Free-form Grid Structure Form Finding based on Machine Learning and Multi-objective Optimisation

Free-form structural forms are widely used to design spatial structures for their irregular spatial morphology. Current free-form form-finding methods cannot adequately meet the material properties, structural requirements or construction conditions, which brings the deviation between the initial 3D geometric design model and the constructed free-form structure. Thus, the main focus of this paper is to improve the rationality of free-form morphology considering multiple objectives in line with the characteristics and constraints of material. In this paper, glued laminated timber is selected as a case. Firstly, machine learning is adopted based on the predictive capability. By selecting a free-form timber grid structure and following the principles of NURBS, the free-form structure is simplified into free-form curves. The transformer is selected to train and predict the curvatures of the curves considering the material characteristics. After predicting the curvatures, the curves are transformed into vectors consisting of control points, weights, and knot vectors. To ensure the constructability and robustness of the structure, minimising the mass of the structure, stress and strain energy are the optimisation objectives. Two parameters (weight and the z-coordinate of the control points) of the free-from morphology are extracted as the variables of the free-form morphology to conduct the optimisation. The evaluation algorithm was selected as the optimal tool due to its capability to optimise multiple parameters. While optimising the two variables, the mechanical performance evaluation indexes such as the maximum displacement in the z-direction are demonstrated in the 60th step. The optimisation results for structure mass, stress and strain energy after 60 steps show the tendency of oscillation convergence, which indicates the efficiency of the proposal multi-objective optimisation.