随机双相介质宏观弹性膜量的边界元法预报

确定多相体材料的宏观性能与其细观组织之间的关系是当今计算结构力学的一个重要课题，本文采用高效率的二次等参边界元及子域法求解了随机双相介质的宏观弹性膜量，计算结果与若干常见的解析公式进行了比较，为评价这些解析公式的可靠性提供了一定的依据，可以看出，边界元法在复合材料的计算中学中具有很大的潜力。     

正交各向异性平面问题边界元素法研究

边界元素法是近年来受到国内外广泛重视并得到迅速发展的一种计算方法。本文系统地研究了正交各向异性平面问题边界元素法的有关基本问题,包括基本解,C矩阵、G_ii矩阵和域内应力的表达式等,并在此基础上建立了常值边界元素和线性边界元素的计算公式。所述理论和公式适用于各类边值问题。最后,按本文所述理论和公式计算了含孔正交各向异性板的应力,数值结果与解析解相符甚好。      

无限域波动问题的有限元模型

本文基于半解析波动方程,推导了无限域粘弹性人工边界单元。在有限元波动模型中,统一了节点计算稳定性问题;提出了合理的人工边界反射系数公式,为有限元模型提供了理论基础。SH波数值分析表明本文有限元模型具有多向波动透射能力。     

保角映射法求解渐开线直齿轮齿根应力

目前国际上确定渐开线齿轮齿廓保角映射函数的方法均为数值回归法,计算复杂,映射精度的提高受到限制．为此,本文给出了渐开线齿轮齿廓保角映射函数的解析解,计算方便,使映射精度大幅度提高。以上述工作为基础,笔者给出了渐开线直齿轮齿根应力的解析公式,并由算例证实了计算结果和边界元法计算值之间的一致性。     

用样条边界元计算振动体的三维稳态声辐射

本文采用三次Ｂ样条边界单元计算振动体的三维稳态声辐射。实际计算表明：采用样条边界元可获得较好的数值计算结果。此外，本文在计算声场内点声压的Ｈｅｌｍｈｏｌｔｚ边界积分公式的基础上，导出了计算声场内点质点振速和声强的边界积分公式。文中还给出了应用本文方法计算的算例结果。     

预测纤维复合材料有效模量的分级模型

为纤维复合材料的有效模量计算建立了一个宏观与细观相结合的分级模型: 即假定共焦点椭圆柱组合体的纤维/基体细观结构单元嵌在宏观上均匀化了的复合材料中。利用解析函数的保角变换与罗朗级数展开, 获得了轴向剪切模量的封闭公式。理论值与实验值吻合很好, 克服了经典模型理论与实验结果偏差太大的缺点。      

边界元法分析中的边界切向应力差分算法

在用边界元法作弹性应力分析中,不能直接计算出弹性体边界切向应力。本文在边界元法分析的基础上,用差分法计算边界切向应力。推导出常边界单元情况下边界切向应力的差分公式。计算表明文中所述方法是可行的,并且简单实用。所研究的方法和公式也适用于高次边界单元的边界切向应力的计算。     

基于有限元-边界元的声学构形灵敏度分析

通过灵敏度分析可以对由结构修改而引起的局部或全部结构状态特性的变化做出估计,为设计指明方向.对结构-声学优化设计中的构形灵敏度进行研究,利用有限元、边界元数值计算方法获得辐射声压关于组合结构各构件旋转角度的半解析声学构形灵敏度公式,扩大了声学灵敏度的范畴.该声学灵敏度公式可以用来预测结构组合方式的改变而导致的空间声学量的改变.对该灵敏度公式进行数值计算,与传统有限差分法对比,证明了本文方法的正确性.     

瞬态弹性动力学问题的半解析边界元法

本文用半解析有限元法对边界积分方程作离散化处理,通过引入基本解函数和半解析半离散试函数的二次半解析过程,使三维弹性动力学问题简化为一维数值计算。文中又采用移动边界元法来模拟波在半无限介质中传播的表面积分问题,分析计算了各种瞬态波在介质内传播,绕射及地面运动问题。计算结果表明,半解析边界元法不仅计算精度高,而且工作量大大降低,具有较高的经济效益与应用价值。     

含非均匀界面相纤维增强复合材料热传导性能预测的递推公式

研究了含非均匀界面相纤维增强复合材料的宏观等效传热性能。将热导率沿径向连续变化的界面相离散为多个热导率均匀的同心圆柱层,采用广义自洽法和复变函数理论,推导了复合材料宏观等效热导率的解析递推公式,并由递推公式给出了均匀界面相和理想零厚度界面的封闭公式。理想零厚度界面复合材料的热导率与已有理论结果一致。理想零厚度界面和非均匀界面相模型的计算结果与实验数据比较表明,当纤维体积分数较小时,2种模型的预测结果与实验数据吻合均较好,当体积分数较大时,与实验数据相比,非均匀界面相模型的精度大大高于理想零厚度界面模型的精度。本文中给出的递推公式亦可用于计算多涂层纤维增强复合材料的热导率。     

多孔材料代表单元的性质

为了弄清多孔材料代表单元的基本性质,对泡沫镍的力学性能进行了实验研究和计算机模拟,两者结果的变化趋势吻合较好。在此基础上,用离散的弹性梁构成代表单元,结合连续介质力学的方法,建立了多孔材料的理想力学模型,导出了其宏观本构关系,讨论了其代表单元各向异性性质和材料常数之间的关系。结果表明由代表单元周期性排列构成的多孔材料,在宏观上呈各向异性,只有当代表单元无序地随机排列时,多孔材料才在宏观上出现统计各向同性。同时指出了一些文献中存在的错误。     

From elastic homogenization to upscaling of non-Newtonian fluid flows in porous media

Upscaling behaviors of heterogeneous microstructures to define macroscopic effective media is of major interest in many areas of computational mechanics, in particular those related to materials and processes engineering. In this paper, we explore the possibility of defining a macroscopic behavior manifold from microscopic calculations, and then use it directly for efficiently performing manifold-based simulations at the macroscopic scale. We consider in this work upscaling of non-Newtonian flows in porous media, and more particularly the ones involving short-fibre suspensions.     

混凝土材料与结构破坏过程模拟分析

采用离散单元法对混凝土材料和混凝土结构破坏机理进行分析。在细观尺度上将混凝土材料视为由粗骨料、水泥砂浆及界面过渡区三相组成,建立了混凝土材料的离散元模型;在宏观尺度上将混凝土视为均质材料建立了混凝土结构离散单元模型。计算分析结果表明:细观尺度上的二维离散单元模型可以用来很好地模拟混凝土材料的单轴受力破坏过程,但不能很好地模拟复合受力状态下的混凝土材料的破坏;宏观尺度上的离散单元模型可以很好地模拟钢筋混凝土构件的破坏过程,但模拟结果对单元的形状有较大的依赖性;宏观尺度上的离散单元模型可以很好地模拟结构的倒塌过程,但计算效率有待提高。     

Multi-scale computational method for elastic bodies with global and local heterogeneity

A multi-scale computational method using the homogenization theory and the finite element mesh superposition technique is presented for the stress analysis of composite materials and structures from both micro- and macroscopic standpoints. The proposed method is based on the continuum mechanics, and the micro–macro coupling effects are considered for a variety of composites with very complex microstructures. To bridge the gap of the length scale between the microscale and the macroscale, the homogenized material model is basically used. The classical homogenized model can be applied to the case that the microstructures are periodically arrayed in the structure and that the macroscopic strain field is uniform within the microscopic unit cell domain. When these two conditions are satisfied, the homogenization theory provides the most reliable homogenized properties rigorously to the continuum mechanics. This theory can also calculate the microscopic stresses as well as the macroscopic stresses, which is the most attractive advantage of this theory over other homogenizing techniques such as the rule of mixture. The most notable feature of this paper is to utilize the finite element mesh superposition technique along with the homogenization theory in order to analyze cases where non-periodic local heterogeneity exists and the macroscopic field is non-uniform. The accuracy of the analysis using the finite element mesh superposition technique is verified through a simple example. Then, two numerical examples of knitted fabric composite materials and particulate reinforced composite material are shown. In the latter example, a shell-solid connection is also adopted for the cost-effective multi-scale modeling and analysis. This revised version was published online in June 2006 with corrections to the Cover Date.     

Modeling of viscoelastic structures with random material properties using time-separated stochastic mechanics

Modeling and simulation of materials with stochastic properties is an emerging field in both mathematics and mechanics. The most important goal is to compute the stochastic characteristics of the random stress, such as the expectation value and the standard deviation. An accurate approach are Monte Carlo simulations; however, they consume drastic computational power due to the large number of stochastic realizations that have to be simulated before convergence is achieved. In this paper, we show that a recently published approach for accurate modeling of viscoelastic materials with stochastic material properties at the material point level in the work of Junker and Nagel is also valid for macroscopic bodies. The method is based on a separation of random but time-invariant variables and time-dependent but deterministic variables for the strain response at the material point (time-separated stochastic mechanics [TSM]). We recall the governing equations, derive a simplified form, and discuss the numerical implementation into a finite element routine. To validate our approach, we compare the TSM simulations with Monte Carlo simulations, which provide the “true” answer but at unaffordable computational costs. In contrast, the numerical effort of our approach is in the same range as for deterministic viscoelastic simulations.     

Variational principles in dissipative electro‐magneto‐mechanics: A framework for the macro‐modeling of functional materials

This paper presents a general framework for the macroscopic, continuum‐based formulation and numerical implementation of dissipative functional materials with electro‐magneto‐mechanical couplings based on incremental variational principles. We focus on quasi‐static problems, where mechanical inertia effects and time‐dependent electro‐magnetic couplings are a priori neglected and a time‐dependence enters the formulation only through a possible rate‐dependent dissipative material response. The underlying variational structure of non‐reversible coupled processes is related to a canonical constitutive modeling approach, often addressed to so‐called standard dissipative materials. It is shown to have enormous consequences with respect to all aspects of the continuum‐based modeling in macroscopic electro‐magneto‐mechanics. At first, the local constitutive modeling of the coupled dissipative response, i.e. stress, electric and magnetic fields versus strain, electric displacement and magnetic induction, is shown to be variational based, governed by incremental minimization and saddle‐point principles. Next, the implications on the formulation of boundary‐value problems are addressed, which appear in energy‐based formulations as minimization principles and in enthalpy‐based formulations in the form of saddle‐point principles. Furthermore, the material stability of dissipative electro‐magneto‐mechanics on the macroscopic level is defined based on the convexity/concavity of incremental potentials. We provide a comprehensive outline of alternative variational structures and discuss details of their computational implementation, such as formulation of constitutive update algorithms and finite element solvers. From the viewpoint of constitutive modeling, including the understanding of the stability in coupled electro‐magneto‐mechanics, an energy‐based formulation is shown to be the canonical setting. From the viewpoint of the computational convenience, an enthalpy‐based formulation is the most convenient setting. A numerical investigation of a multiferroic composite demonstrates perspectives of the proposed framework with regard to the future design of new functional materials. Copyright © 2011 John Wiley & Sons, Ltd.     

A nonlocal computational homogenization of softening quasi-brittle materials

In this paper, a computational counterpart of the experimental investigation is presented based on a nonlocal computational homogenization technique for extracting damage model parameters in quasi-brittle materials with softening behavior. The technique is illustrated by introducing the macroscopic nonlocal strain to eliminate the mesh sensitivity in the macroscale level as well as the size dependence of the representative volume element (RVE) in the first-order continuous homogenization. The macroscopic nonlocal strains are computed at each direction, and both the local and nonlocal strains are transferred to the microscale level. Two RVEs with similar geometries and material properties are introduced for each macroscopic Gauss point, in which the microscopic damage variables and the macroscale consistent tangent modulus and its derivatives are obtained by imposing the macroscopic nonlocal strain on the first RVE, and the macroscopic stress is computed by employing the microscopic damage variables and imposing the macroscopic local strain over the second RVE. Finally, numerical examples are solved to illustrate the performance of the proposed nonlocal computational homogenization technique for softening quasi-brittle materials.     

高分子材料结构构件的失效分析

根据材料力学、断裂力学理论,用随机过程的方法,得到高分子材料结构构件的失效分布函数,并讨论了高分子材料结构构件的可靠使用寿命。     

硫酸盐侵蚀下水泥净浆膨胀应变计算

针对硫酸盐侵蚀过程中水泥净浆体积膨胀问题,运用微孔力学理论,建立了水泥净浆基体与其孔隙内钙矾石晶体相互作用的代表性体积单元(RVE)及其力学分析模型;分析了一定钙矾石生成量下的RVE内膨胀应变在微观尺度上的空间分布规律;通过均匀化方法,将微观尺度上的RVE内膨胀应变转化为宏观尺度上RVE所在位置点的等效应变,分析了该等效应变随钙矾石生成量的变化规律。分析结果表明:微观尺度上,孔隙率为0.1的RVE内钙矾石晶体和侵蚀溶液组成的内球体各向为拉应变,水泥净浆外球壳径向为压应变、环向为拉应变;宏观尺度上,孔隙率为0.1的RVE所在位置点的径向等效应变为压应变,且随钙矾石生成量的增加而增大,而环向等效应变为拉应变,且随钙矾石的生成量的增加而增大。     

计算智能在微尺度力学研究中的应用

微尺度力学的研究常遇到力学模型分析、复杂本构方程求解和跨尺度计算等问题,而传统的数学方法很难给出所研究的微尺度力学问题的解析解。该文探讨运用计算智能方法(主要包括人工神经网络、遗传算法和模糊数学等知识)对微尺度材料的力学行为进行研究。首先,采用人工神经网络建立微尺度材料的纳米压痕硬度随压痕深度变化的力学模型,并用其预测氧化镁材料的纳米压痕硬度;其次,运用遗传算法对A533-B号钢的球形压痕的载荷-位移曲线进行反分析,进而获取其力学参数。