Smooth topological design of structures using the floating projection

This paper presents an element-based topology optimization using the ersatz material model, which enables us to achieve a smooth design for a wide range of topology optimization problems. The traditional element-based topology formation algorithms based on the solid isotropic material with penalization (SIMP) model seek the pure 0/1 design with a zig-zag boundary, which is less practical for engineering applications. 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 paper proposes the floating projection constraint which gradually pushes the design variables to a desired 0/1 level for a smooth design. The applications on a series of engineering optimization problems demonstrate the effectiveness of the proposed topology optimization algorithm. Numerical results show that the proposed topology optimization algorithm based on the floating projection and ersatz material model can achieve optimized structures with a smooth boundary for practical applications.