Robust Design Of Ultra-light Structures

With the improvement of living standards, people are more and more point to products’ portability, mobility and security requirements. Therefore, light weight design of structures makes a lot of attention. The uncertainty of parameters is introduced in the lightweight design。 The structure not only has the best light weight design, but also has the better robustness or security.This paper proposes a concurrent topology optimization for macrostructure and microstructure design problem subject to an uncertain load, which can be described by ellipsoid models. Macrostructure assumption is made up of uniform microstructure. And microstructure assumption is made up of isotropic material.Then, a bi-level program formulation for minmax system compliance is proposed. The dual theorem and SDP (Semi-Definite Programming) relaxation technique are used for reformulating the no-convex program as a standard convex NSDP(Linear Semi-Definite Programming) program to ensure the global optimum of the lower level program. The "aggregation" solution technique provides the direct relationship between the uncertain load and displacement, as a system composed of these vectors and reduced size of an elasticity matrix. Finally, several numerical experiments demonstrated the validity of the proposed method.