Achieving diverse morphologies using three-field BESO with variable-radius filter

Topology optimisation methods are widely used to produce efficient and innovative structures. However, while the traditional methods typically yield free-form structures, there is an increasing need for control over geometric features, particularly in response to manufacturing and functionality considerations. To address this problem, this study introduces a novel approach using a three-field Bi-directional Evolutionary Structural Optimisation (BESO) method. This approach combines the density of elements and the filter radius as design variables in the optimisation process. Moreover, both isotropic and anisotropic filters are employed to enhance the capability of the approach to generate diverse designs. The effectiveness of this approach is demonstrated through several 2D and 3D design examples. The results show that by applying hard or soft constraints to the filter radius, our approach enables the creation of a variety of structural forms, such as extruded shapes, plate-like structures, and blends of free-form structures with the aforementioned types. This advancement increases the diversity of solutions available in topology optimisation, offering engineers and architects new ways to craft designs with a wider range of morphologies. • A three-field BESO with variable-radius filter is proposed. • Diverse forms of structures can be achieved in topology optimisation. • Composite designs featuring a variety of structural morphologies can be generated.