Name Correction for Design Variable of Structural Topology Optimization and Presentation of Its Corresponding Treatment Method

To clarify the concepts and promote developments of the structural topology optimization by analyzing the basic concepts, the necessity and urgency of name correction of the design variable of structural topology optimization and presenting its corresponding mapping method are discussed. For the topology optimization of continuum structures, the concept of topology variable was not clarified. The independent level of the topology variable was not discussed and the topology variable was attached to the variables of the structural optimization in lower levels. A penalty function method was adopted to assure the design variables of lower levels to approach to 0/1. In 2004, the Heaviside function was introduced to replace the penalty function by some researchers. Actually, the above problems and their treatments were solved completely in the independent continuous mapping (ICM) method, which was put forward in 1996. The one was the definition of the topology variable with independent level. The other was the approximations of the step function and its inverse function. In this paper, the basic concepts in the ICM method were first introduced. The process of modeling and solution was described by taking the topology optimization problem with frequency constraints as an example. Some examples show that the ICM method has obvious advantages in the aspects of modeling and solution because of its clear concepts. The Zi lu article in the Analects said that a speech will not be in right order if a name is not correct, and nothing will be successful if a speech is not in right order. It is time to correct the name of design variable of structural topology optimization and present its corresponding treatment method.