The performance of the proposed model is demonstrated in a finite element analysis of a simplified human heart model. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

FEM Simulation of a Micromechanical Model for Textured Polycrystalline Shape Memory Alloys with n-Variants

This paper is about the numerical implementation of a known, but advanced model with a projected Newton algorithm and a residual including only two vectors of unknowns. In a complex stress driven example the superelastic behavior is investigated. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

有限元和直接积分法瞬态动力计算的时空离散协调问题

本文对有限元和直接积分法瞬态动力计算的时空离散协调问题进行了研究,本文分别分析了空间离散和时间离散所引起的数值误差,提出了均衡空间离散引起的能量误差和时间离散引起的能量误差的原则,并给出时空离散协调的前处理方案和自适应方案。     

Composite Waves for a Cell Population System Modelling Tumor Growth and Invasion

In the recent biomechanical theory of cancer growth, solid tumors are considered as liquid-like materials comprising elastic components. In this fluid mechanical view, the expansion ability of a solid tumor into a host tissue is mainly driven by either the cell diffusion constant or the cell division rate, with the latter depending on the local cell density (contact inhibition) or/and on the mechanical stress in the tumor. For the two by two degenerate parabolic/elliptic reaction-diffusion system that results from this modeling, the authors prove that there are always traveling waves above a minimal speed, and analyse their shapes. They appear to be complex with composite shapes and discontinuities. Several small parameters allow for analytical solutions, and in particular, the incompressible cells limit is very singular and related to the Hele-Shaw equation. These singular traveling waves are recovered numerically.     

位于两不同正交各向异性半平面间张开型界面裂纹的性能分析

利用Schmidt方法分析了位于正交各向异性材料中的张开型界面裂纹问题．经富立叶变换使问题的求解转换为求解两对对偶积分方程,其中对偶积分方程的变量为裂纹面张开位移．最终获得了应力强度因子的数值解．与以前有关界面裂纹问题的解相比,没遇到数学上难以处理的应力振荡奇异性,裂纹尖端应力场的奇异性与均匀材料中裂纹尖端应力场的奇异性相同．同时当上下半平面材料相同时,可以得到其精确解．     

Mixed Problem for a General 1D Wave Equation with Characteristic Second Derivatives in a Nonstationary Boundary Mode

Mathematical Notes - We use a modified method of characteristics to derive an explicit formula for the unique stable classical solution of a linear mixed problem for a general one-dimensional wave...     

有限元混合法自动网格划分技术分析贴边岔管

本文应用有限元混合法分析水电站贴边岔管于内水压力作用时的应力问题.岔管系当作为二个薄壳相交的组合壳体.由于需要计算大量的岔管,发展了自动网格划分技术用于有限元混合法.根据三个参数即二个交叉管道的轴线交角、管壁厚度及交叉口二管道直径之比,区分出八种网格,十二种单元信息,编出自动确定节点坐标及形成边界条件信息的程序,业已计算了101个岔管,计算效果优良.     

理想弹塑性I型平面应力裂纹线场的精确解

本文纠正了过去在裂纹弹塑性场匹配上存在的问题,采用线场分析方法,通过求得塑性区应力场的合理解答,使之与弹性精确场在裂纹线附近的弹塑性边界上匹配。本文就远场受单向拉伸及双向拉伸的理想弹塑性平面应力裂纹无限板,在完全放弃了小范围屈服条件的情况下求得了塑性区应力场、塑性区长度以及弹塑性边界的单位法向量在裂纹线附近足够精确的表达式。结果表明,无论单向拉伸和双向拉伸,塑性区应力分量σ_y,σ_xy,塑性区长度以及弹塑性边界的单位法向量在裂纹线附近的表达式完全相同,但塑性区沿X方向的正应力σ_x存在差别。