具有多约束连续体结构仿生拓扑优化方法

通过浮动参考区间法分析具有多约束连续体结构拓扑优化问题。浮动区间法是指将结构的拓扑优化过程看作是骨骼重建过程,通过引入参考应变区间,将结构中所有各点处主应变绝对值落入参考应变区间作为重建平衡状态,当结构处于重建平衡状态时获得结构的最优材料分布。为了使得优化结果满足给定的性态约束,参考应变区间在优化迭代过程中须不断变化。讨论了几种常见性态约束对结构性能的要求。给出了结构具有多约束时优化问题的算法。数值算例表明该方法可行。     

基于类桁架材料模型的不确定荷载下结构拓扑优化

用区间分析方法研究了不确定荷载下结构拓扑优化方法。采用类桁架材料模型建立拓扑优化类桁架连续体结构。根据区间变量运算法则推导出不确定荷载下应力约束体积最小类桁架结构的拓扑优化方法。首先采用区间分析方法得到任一点的最不利荷载工况下应变状态。在此应变状态下,利用满应力准则优化类桁架材料中杆件的方向和密度。如此反复分析和优化,直至迭代收敛。最后由类桁架中杆件分布场可以近似离散得到桁架结构。通过几个数值算例验证了方法的有效性。数值算例显示了不确定荷载下的结构拓扑优化布局更合理。     

基于种群动力学模型的连续体结构拓扑优化仿生方法

通过种群动力学模型和有限元方法的耦合建立了骨骼重建数学模型,然后用像素单元的添加和删除准则把骨重建过程转化为材料形成和吸收过程,对连续体结构提出了仿生拓扑优化计算方法。通过对两个连续体结构拓扑优化中被广泛应用的典型数值算例进行拓扑优化计算,并将其结果与其它几种拓扑优化方法进行比较,验证了该方法的有效性。最终在三种不同边界条件下对长悬臂梁模型进行拓扑优化计算,以及在四种不同边界条件下拱桥模型进行拓扑优化计算,获得规则性和对称性的拓扑形式,该结果进一步说明了该仿生方法的合理性和可行性。     

区间参数平面连续体结构频率非概率可靠性拓扑优化

研究了具有区间参数的平面连续体结构在固有频率非概率基频约束和频率禁区约束下的拓扑优化设计问题。考虑结构弹性模量、质量密度和频率约束限具有区间不确定性,根据SIMP材料插值方法和区间变量运算法则,构建了基于频率非概率可靠性约束的弯曲薄板和平面应力薄板结构的拓扑优化数学模型表达式,并给出了进化优化准则。算例及其结果表明文中模型和方法的有效性。     

结构拓扑优化中敏度过滤技术研究

为了抑制连续体结构拓扑优化结果中的棋盘格和灰度单元问题,借鉴粒子群优化算法中粒子状态的更新方法,提出一种改进的敏度更新技术.以结构的柔度最小为优化目标,构建了基于固体各项同性微惩罚结构的结构拓扑优化模型,根据结构的力学响应分析,采用优化准则法进行设计变量更新,进行载荷作用下二维连续体结构的拓扑优化设计,得到了材料在设计域内的最优分布.通过与已有敏度过滤技术的对比分析,验证了文中方法的正确性和有效性．     

考虑材料参数不确定性结构动力学稳健性拓扑优化设计

本文在考虑材料参数不确定性的条件下,对连续体结构动力学稳健性拓扑优化设计进行研究。在使结构的第一阶固有频率最大化的同时,显著减小其对材料性能不确定性的影响。基于非概率凸集模型,将材料参数的不确定性用有界区间变量表示;建立了能够抑制频率改变的结构动力学拓扑优化模型,用单层优化策略求解稳健性优化设计问题。通过对材料参数的导数分析,获得了在材料性能不确定情形下结构第一阶固有频率的二阶泰勒展开式,并推导出了频率对拓扑变量的一阶灵敏度显性表达式。基于变密度法,开展了结构动力学稳健性拓扑优化设计,并与确定性优化结果进行对比,验证了用本文方法获得的结构第一阶固有频率稳健性更高,受材料参数不确定性扰动影响更小,展示了考虑材料参数不确定性的重要性。     

一种基于Yeoh函数的非线性粘超弹本构模型及其在冲击仿真中的应用

以粘超弹理论为基础,将L M Yang等提出的本构模型中Rivlin函数改进为Yeoh,提出了一种基于Yeoh函数的描述橡胶材料中高应变率效应的粘超弹本构模型,该模型以左Cauchy变形张量B第一不变量I1^B作为唯一变量,简化了原模型结构,并开发了相应模型的ABAQUS软件材料用户子程序（VUMAT）。通过高应变率橡胶垫片及中低应变率橡胶缓冲器的冲击试验与数值仿真对比,验证了本构模型及材料用户子程序的有效性与实用性。     

带隙特性计算的等效梁元法与等效平面应变法

针对可简化为平面应变类力学问题的超材料，根据矩形薄板筒形弯曲理论，提出该类超材料带隙特性计算的等效梁元法。应用等效梁元法和常规等效平面应变法对负泊松比超材料的多种典型构型(内六角、星形、箭形和旋转三角形)的带隙特性进行数值计算，比较两种方法在带隙计算精度、计算效率及拓扑优化中适用性等方面的差异，并经试验测试结果进行验证。研究表明，等效梁元法和等效平面应变法的带隙计算精度均较高，与实测值误差在7%以内。等效梁元法在带隙计算效率上比等效平面应变法高约50%,但拓扑优化基结构模型的规模较大，适用于杆件类超材料结构拓扑优化。等效平面应变法带隙计算效率较低，拓扑优化基结构模型的规模较小，适用于连续体类及骨架类超材料结构的拓扑优化。该研究可为带隙超材料的拓扑优化设计提供参考。     

两面可构视图的空间构形方法研究

重点研究了两面单框可构视图及两面多框可构视图的空间构形设计方法。对于两面单框可构视图的空间构形应在最大公共点群域内来构造形体,且构造的形体应随同面点集形状的变化而变化;对于两面多框可构视图的空间构形,应在各封闭图框的最大公共点群域内来构造形体,构造的形体也应随各同面点集形状的变化而变化。     

基于宏观性能的微观多孔材料拓扑优化

基于均匀化理论,建立与微观材料拓扑形状相关的宏观结构材料等效弹性张量。集成宏观结构所得到的位移场,推导出带有宏观结构力学特性的微观敏度。从而实现在给定材料体积分数前提下,以宏观结构最大刚度为目标,对材料微结构进行拓扑优化的目的。相关算例说明该方法可以得到与宏观力学性能相对应的各种微观结构蜂窝材料或复合材料。揭示了材料的微观结构拓扑形状依赖于宏观结构尺寸、载荷及初始边界条件等因素。     

Inversions related to the stress-strain-fabric relationship

The stress-strain-fabric relationship is an extension of the anisotropic form of Hooke's law to include a dependence of the elastic coefficients upon a second-rank tensor called the fabric tensor. The fabric tensor represents features of the material microstructure associated with the type and the degree of the anisotropy. The inversion considered first in this work is that in which the stress-strain-fabric relation is constructed from the strain-stress-fabric relation and vice versa. Next, a semi-inversion of the relationship between the fourth-rank tensor of elastic coefficients and the fabric tensor is developed. This latter inversion permits the determination of the fabric tensor from a fourth-rank tensor of elastic constants. Explicit, approximate forms of these results, including a numerical example, are given for the case when the fabric tensor is normalized and terms of order three and higher in the fabric tensor are neglected.     

The relationship between the elasticity tensor and the fabric tensor

An algebraic relationship between the fourth rank elasticity tensor of a porous, anisotropic, linear elastic material and the fabric tensor of the material is considered. The fabric tensor is a symmetric second rank tensor which characterizes the geometric arrangement of the porous material microstructure. In developing this result it is assumed that the matrix material of the porous elastic solid is isotropic and, thus, that the anisotropy of the porous elastic solid is determined by the fabric tensor. It is then shown that the material symmetries of orthotropy, transverse isotropy and isotropy correspond to the cases of three, two and one distinct eigenvalues of the fabric tensor, respectively.     

Generalized elastic damage theory and its application to composite plate

Based on continuum mechanics, a generalized damage theory for elastic material which can be used for anisotropic composite is presented in this paper. This theory for anisotropic elastic material has been proposed here from the stress-strain relation of the actual damaged material. Introducing a fourth order damage operator that may be formed by a symmetrical second order damage factor tensor, the constitutive equation of the damaged material has been set up. The expressions of components of both the stress tensor and the strain tensor of the damaged material and their first order invariants have been also derived. The application of this theory to the 2-dimensional composite laminate, including the technique estimating the components of the damage factor tensor and the damage variable tensor and also the practical measure technique of the damage in the whole process, have been explained in detail. Finally, the changes of the anisotropic elastic properties and the actual stress state of damaged material have been discussed and some interesting results have been obtained in this paper.     

A symmetry invariant formulation of the relationship between the elasticity tensor and the fabric tensor

The fabric tensor is employed as a quantitative stereological measure of the structural anisotropy in the pore architecture of a porous medium. Earlier work showed that the fabric tensor can be used additionally to the porosity to describe the anisotropy in the elastic constants of the porous medium. This contribution presents a reformulation of the relationship between fabric tensor and anisotropic elastic constants that is approximation free and symmetry-invariant. From specific data on the elastic constants and the fabric, the parameters in the reformulated relationship can be evaluated individually and efficiently using a simplified method that works independent of the material symmetry. The well-behavedness of the parameters and the accuracy of the method was analyzed using the Mori–Tanaka model for aligned ellipsoidal inclusions and using Buckminster Fuller’s octet-truss lattice. Application of the method to a cancellous bone data set revealed that employing the fabric tensor allowed explaining 75–90% of the total variance. An implementation of the proposed methods was made publicly available.     

A 3D fourth order fabric tensor approach of anisotropy in granular media

We propose a micromechanical approach for granular media, with a particular account of the texture-induced anisotropy and of the strain localization rule. The approach is mainly based on the consideration of a fourth order fabric tensor able to capture general anisotropy which can be induced by complex distribution of contacts. Incorporation of this fourth order fabric tensor in a suitable homogenization scheme allows to determine the corresponding macroscopic elastic properties of the granular material. For this purpose, in addition to the classical Voigt upper bound, a new kinematics-based localization rule is proposed. It generalizes the one formulated by Cambou et al. [B. Cambou, Ph. Dubujet, F. Emeriault, F. Sidoroff, Eur. J. Mech. A/Solids 14 (1995) 225–276] in the case of an isotropic contact distribution. The results of the complete model compare well to numerical simulations results when available [C.S. Chang, C.L. Liao, Appl. Mech. Rev. 47 (1 Part 2) (1994) 197–207] (case of isotropic distribution of contacts). Finally, the interest of the fourth order fabric tensor based approach combined with the proposed localization rule is shown for different distributions of contacts by comparing its predictions to those given by a second order fabric tensor approach.     

An alternative model for anisotropic elasticity based on fabric tensors

Motivated by the mechanical analysis of multiphase or damaged materials, a general approach relating fabric tensors characterizing microstructure to the fourth rank elasticity tensor is proposed. Using a Fourier expansion in spherical harmonics, the orientation distribution function of a positive, radially symmetric microstructural property is approximated by a scalar and a symmetric, traceless second rank tensor. Following this approximation, a general expression of the elastic free energy potential is derived from representation theorems for anisotropic scalar functions. Based on a homogeneity assumption for the elastic constitutive law with respect to the microstructural property, a particular elasticity model is developed that involves three independent constants beside the fabric tensors. Strict positive definiteness of the corresponding elasticity tensor is ensured under explicit conditions on the independent constants for arbitrary fabric tensors.     

基于数字图像技术的纤维织物面内渗透率表征

材料渗透率的表征受其结构空间离散性和求解方式准确性的严重影响。基于数字图像技术,评估了纤维织物渗透率的空间分布,并探讨了阶梯铺层对灌注工艺的影响。首先,从恒压单向注射实验的视频流中动态提取了流动前沿的流速分布和流动前沿角,通过织物渗透率与结构的关系仅一次实验便可求得纤维织物的面内局部渗透率分布;其次,利用正态分布函数拟合,建立了基于数字图像技术的纤维织物面内主方向渗透率张量的求解方法,并利用该方法研究了编织形式对渗透率的影响;最后,研究了阶梯铺层和恒定铺层对灌注过程的影响。结果表明:建立的基于数字图像技术的渗透率表征方法可以通过一次实验同时获取面内主方向上的渗透率及其空间离散型;在恒定铺层下缎纹织物渗透率随着纤维层数增大而增大,从厚铺层向薄铺层的灌注方式可以达到最优的灌注时间。      

Stress-induced anisotropy in sand under cyclic loading

The anisotropy of a granular material’s structure will influence its response to applied loads and deformations. Anisotropy can be either inherent (e.g. due to depositional process) or induced as a consequence of the applied stresses or strains. Discrete element simulations allow the interactions between individual particles to be explicitly simulated and the fabric can be quantified using a fabric tensor. The eigenvalues of this fabric tensor then give a measure of the anisotropy of the fabric. The coordination number is a particle scale scalar measure of the packing density of the material. The current study examines the evolution of the fabric of a granular material subject to cyclic loading, using two-dimensional discrete element method (DEM) simulations. Isotropic consolidation modifies and reduces the inherent anisotropy, but anisotropic consolidation can accentuate anisotropy. The ratio of the normal to shear spring stiffness at the particle contacts in the DEM model affects the evolution of anisotropy. Higher ratios reduce the degree of anisotropy induced by anisotropic consolidation. The anisotropy induced by cyclic loading depends on the amplitude of the loading cycles and the initial anisotropy.