A STRUCTURAL TOPOLOGICAL OPTIMIZATION METHOD BASED ON EXPLORING CONCEPTUAL ROOT

This paper introduces the transformation of the 0-1 discrete variables into continuous variables in topological optimization problem by ICM (Independence, continuous and Mapping) method. The first step is to convert equivalently the discrete problem into continuous problem taking advantages of the step-up function; The second step is to define the polish function to approach the step-up function; The third step is to establish the mapping model by introducing the filter function which is the inverse function of the polish function; The fourth step is to solve the model with continuous variables by some smooth algorithms. Some representative numerical examples of continuous structures have illustrated the process of transforming the topological optimization model into independent level one. This method and the numerical solutions show that the method is also suitable for pure mathematical optimization problems with 0-1 discrete variables.