Asymptotic numerical analysis of the diffusion‐discrete absorption equation

The diffusion‐discrete absorption (DDA) equation is considered. This equation contains the standard diffusion term and the discrete sorption expressed by a sum of large number of δ‐functions with the support at a non‐uniform mesh multiplied by the unknown function (concentration). The main result of the paper is the homogenization (continualization) of this equation when the small parameter is the characteristic step h of the mesh. The error estimates are proved for the difference of the exact solution of the DDA equation and the solution of the homogenized differential equation. Copyright © 2012 John Wiley & Sons, Ltd.     

基于均匀材料微结构模型的热弹性结构与材料并发优化

研究由宏观上均匀多孔材料制成的结构的优化设计问题,待设计的结构受到给定的外力与温度载荷作用,优化设计旨在给定结构允许使用的材料体积约束下,设计宏观结构的拓扑及多孔材料的徼结构,使得结构柔度最小.本文提出了一种宏观结构与微观单胞构型并发优化设计的方法.在此方法中,引入宏观密度和微观密度两类设计变量,在微观层次上采用带惩罚的实心各向同性材料法SIMP(Solid Isotropic Material with Penalty),在宏观层次上采用带惩罚的多孔各向异性材料法PAMP(Porous Anisotropic Material with Pemlty),借助均匀化方法建立两个层次阃的联系,通过优化方法自动确定实体材料在结构与材料两个层次上的分配,得到优化设计;提供的数值算例检验了本文所提方法及计算模型,并讨论了温度变化、材料体积及计算参数对优化结果的影响.研究结果表明同时考虑热和机械载荷时,采用多孔材料可以降低结构柔顺性.     

PLASTIC LIMIT ANALYSIS OF DUCTILE COMPOSITE STRUCTURES FROM MICRO-TO MACRO-MECHANICAL ANALYSIS

The load-bearing capacity of ductile composite structures comprised of periodic composites is studied by a combined micro/macromechanicai approach. Firstly, on the microscopic level, a representative volume element （RVE） is selected to reflect the microstructures of the composite materials and the constituents are assumed to be elastic perfectly-plastic. Based on the homogenization theory and the static limit theorem, an optimization formulation to directly calculate the macroscopic strength domain of the RVE is obtained. The finite element modeling of the static limit analysis is formulated as a nonlinear mathematical programming and solved by the sequential quadratic programming method, where the temperature parameter method is used to construct the self-stress field. Secondly, Hill＇s yield criterion is adopted to connect the micromechanicai and macromechanical analyses. And the limit loads of composite structures are worked out on the macroscopic scale. Finally, some examples and comparisons are shown.     

Characterization of cuttlebone for a biomimetic design of cellular structures

Cuttlebone is a natural material possessing the multifunctional properties of high porosity, high flexural stiffness and compressive strength, making it a fine example of design optimization of cellular structures created by nature. Examination of cuttlebone using scanning electron micros- copy （SEM） reveals an approximately periodic microstruc- ture, appropriate for computational characterization using direct homogenization techniques. In this paper, volume fractions and stiffness tensors were determined based on two different unit cell models that were extracted from two different cuttlefish samples. These characterized results were then used as the target values in an inverse homogenization procedure aiming to re-generate microstructures with the same properties as cuttlebone. Unit cells with similar topologies to the original cuttlebone unit cells were achieved, attaining the same volume fraction （i.e. bulk density） and the same （or very close） stiffness tensor. In addition, a range of alternate unit cell topologies were achieved also attaining the target properties, revealing the non-unique nature of this inverse homogenization problem.     

层状岩体的Cosserat介质均匀化

将层状岩体视为由Cosserat介质组成的复合体,对其进行均匀化等效,在MATLAB平台上进行有限元编程,得到新等效本构关系。不仅能反映层状岩体的弯曲特性,而且可以对节理岩体的力学性能进行宏观和细观描述。通过对洞室算例进行显式节理模型、横观各向同性模型以及均匀化Cosserat等效模型三种方法的数值计算比较,证明理论分析与计算方法可行有效。     

Polydisperse structures of composites with random elastic properties of inclusions

A generalized self-consistent method [1, 2] is developed and applied to the boundary-value problems of composites with random elastic properties of inclusions. The approach suggested makes it possible to allow for a random mutual arrangement, statistical dispersion of elastic properties and sizes of the inclusions, and their mutual correlation in terms of special homogenized indicator functions. For comparison, the analytical solutions and those obtained from a corresponding sequence of H+1 (H=0,1,…) linked homogenized problems of the self-consistent method for the strain distribution in the inclusions and for the tensor of effective elastic properties of the composite are given. A numerical calculation of the effective transversely isotropic elastic characteristics for a unidirectional polydisperse fibrous composite is also presented. Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 1, pp. 33–58, January–February, 2000.     

椭圆问题的非线性边界条件均匀化

在本文我们讨论了在等值面边值问题中的非线性边界条件的均匀化,推广了相应的边界条件均匀化结果,而且可应用到用于处理热敏电阻问题中的一类非线性非局部边值问题的边界条件均匀化问题。     

Flow of electrolytes in a porous medium

A two-scale model of ion transfer in a porous medium is obtained for one-dimensional horizontal flows under the action of a pressure gradient and an external electric field by the method of homogenization. Steady equations of electroosmotic flows in flat horizontal nano-sized slits separated by thin dielectric partitions are averaged over a small-scale variable. The resultant macroequations include Poisson’s equation for the vertical component of the electric field and Onsager’s relations between flows and forces. The total horizontal flow rate of the fluid is found to depend linearly on the pressure gradient and external electric field, and the coefficients in this linear relation are calculated with the use of microequations. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 162–173, July–August, 2008.     

HOMOGENIZATION OF SOME LINEAR AND SEMILINEAR SCHRDINGER EQUATIONS WITHREAL POTENTIAL

1 IntroductionIn this paPer, we collsider the initial and boundaxy value probIem of linear and sentilillearScl1r5dinger equation as fOllows:l ie(x):5:i".,'<">"'>.'<",,'>,"=' 1:!\:?0t:)t>, (l1)wllere E > 0, fl C RN is a bounded open dolllain and T is an ar…     

一种基于自适应单元删除率的BESO方法

在ESO中采用动态删除率能有效地提高优化效率和稳定性,但现有的动态删除率策略都含有经验参数,确定删除率的过程较为复杂。本文提出了一种用于BESO的无经验参数自适应单元删除率确定方法。通过分析单元删除率对优化稳定性的影响,得到了结构优化过程中单元删除率的理想变化规律和单元灵敏度均匀化信息对删除率的影响情况,并据此分析了经验参数引入的原因,从而构造了评价单迭代步的单元灵敏度均匀化程度指标。然后,基于单迭代步的单元灵敏度均匀化程度指标,构造了全部迭代步信息下的单元灵敏度均匀化程度相对指标,结合单元删除率的推荐范围值,给出了一种自适应于结构优化进程的单元删除率自适应函数。最后,给出了基于自适应单元删除率的BESO方法实现流程。经典算例的结果对比说明,本文方法在保证优化质量相近的情况下,具有更好的优化效率和稳定性。