期刊论文

中文

力学学报

0459-1879

2017

49

5

1135-1144

10.6052/0459-1879-17-176

国家自然科学基金(11672103) 和湖南省自然科学基金(2016JJ6016) 资助项目.

本校为其他机构

推导对偶目标函数的精确显式表达式,可选用更多成熟高效的求解方法,从而进一步提高了非线性规划对偶理论求解结构拓扑优化问题的效率.研究工作来源于非线性凸规划同其对偶规划的间隙为零,可以等价转化为对偶问题求解,通常可以大大地缩小问题的规模,可是二者不具有显式关系却影响了对偶解法的应用.所幸的是,结构优化当中一大类问题包括连续体结构拓扑优化问题,不仅具有凸性,而且具有变量可分离性,于是原变量和对偶变量之间有了显式关系,因此,对偶解法成了38年来被应用的有效方法之一.然而长期以来,对偶问题的目标函数并不是显式,这缘于含参数的极小化问题导致目标函数为隐式表达,常见的显式化方法...

An explicit exact formula is derived for the objective function of the dual model of a class of separable convex programming problems. It makes more mature and efficient methods can be chose to solve the dual model. Therefore, the advantage of applying the duality theory of nonlinear programming to efficiently solve structural topology optimization problems is fully exploited. The research work is rooted in that the gap of a nonlinear convex programming with its dual programming is zero. Solving original programming can be equivalently transfor...