基于可靠度的结构优化的序列近似规划算法

基于可靠度的优化的最直观解法是把可靠度和优化的各自算法搭配一起形成嵌套两层次迭代。为改善其收敛性提高计算效率,人们提出了功能测度法、半无限规划法、单层次算法等多种改进方法。本文对传统结构优化界的经典序列近似规划法改造并扩展应用于求解基于可靠度的结构优化问题,构造该问题的序列近似规划模型和求解过程;其核心思想是在每个近似规划子问题中采用近似可靠度指标对设计变量的线性近似,在优化迭代过程中同步更新设计变量和随机空间中的近似验算点坐标,以达到可靠度分析和优化迭代同步收敛的目标。为了算法的实施,还推导出近似可靠度指标的半解析灵敏度计算公式,编制了程序,最终实现与通用软件的连接。论文用算例证实算法的有效性。     

极限分析的无搜索数学规划算法

本文研究理想刚塑性介质极限载荷因子的计算方法。根据极限分权理论的上限定理,建立了计算极限载荷因子的一般数学规划有限元格式。针对这种格式的特点,提出了一个求解极限载荷因子的无搜索迭代算法。这个算法中采用逐步识别刚性、塑性分区,不断修正目标函数的方案,克服了目标函数非光滑所导致的困难。本文提出的算法建立于位移模式有限元基础上,有较广的适用范围,且具有计算效率高,稳定性好,格式简单易于程序实现等优点。     

Thermomechanical behavior of thermoset shape memory polymer programmed by cold-compression: Testing and constitutive modeling

Programming is a key process for thermally activated stress or strain recovery of shape memory polymers (SMPs). Typically, programming requires an initial heating above the glass transition temperature (T_g), subsequent cooling below T_g and removal of the applied load, in order to fix a temporary shape. This work adopted a new approach to program thermoset SMPs directly at temperatures well below T_g, which effectively simplified the shape fixing process. 1-D compression programming below T_g and free shape recovery of a thermoset SMP were experimentally investigated. Functional stability of the shape fixity under various environmental attacks was also experimentally evaluated. A mechanism-based thermoviscoelastic-thermoviscoplastic constitutive model incorporating structural and stress relaxation was then developed to predict the nonlinear shape memory behavior of the SMP trained below T_g. Comparison between the prediction and the experiment showed good agreement. The structure dependence of the thermomechanical behavior of the SMP was further discussed through a parametric study per the validated constitutive model. This study validates that programming by cold-compression is a viable alternative for thermally responsive thermoset SMPs.     

Fully Invariant Subgroups of Abelian p-Groups with Finite Ulm–Kaplansky Invariants

We study primary groups containing proper fully invariant subgroups isomorphie to the group. The admissable sequence of Ulm–Kaplansky invariants for primary groups is introduced. Using these sequences, If-groups are described in the classes of seperable and periodically complete groups.     

On duality concepts in fractional programming

The paper (Part I) describes an approach to duality in fractional programming on the basis of another kind of conjugate functions. The connections to some duality concepts (the Lagrange-duality and duality concepts of Craven and Schaible) are investigated and some new proofs of strong duality theorems are given.     

Extensions of algorithmic senstivity calculations nonlinear programming using barrier and penalty functions

We provide a theoretical basis for approximating the sensitivity of a perturbed solution and the local optimalvalue function, using information generated by a sequential unconstrained minimization technique in the normal course of solving a mathematical program. We show that various algorithmic sensitivity results can be obtained without other assumptions than those needed for the corresponding nonalgorithmic results. Our results extend the algorithmic calculation of sensitivity information introduced by Fiacco, utilizing the logarithmic barrier function and quadratic penalty function     

The Möbius function of separable and decomposable permutations

We give a recursive formula for the Möbius function of an interval [σ,π] in the poset of permutations ordered by pattern containment in the case where π is a decomposable permutation, that is, consists of two blocks where the first one contains all the letters 1,2,…,k for some k. This leads to many special cases of more explicit formulas. It also gives rise to a computationally efficient formula for the Möbius function in the case where σ and π are separable permutations. A permutation is separable if it can be generated from the permutation 1 by successive sums and skew sums or, equivalently, if it avoids the patterns 2413 and 3142.We also show that the Möbius function in the poset of separable permutations admits a combinatorial interpretation in terms of normal embeddings among permutations. A consequence of this interpretation is that the Möbius function of an interval [σ,π] of separable permutations is bounded by the number of occurrences of σ as a pattern in π. Another consequence is that for any separable permutation π the Möbius function of (1,π) is either 0, 1 or −1.     

长周期光纤光栅的透射光谱特征

用Matlab编程的方法对长周期光纤光栅的透射光谱谱线特性进行了研究,数值模拟了长周期光纤光栅周期对光谱谱线的影响.研究结论为长周期光纤光栅的设计提供了理论依据.     

长周期光纤光栅的功率特性

用Matlab编程的方法对长周期光栅功率特性进行了研究,数值模拟了长周期光栅入射角度、光栅长度与功率分布的图像关系.研究结论为长周期光纤光栅的设计提供理论依据.