Continuous Method About 0-1 Programming By Using Synthetical Constraints And Applications For Structural Topology Optimization

Structural topology optimization belongs to 0-1 programming problem essentially. The 0-1 programming problem is converted to an equivalent nonconvex nonlinear continuous programming problem by the synthetical constraints method. It is difficult to solve the programming problem that was converted by Ordinary approximate solutions for common convex programming. The genetic algorithm program, which is based on operator amendment method, is used to solve the converted programming problem in this paper because of its excellent capability for global search and relaxed solving conditions. And then the synthetical constraints method and the genetic algorithm are used in structural topology optimization problem. The research mainly includes following parts:1. The synthetical constraints method is deduced and proved in this paper. 0-1 linear programming, 0-1 nonlinear programming and common discrete programming can be mapped into continuous programming by synthetical constraints.2. The solving method of 0-1 linear programming problem is researched, and it is proved to be effective and accurate in some examples. 0-1 nonlinear programming problem is discussed. The conclusion is that the method of this paper is effective to 0-1 nonlinear programming problem too. Variable substitution is used to convert discrete programming to 0-1 programming, which is converted to continuous programming by the synthetical constraints method. The solution of the 0-1 programming can be inversed to the solution of the discrete programming.3. The structural topology optimization of two-dimension continuous structure under displacement constraints is researched. An accurate mathematic model is established by ICM (independent continuous mapping) model building idea, that the object is structural weight and the design variables are topology variables. The model is converted to a continuous programming by the synthetical constraints method, and the continuous programming is solved by genetic algorithm. Some numerical examples indicate that the algorithm is credible to 0-1 programming problem,and is feasible to structural topology optimization. Based on MSC/NASTRAN software, the PCL code (PATRAN Command Language) was adopted to secondary development for topology optimization of two-dimension continuous structure under displacement constraints. The optimum design module was integrated into PATRAN interface.