A systematic approach for generating velocity fields in shape optimization

Design velocity fields affect every stage of the shape optimization process. The progress of the optimization process, distortion of the finite element mesh, and final shape are sensitive to the quality of velocity fields. It is important to identify and generate effective velocity fields at the beginning of the process. This paper provides several criteria to determine the effectiveness of velocity fields. A systematic approach for generating these velocity fields using deformation fields is developed. The use of interactive procedures is shown to be indispensable for ensuring the effectiveness and quality of design velocity fields. General strategies and guidelines for generating velocity fields are given. Concepts of weight-reducing, stress-reducing, form-preserving, and smooth basis shapes are presented. Normalization of velocity fields is discussed. A method for controlling mesh distortion during the shape optimization process is given based on an explicit limit on the design change to prevent the Jacobian from vanishing. Two- and three-dimensional design problems are solved.