期刊论文

WIDENING AND DEEPENING OF RECIPROCAL PROGRAMMING AND ITS APPLICATION TO STRUCTURAL TOPOLOGY OPTIMIZATION

中文

力学学报

0459-1879

2020

52

6

1822-1837

10.6052/0459-1879-20-188

国家自然科学基金资助项目（11672103）；

本校为其他机构

本文的工作涉及数学与力学两方面,数学方面:(1)将数学规划论中新提出的互逆规划,从s-m型(或称为m-s型)发展出s-s型和m-m型互逆规划(其中s意为单目标,m意为多目标),从而使互逆规划的定义完备成为3种;(2)从KKT条件审视互逆规划的两方面,得到了互逆规划双方求解涉及拟同构和拟同解的3个定理,并且予以证明,提供了在求解中对于互逆规划双方在求解中相互借鉴的理论基础;(3)对一对互逆规划双方皆合理的情况和某一方不合理的情况,皆给出了求解策略和具体解法.力学方面:(1)给出结构优化设计模型合理与否的诠释;(2)在互逆规划对结构拓扑优化的应用中,提出了不合理结构拓扑优化模型的求解策略;(3)给出了借助...

The work of this paper involves two aspects of mathematics and mechanics. In terms of mathematics: (1) The reciprocal programming newly proposed in the mathematical programming theory is developed from the s-m type (or called m-s type) to the s-s type and m-m type reciprocal programming (among which s means single goal, m means multiple goals), so that the definition of reciprocal programming is complete into three types; (2) From the KKT condition to examine the two aspects of reciprocal programming, it is obtained that the three theorems of t...