Optimization of support positions to minimize the maximal deflection of structures

In this paper, the design sensitivity analysis for the deflection of a beam or plate structure is first investigated with respect to the position of a simple support using the discrete method. Both elastic and rigid supports are taken into account, and closed-form formulae for the deflection sensitivity are developed straightforwardly. Then, on the basis of the design sensitivity analysis, a heuristic optimization algorithm, called the evolutionary shift method, is presented for support position optimization to minimize the maximal deflection of a structure with a fixed grid mesh scheme. In each iterative loop, the support with the highest efficiency is shifted in priority. To facilitate the convergence of the process, a polynomial interpolation technique is employed to evaluate the solution more accurately. The optimal solution is achieved gradually with a minimum modification of the support layout design. Finally, three numerical examples are presented to demonstrate the validities of the sensitivity analysis and the optimization method. Results show that support optimization can improve the structural behavior significantly.     

基于拓扑描述函数的连续体结构拓扑优化方法

提出了一种利用拓扑描述函数(TDF)作为拓扑设计变量求解连续体结构拓扑优化问题 的新方法. 优化问题的目标函数是结构的整体柔顺性，约束条件为对于可利用材料的体积限 制. 这种方法不仅可以消除拓扑优化中经常出现的棋盘格式等数值不稳定现象，而且能够有 效地抑制传统算法处理此类优化问题时所引发的边界扩散效应. 与其它的基于水平集描述函 数的拓扑优化方法相比，所提出的算法不仅无需求解控制水平集函数演化的双曲守恒方 程，而且合理地考虑了目标函数的拓扑导数信息，因而使得算法的计算效率有了显著的提高.     

简单柔性机械臂的构造性逆动力学方法

本文提出了适于简单柔性机械臂的一种基于谱分析的构造性逆动力学方法。数值模拟和实验结果表明，这种方法提供的开环输入力矩，不仅可以实现机械臂特定的刚体转动，而且可以有效地减弱柔性对机械臂精确定位的影响。     

应力约束下薄板结构的拓扑优化

研究了应力约束下薄板结构的拓扑优化问题，分析了极限应力的影响，建立了拓扑优化的数学模型，讨论了若干优化过程中的技术问题，最后，进行了实例计算。     

结构形状优化设计数值方法的研究和应用

本文论述了连续体结构形状优化设计数值方法的研究和应用进展,讨论了结构模型化、灵敏度分析、优化方法改进、优化实用软件开发以及同CAD技术相结合等问题,介绍了在结构优化设计软件MCADS中采用的方法,并通过工程实例说明了结构形状优化设计的应用及其价值。     

An efficient method for structural optimization

Based on the dual theory of nonlinear mathematical programming and the second order Taylor series expansions of functions, an efficient algorithm for structural optimum design has been developed. The main advantages of this method are the generality in use, the efficiency in computation and the capability in identifying automatically the set of active constraints. On the basis of the virtual work principle, formulas in terms of element stresses for the first and second order derivatives of nodal displacement and stress with respect to design variables are derived. By applying the Saint-Venant's principle, the computational efforts involved in the Hessian matrix associated with the iterative expression can be significantly reduced. This method is especially suitable for optimum design of large scale structures. Several typical examples have been optimized to test its uasefulness.     

多约束膜结构截面优化及在MSC/Nastran上的程序实现

将准则法和数学规划法相结合，借助满应力准则将应力约束转化为动态尺寸约束，利用单位虚载荷法将位移约束转化为设计变量的显式表达式建立优化模型，然后用数学规划法求解；采用无量纲设计变量实现设计变量连接，对膜结构的厚度进行优化设计；根据对偶理论，应用对偶规划精确映射原问题，再按泰勒展式建立对偶问题的二阶近似。为了提高优化效率，采用射线步调整结构性态，运用粗选有效约束技术筛选约束，并采用主、被动变量循环确保收敛稳定。以MSC／Nastran软件作为结构分析的求解器，以MSC／Patran软件作为开发平台，完成了膜结构截面优化程序。对膜结构的单变位、多变位的结构优化问题进行了优化计算，并与MSC／Nastran优化模块的计算结果进行比较。算例结果表明程序的可靠性、高效性和稳定性以及理论算法的优越性。     

FEEDBACK CONTROL OPTIMIZATION FOR SEISMICALLY EXCITED BUILDINGS

A feedback control optimization method of partially observable linear structures via stationary response is proposed and analyzed with linear building structures equipped with control devices and sensors. First, the partially observable control problem of the structure under horizontal ground acceleration excitation is converted into a completely observable control problem. Then the It6 stochastic differential equations of the system are derived based on the stochastic averaging method for quasi-integrable Hamiltonian systems and the stationary solution to the Fokker-Plank-Kolmogorov （FPK） equation associated with the It6 equations is obtained. The performance index in terms of the mean system energy and mean square control force is established and the optimal control force is obtained by minimizing the performance index. Finally, the numerical results for a three-story building structure model under E1 Centro, Hachinohe, Northridge and Kobe earthquake excitations are given to illustrate the application and the effectiveness of the proposed method.     

结构拓扑优化研究方法综述

结构拓扑优化研究方法目前有解析方法和数值方法两大类.首先介绍了解析方法中的 Michell理论,它在结构拓扑优化领域研究较早,影响最为深远.随后着重讨论了杆系和连 续体结构拓扑优化的数值方法.杆系结构常采用基结构方法,通过删除部分杆件达到结构 拓扑优化的目的.连续体结构一般要划分为有限单元,通过删除单元形成带孔的连续体, 以实现拓扑优化.介绍了连续体结构拓扑优化常采用的材料模型:各向同性、各向异性和 带微结构材料.并对连续体结构(0-1)拓扑优化中的数值计算不稳定问题的机理进行了分 析,给出了解决方法.此外,对应力约束问题存在解的奇异性现象也作了简要介绍.最后, 对数值方法中的主要数学求解方法进行了简单介绍.     

结构拓扑优化设计的三角网格进化法

针对进化或拓扑优化方法的不足，提出了一种基于遗传算法的新型进化式拓扑优化方法－－三角网格进化法，该方法不仅能够同时进行拓扑，形状与截面变量优化设计，而且在优化过程中实现了退化和进化的统一，提高了优化效率。另外本文还首次对结构类型变量进行了优化计算，取得了有益的结果。最后几个数值算例证明了本方法的可行性和有效性。