A COMPREHENSIVE ALGORITHM FOR SHAPE OPTIMIZATIONOF STRUCTURE WITH DISCRETE VARIABLES
离散变量结构形状优化设计的综合算法

In this paper, an algorithm for shape optimization of structure with discrete variablesis given. First, the mathematical model of truss configuration problem is given, which include twokinds of variables such as sizing variables and joint coordinates. The objective function for trussconfiguration problem is the total weight of structure and the constraints are stress constraintsand joint displacements. In general, the structural responses, such as forces and displacementsare implicit functions of design variables. To increase the efficiency the algorithm, the forces canbe approximated by a first order Taylor expansion, so that an explicit approximate problem canbe obtained. In order to decrease the computational error and assure the iteration procedure tobe convergent, moving limits are imposed to two kinds of design variables. In the procedure ofsolving, two kinds of variables are considered simultaneously and the relative difference quotientmethod is used. The algorithm has a high efficiency and accuracy. The relative difference quotientvalues with respect to two kinds of variables can be used to determine which variable should beoptimized in each iteration. The algorithm is applied to several classical structural optimizationexamples and the results indicate that algorithm has higher computational accuracy.