Topology optimization is often carried out to obtain an optimal structural layout during design. Technically, structural topology optimization boils down to determine the optimal layout of the solid/void of structural subsystems that construct the structures. According to traditional topology variables, the solid is represented by the value of 1 and the void is represented by the value of 0. Thus, the optimization problems established according to discrete topology variables are a 0–1 integer programming. Generally, the well-established gradient-based topology optimization methods can be classified into two categories according to the definition of the design variables: i.e. element-based and boundary-based methods. Existing literature has shown that the former topology optimization method is straightforward and has its advantage with easy implementation. Nonetheless, researchers have acknowledged that traditional element-based topology formation algorithms based on the solid isotropic material with penalization model seek the pure 0/1 design with a zig-zag boundary, which is less practical for engineering applications. To be specific, the ersatz material model suits for the simulation of a smooth design under the fixed mesh, but the element-based topology optimization using the ersatz material model does not provide a clear topology. This contradicts the desire to achieve a smooth design, which could seamlessly integrate with additive manufacturing.
In general, the element-based topology optimization methods using the ersatz material model result in the well-known “variable-thickness-sheet” problem, whose solution contains a large volume of “grey” elements. To resolve this conflict, Professor Xiaodong Huang from the Faculty of Science, Engineering and Technology at Swinburne University of Technology in Australia, proposed a floating projection constraint, which could gradually push the design variables to the desired 0/1 level required for a smooth design. His work is currently published in the research journal, Engineering Structures.
In his approach, Professor Xiaodong Huang applied the proposed element-based topology optimization algorithm to various engineering optimization problems, which included: compliance minimization, frequency maximization, optimization of compliant mechanisms, and lightweight design subject to multiple displacement constraints. He then implemented several numerical simulations in a short cantilever, 2D structures and 3D structures, for compliance minimization.
The author reported that his algorithm retained the advantages of the element-based topology optimization method, meanwhile achieving a smooth design. In fact, compared with the traditional 0/1 optimized design with a zig-zag boundary, the smooth optimized design via his approach was more practical for engineering applications.
In summary, Professor Huang demonstrated an element-based topology optimization using the ersatz material model. The presented approach was reported to enable one achieve a smooth design for a wide range of topology optimization problems. Specifically, applications on a series of engineering optimization problems confirmed the effectiveness of the proposed topology optimization algorithm. In a statement to Advances in Engineering, Professor Xiaodong Huang highlighted that his findings showed that the proposed topology optimization algorithm could achieve optimized structures with a smooth boundary for practical applications, thus solving shortfalls popular with prior approaches.
Xiaodong Huang. Smooth topological design of structures using the floating projection. Engineering Structures, volume 208 (2020) 110330.