Research On Member Size Optimization Of Truss/Beam Structure With Discrete Variables

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,â‘ A fully stressed design method based on the idea of area matching is proposed;â‘¡Interpolation 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.â‘¢E 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.