多孔材料/结构尺度关联的一体化拓扑优化技术

针对多孔材料的尺度效应和微结构构型的可设计性，提出以宏观结构最大刚度为目标，材料表征体胞构型为变量的材料／结构尺度关联一体化设计新方法．采用有限元超单元技术，验证了材料表征体胞尺度、边长比、平移、对称周期分布方式对构型设计结果的影响，实现了材料宏观布局设计、材料表征体胞构型精细设计以及多尺度均匀化设计的统一。基于凸规划对偶优化求解技术与二次型周长控制约束，完成了快速设计与材料分布棋盘格效应的控制。计算结果表明，在给定材料用量的情况下，该方法能有效地实现蜂窝结构的拓扑优化设计，设计结果充分反映了蜂窝夹层结构的尺度效应，为轻质结构设计提供了新的设计方法。     

离散变量结构拓扑优化设计研究

研究了离散变量结构拓扑优化设计的若干问题，讨论了离散型优化模型的合理性，提出截面设计变量的离散程度和全局约束影响最优拓扑，是优化中不可忽视的因素，文中还提出了一种解离散变量桁架，刚架结构拓扑优化的启发式算法。     

SIMULTANEOUS SHAPE AND TOPOLOGY OPTIMIZATION OF TRUSS UNDER LOCAL AND GLOBAL STABILITY CONSTRAINTS

A new approach for the solution of truss shape and topology optimization problem sunder local and global stability constraints is proposed. By employing the cross sectional areas of each bar and some shape parameters as topology design variables, the difficulty arising from the jumping of buckling length phenomenon can be easily overcome without the necessity of introducing the overlapping bars into the initial ground structure. Therefore computational efforts can be saved for the solution of this kind of problem. By modifying the elements of the stiffness matrix using Sigmoid function, the continuity of the objective and constraint functions with respect to shape design parameters can be restored to some extent. Some numerical examples demonstrate the effectiveness of the proposed method.     

基于可靠性的桁架结构拓扑优化设计

建立了以杆截面为设计变量、结构重量极小化为目标、具有位移、应力等性态可靠性约束的桁架结构拓扑优化设计数学模型．通过引入可靠性安全系数，并利用结构力学的三个基本方程，将结构的位移和杆件应力可靠性约束等价显示化为设计变量的线性函数，使原基于可靠性的优化模型转化为常规的序列线性规划问题，利用修正的单纯形法求解．算例表明文中提出的方法既简单又有效．     

基于柔性四羧酸的三个一维/二维/三维Zn(Ⅱ)/Co(Ⅱ)配合物的晶体结构及荧光性质

通过水热/溶剂热合成的方法制备了3个Zn(Ⅱ)/Co(Ⅱ)配合物{[Zn(H₂L)(H₂O)₃]·H₂O·0.5H₄L}_n(1)、{[Co(L)_0.5(4,4'-bpy)]·0.5H₂O}_n(2)和{[Co(L)_0.5(pbmb)(H₂O)]·H₂O}_n(3)(H₄L=5,5'-(hexane-1,6-diyl)-bis(oxy)diisophthalic acid,4,4'-bpy=4,4'-bipyridine,pbmb=1,1'-(1,3-propane)bis-(2-methylbenzimidazole))。结构分析表明配合物1为一维链结构。2为拓扑符号为(6⁴·7·8)(6·7²)的三重穿插网络结构。3是拓扑符号为(4·6²)(4²·6²·8²)的(3,4)-连接的二维网络结构。配合物1呈现出较好的荧光性质。     

基于2,6-二(4-羧基苯亚甲基)环己酮的金属-有机框架化合物的合成与表征

以2,6-二(4-羧基苯亚甲基)环己酮(H₂L)为配体得到一例锰金属-有机框架化合物[MnL]_n,并运用红外、热重、循环伏安、固体紫外、X射线光电子能谱和X射线单晶衍射对其进行表征。单晶衍射分析表明该配合物属于三斜晶系,空间群P1^-,不对称单元由Mn(Ⅱ)离子和一个L^2-配体组成。配体两端的羧基均为单齿配位,配体中间羰基上的氧参与配位,每个配体L^2-和3个Mn.离子配位,形成相对稳定的三角形配位构型。配合物中的Mn.与氧原子形成六配位构型,其中赤道面中的4个氧原子来自4个配体L^2-中单齿配位的羧基,上下顶点的2个氧原子分别来自配体L^2-中的羰基,从而形成八面体构型[MnO₆]。拓扑分析表明该金属-有机框架化合物具有二维kgd结构特征。循环伏安测试表明在扫速为30 mV·s^-1时,半波电位为171 mV,固体紫外光谱表明该化合物的带隙为1.76 eV。该化合物在染料分子如亚甲基蓝、甲基橙的降解过程中,具有一定的光催化活性。     

连续体拓扑优化的一种光滑化方法

利用有限元离散后的水平集函数的节点值作为拓扑设计变量来求解连续体拓扑优化问题。利用阶跃函数把水平集函数转化为0-1变量。引进无穷次连续可微的sigmoid函数对阶跃函数进行光滑化。通过对sigmoid函数中陡度参数的不断调整来达到加快收敛速度的目的。利用拓扑导数的概念分析了这种做法的可行性。数值算例表明采用sigmoid函数作为光滑函数不但可以使算法的选取和实现变得更加容易,而且可以获得相对较快的收敛速度。     

SOLUTIONS FOR SECOND ORDER IMPULSIVE INTEGRO- DIFFERENTIAL EQUATION ON UNBOUNDED DOMAINS IN BANACH SPACES

Under loose conditions, the existence of solutions to initial value problem are studied for second order impulsive integro-differential equation with infinite moments of impulse effect on the positive half real axis in Banach spaces. By the use of recurrence method, Tonelii sequence and the locally convex topology, the new existence theorems are achieved, which improve the related results obtained by Guo Da-jun.     

Metalated Hexaphyrins: From Understanding to Rational Design

The heretofore unpredictable behavior of [26] and [28]hexaphyrins upon metalation has been elucidated through quantum chemical calculations. It is demonstrated that the molecular topology of Group 10 and Group 11 metal complexes of hexaphyrins depends on sensitive interplay between the intrinsic ligand strain and the metal–ligand interaction strength. As such, the aromaticity of the ligand and effective charge of the metal are revealed as key factors determining the binding mode and the preference for Möbius or Hückel structures. These findings offer a new perspective to rationalize experimental observations for metalated hexaphyrins. More importantly, the proposed guidelines could be useful for designing novel complexes of hexaphyrins, such as a hitherto unknown Möbius [26]hexaphyrin complex.