Resumen
The aim of topology optimisation is to determine the optimal distribution of material phases within the periodic cells of a microstructure. In this paper, the density of grid points under element volume fraction is constructed to replace the finite elements in the traditional SIMP framework, avoiding jagged and blurry boundaries in the computational process due to grid dependence. This is then combined with homogenisation theory, a microstructure topology optimisation algorithm with maximum bulk modulus under prescribed volume constraints is proposed, which can obtain 2D and 3D topologies with smooth boundaries. In addition, a closed form expression for the two-dimensional topological concave edge structure (taking the most typical topology as an example) was derived, and a compression experiment was conducted on the topological microstructure based on 3D metal printing technology. Scanning electron microscopy showed that the powder bonded on the surface of the printed structure was not completely melted and the step effect caused the finite element analysis results to be higher than the experimental results. Overall, the finite element simulation and experimental results of the concave surface structure have good consistency, with high strength and energy absorption effects. Topologies based on grid point density obtain microstructures with smooth boundaries, and the introduction of the Heaviside smoothing function and multiple filtering steps within this algorithm leads to more robust optimisation, facilitating 3D or 4D printing of microstructures that meet specific design requirements and confirming the feasibility of the proposed topology for lightweighting studies.