【作者】 吕永涛；

【导师】 刘小虎；

【作者基本信息】 华中科技大学 ， 固体力学， 2007， 硕士

【摘要】 目前大多数结构优化设计方面的研究都是针对连续变量的,离散变量结构优化设计的研究比较少。而实际工程中,各种约束条件的限制,导致设计变量往往都是离散变量。因此,建立适用于离散变量结构优化设计计算的算法是很有工程实用价值的。本论文的主要工作及创新点有:(1)建立了离散变量结构优化问题的数学模型。(2)针对结构构件截面尺寸优化问题,①提出了基于面积匹配思路的离散变量满应力齿行法,求解桁架结构离散变量尺寸优化问题。②提出了将离散变量优化问题转换为连续变量优化问题的方法一—插值法。插值法是以杆单元的截面积或梁单元的截面编号为伪设计变量,以杆单元的离散截面积或梁单元的离散截面编号为插值基点,将离散设计变量转换为含约束的连续设计变量。③提出将离散变量优化问题转换为连续变量优化问题的方法二—增广变量法。增广变量法中,选取结构构件截面的所有几何参数作为设计变量,其中,以不随截面编号递减的参数为主设计变量,其它为次设计变量,次设计变量的约束随主设计变量变化而改变。(3)利用本文提出的处理离散变量结构优化问题的方法,计算了几个经典的桁架和框架结构算例,以及造桥机底框架工程实例。验证了所提方法的合理性。更多还原

【Abstract】 In the area of structure optimization design, most studies aim at continuous variables; papers in structure optimization design problems with discrete variables are deficit. In the practical structure design of engineering, because of the limit of constraint conditions, almost all optimization problems are the optimization design with discrete variables. Therefore, it is important to develop the approach for discrete structural optimization.The main works completed and innovative contributions of this thesis are as follows:(1) The mathematic models for discrete optimization problems were built.(2) In order to solve size member optimization problems with discrete variables,①A fully stressed design method based on the idea of area matching is proposed;②Interpolation by pseudo variables method is proposed to transfer the original discrete optimization problems to continuous optimization problems. In this method, the cross section areas of truss or the pseudo size numbers of beam are chose as the design variables. The discrete truss areas or the discrete size numbers are chose as the interpolation points.③E nlarging design variables method is proposed to transfer the original discrete optimization problems to continuous optimization problems. In this method, all the cross section geometry parameters are chose as the design variables. But some of them are main design variables and the others are minor design variables. The bounds of the minor design variables vary with the change of the main design variables.(3) Several classical truss and beam structure examples and an engineering example of the optimization of the lower frame structure of the bridge-making machine are given using the methods proposed in this thesis. The results prove the validity of the methods proposed.更多还原