Linear Programming and Moving Morphable Components Approach in 2D Structural Topology Optimization

Moving morphable components (MMC) is a relatively new and effective approach in structural topology optimization. In comparison with other common methods in topology optimization such as density-based methods and level-set-based methods, it requires fewer design variables, and the boundary of the structure is defined explicitly. However, the obtained topology is highly dependent on the initial shape and position of the components. On the other hand, plastic layout optimization utilizes linear programming to find the global optimum of the structural optimization problem. Assuming rigid plastic behavior for material, the optimum layout can be obtained quickly and accurately. The optimum layout gives only the area of members which is constant along the members, therefore, there is no detail about the connection between members. Hence, the obtained optimum layout cannot be used directly for manufacturing methods such as additive manufacturing. It can be shown that the minimum compliance optimization problem for a single load case is equivalent to a minimum-weight plastic layout optimization formulation. This study utilizes the idea and presents a two-step method to take advantage of and compensate for the shortcomings of these two methods in the topology optimization of 2D structures. To this end, in the first step, the optimum layout is obtained using linear formulation in layout optimization and then, the obtained layout is utilized as an initial point in the MMC approach. The results show the efficiency, accuracy, and high convergence rate of the proposed method.