A twofold interpenetrating three‐dimensional heterometallic metal–organic framework with pcu topology based on 2‐methylbiphenyl‐4,4′‐dicarboxylic acid

The 2‐methylbiphenyl‐4,4′‐dicarboxylate (mbpdc²⁻) ligand has versatile coordination modes and can be used to construct multinuclear structures. Despite this, reports of the synthesis of coordination complexes involving this ligand are scarce. The title compound, poly[[triaquadi‐μ₃‐hydroxido‐hexakis(μ₄‐2‐methylbiphenyl‐4,4′‐dicarboxylato)calcium(II)hexazinc(II)] monohydrate], {[CaZn₆(C₁₅H₁₀O₄)₆(OH)₂(H₂O)₃]·H₂O}_n , has been prepared by the hydrothermal assembly of Zn(NO₃)₂·6H₂O, CaCl₂ and 2‐methylbiphenyl‐4,4′‐dicarboxylic acid. Two Zn^II atoms adopt a four‐coordinated distorted tetrahedral geometry by bonding to three O atoms from three different 2‐methylbiphenyl‐4,4′‐dicarboxylate (mbpdc²⁻) dianionic ligands and one bridging hydroxide O atom. For the remaining Zn^II atom, a five‐coordinate environment is completed half the time by one carboxylate O atom, and then the same carboxylate O atom and an aqua O atom are present the other half of the time, giving a six‐coordinate environment. The Ca^II atom is coordinated by six O atoms to give an octahedral coordination geometry. The supramolecular secondary building unit (SBU) is a hamburger‐like heptanuclear unit (Zn₆CaO₃₀) and these units are interconnected through mbpdc²⁻ carboxylate groups to generate a three‐dimensional framework with the pcu topology. The single net leaves voids that are filled by mutual interpenetration of an independent equivalent framework in a twofold interpenetrating architecture. The title compound shows thermal stability up to 673 K. The excitation and luminescence data showed the emission of a bright‐blue fluorescence.     

Hydrogen‐bonded structures and interaction energies in two forms of the SGLT‐2 inhibitor sotagliflozin

The sotagliflozin molecule exhibits two fundamentally different molecular conformations in form 1 {systematic name: (2S ,3R ,4R ,5S ,6R )‐2‐[4‐chloro‐3‐(4‐ethoxybenzyl)phenyl]‐6‐(methylsulfanyl)tetrahydro‐2H‐pyran‐3,4,5‐triol, C₂₁H₂₅ClO₅S, (I)} and the monohydrate [C₂₁H₂₅ClO₅S·H₂O, (II)]. Both crystals display hydrogen‐bonded layers formed by intermolecular interactions which involve the three –OH groups of the xyloside fragment of the molecule. The layer architectures of (I) and (II) contain a non‐hydrogen‐bonded molecule–molecule interaction along the short crystallographic axis (a axis) whose total PIXEL energy exceeds that of each hydrogen‐bonded molecule–molecule pair. The hydrogen‐bonded layer of (I) has the topology of the 4‐connected sql net and that formed by the water and sotagliflozin molecules of (II) has the topology of a 3,7‐connected net.     

随机参数连续体结构的动力学拓扑优化

构造了基于概率的连续体结构动力特性拓扑优化设计数学模型,以结构的形状拓扑信息为设计变量,结构总重量极小化为目标函数,满足结构多阶固有频率约束的可靠性要求为约束条件。利用分布函数法对模型中的可靠性约束进行了等价化处理。采用了渐进结构优化(ESO)的求解策略与方法。通过算例验证了文中所提出的设计模型及求解策略与方法的合理性和有效性。     

多工况下结构拓扑优化设计

考虑单元删除和增加对结构应力约束的影响，提出了一种新的多工况下结构的双方向渐进优化方法．首先，基于在结构孔洞或边界周围附加人工材料的思路，建立了结构优化模型和应力灵敏度公式．然后，结合结构应力和应力灵敏度，给出了多工况静力载荷下考虑静应力约束的结构优化准则和算法．开展了结构仿真设计，结果表明给出的方法是正确和有效的，并具有较好的工程应用价值．     

TOPOLOGY OPTIMIZATION OF TRUSS STRUCTURE WITH FUNDAMENTAL FREQUENCY AND FREQUENCY DOMAIN DYNAMIC RESPONSE CONSTRAINTS

In this paper, adaptive genetic algorithm (AGA) is applied to topology optimization of truss structure with frequency domain excitations. The optimization constraints include fundamental frequency, displacement responses under force excitations and acceleration responses under foundation acceleration excitations. The roulette wheel selection operator, adaptive crossover and mutation operators are used as genetic operators. Some heuristic strategies are put forward to direct the deletion of the extra bars and nodes on truss structures. Three examples demonstrate that the proposed method can yield the optimum structure form and the lightest weight of the given ground structure while satisfying dynamic response constraints.     

基于应力及其灵敏度的结构拓扑渐进优化方法

在导出应力灵敏度的基础上，建立了一种改进的基于应力及其灵敏度的结构拓扑双方向渐进优化算法．该方法是对传统ESO和BESO方法的改进和完善．算例表明该方法能较大程度减少解的振荡状态数，获得更佳的拓扑结构．具有概念上的简洁性和应用上的有效性。     

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．