Optimal design for stiffeners with a two-level approximation method involving size, shape and topology variables

This work presents an engineering method to solve integrated size, shape and topology optimization problems for stiffeners. Based on the ground structure approach, a generalized formulation of the problem is clearly defined. Because the primal problem is implicit, an explicit first-level approximation problem is established using a branched multipoint approximate function. Then, a genetic algorithm is utilized to address the discrete topology variables, and a second-level approximation problem is created to perform the individual fitness calculation, where only retained size and shape variables are involved. Using dual methods, the solution to the second-level approximation problem can be easily obtained. Typical examples are given to illustrate the effectiveness of the proposed method. The optimization results show that this method is quite efficient and that the obtained structure can be used with little processing work. A comparison with the literature reveals that lighter results are available by introducing shape variables. Furthermore, an application on a practical microsatellite validates the capability of this method in dealing with engineering problems.