A New Topological Shape Optimization Method Using Artificial Bee Colony Algorithm

Abstract

This thesis proposes a new method for simultaneous topology and shape optimization, namely topological shape optimization (TSO), using the artificial bee colony algorithm (ABCA). The proposed method can create the holes in the topology naturally, although only boundary region of the topology is optimized. Therefore, it can be expected that the proposed method would be much effective than the level set method (LSM) or phase field method (PFM). The reason is that the LSM and PFM cannot create the holes in the structure naturally without topological sensitivity. In this study, a variable called the “Boundary Element Indicator (BEI)”, which is to define the boundary elements is introduced. Once the BEI is updated at each iteration, shape optimization (SO) is performed, and if the BEI is updated whenever a temporary candidate solution is searched in the employed and onlooker bee phases, TSO is performed. Finally, numerical examples are provided to examine the performance of the proposed method. The proposed method is applied to three kinds of problems, that is SO for linear static stiffness problems, TSO for linear static stiffness problems and TSO for nonlinear static stiffness problems. For the SO for linear static stiffness problems, the SO method using the ABCA is employed and compared with the bi-directional evolutionary structural optimization (BESO) method. For the TSO for both linear and nonlinear static stiffness problems, the TSO method using the ABCA is employed and compared with the discrete LSM and the topology optimization (TO) method using the ABCA. From the results of the SO for linear static stiffness problems, the SO method using the ABCA began from an appropriate initial design satisfying the volume constraint, not fully or minimally packed with solid elements, although the computational time for the BESO method is highly dependent on the initial design and the own optimization parameter which is used to determine the amount of removed elements in the design domain. From the results of the TSO for both linear and nonlinear static stiffness problems, the TSO method using the ABCA is much effective than the discrete LSM since it may freely create holes in design domain and optimized the boundaries of topology by only suitably defining boundary elements, and the recommended ranges for the parameters of the TSO method using the ABCA do not influence the optimized design as much as parameters for the discrete LSM. Also, it is found that the objective function value of the TSO method using the ABCA is lower than that of that of the TO method using the ABCA and similar to that of the discrete LSM. In case of the convergence rate, both SO and TSO method using the ABCA are faster than the comparison methods.