Integrated layout design of multi-component systems using XFEM and analytical sensitivity analysis

This study presents the integrated layout optimization of multi-component systems using a fixed mesh. The optimization formulation is established under the framework of the extended finite element method (XFEM). The level set method is used to represent components and is combined with the XFEM to describe material discontinuities across elements. Sensitivity analysis is proposed with respect to geometric variables of components and pseudo-densities of the basic structure. An analytical shape sensitivity analysis method with respect to positions and shapes of components is developed. Both solid and void components are considered to show the efficiency and accuracy of the proposed shape sensitivity analysis method. Furthermore, a revised finite circle method that adapts shape changes of elliptical components is proposed for the definition of non-overlapping constraints. Finally, numerical examples of maximizing the structural stiffness are tested to demonstrate the proposed method.