Regularization solutions to shape and topology optimization problems of domains for elliptic boundary value problems

点击翻译按钮获取中文摘要

Optimization problem of shape of domain in which an elastic body or a flow field is defined is called the shape optimization problem. Here, a deformation field of an elastic body for example is given as a solution of a boundary value problem of a partial differential equation (main problem). Cost functions are defined as functionals of the domain in which the main problem is defined and the solution of the main problem. In the present research, an admissible set of a design variable representing domain variation was defined. Based on the definition, an evaluation method of the shape derivatives of cost functions and a gradient method (H1 gradient method) for reshaping were presented. Moreover, it was confirmed that the domain sequence obtained by the method remains in the admissible set.