期刊论文

RECIPROCAL PROGRAMMING THEORY AND ITS APPLICATION TO ESTABLISH A REASONABLE MODEL OF STRUCTURAL TOPOLOGY OPTIMIZATION

中文

力学学报

0459-1879

2019

51

6

1940-1948

10.6052/0459-1879-19-259

国家自然科学基金资助项目(11672103).

本校为其他机构

在数学规划的领域里定义了互逆规划——各自目标函数与约束条件位置相互交换的一对规划.接着指出,尽管互逆规划与对偶规划在表面上似乎类似,但是二者存在5点不同:（1）是否为同一个问题的不同;（2）存在"对偶间隙"与否的不同;（3）设计变量数目的不同;（4）是否单目标与多目标问题的不同;（5）问题合理与否的不同.然后,基于互逆规划的定义,用以审视结构拓扑优化模型,给出如下结果:（1）从这个角度洞悉,在结构优化中,确实有不合理的模型一直被沿用着;（2）找到了修正不合理模型使之合理化的方法;（3）对于给定体积下的柔顺度最小化（MCVC）模型,指出了其不合理的原因;（4） MCVC模型实际是互逆规...

Based on mathematical programming theory, the reciprocal programming is defined as a pair of programming which objective and constraint functions are changed each other. After that, it is pointed out that reciprocal programming and dual programming seem similar but there are five differences between them: (1) the difference in whether they are the same problem or not; (2) the difference in whether there exists a dual gap or not; (3) the difference in the number of design variables; (4) the difference between single-objective and multi-objective...