An efficient evolutionary structural optimization method with smooth edges based on the game of building blocks

Although bi-directional evolutionary structural optimization (BESO) has the advantages of a simple concept and clear-cut solutions, the edges of the optimal solution are normally non-smooth. This article proposes an approach that directly represents the smooth structure using finite elements. The pseudo-auxiliary line is introduced to make the staggered boundary approach a smooth one, and a rule is presented to make the boundary element deformable to describe the structure?s edges. To improve the efficiency, the game of building blocks is incorporated into the classical BESO algorithm. A set of basic blocks is predefined and is positioned in a suitable location to assemble the optimal structure. In this way, the optimal structure has better mechanical performance and smooth edges with acceptable computational cost. The roundness of corners is easily controlled by adjusting the configuration of the basic blocks. Several two- and three-dimensional numerical examples investigate the effects of the parameters of auxiliary lines and the shape of basic blocks on the boundary smoothness and optimization performance. The efficiency of the proposed method is justified through these examples.