Periodic Layout Optimization of Cyclic Symmetric Structure

This paper proposes a new optimization method to solve periodic layout optimization of a cyclic symmetric structure by means of the guide-weight method. The mathematical model for periodic layout optimization under multiple constraints is built on a single working condition. By constructing a virtual fan-shaped subdomain, periodic layout optimization of the cyclic symmetric structure is transformed into the conventional topology optimization of the virtual fan-shape subdomain. Starting from the Lagrange equation, the general iterative criterion of the virtual fan-shaped subdomain is deduced by the guide-weight method. Taking the problem of minimum compliance as an example, the iterative criterion between relative density and strain energy density of elements in the virtual fan-shaped subdomain is obtained under the condition of mass constraint. The physical significance of iterative criterion is explained and the optimization flow of periodic layout optimization is provided. Two examples of the cyclic symmetric structure show that the proposed method is effective and robust to solve the problem of periodic layout optimization.