Target shape approximation of funicular surfaces by load control using RBF interpolation

Abstract

Existing methods for form-finding prioritize discovering optimal shapes under design load conditions, often overlooking the designer’s shape preferences. To address this problem, this research relaxes the load condition and develops a user-friendly form-finding tool that encapsulates a new method for obtaining funicular surfaces that pass through user-prescribed points through load control. The method involves generating smooth load distributions via RBF interpolation of nodal loads, which are repeatedly adjusted so that the equilibrium shape is close enough to the target points. For faster convergence, the step size of the load adjustment is automatically determined through a coarse line search, and a warm start is introduced in form-finding with the dynamic relaxation method. Despite uneven load distributions, the method ensures high accuracy in approximating the surface shape to the desired points while preserving funicularity against the load distributions. Additionally, the resulting load distribution gives designers valuable feedback on the specified target points, as the degree of load non-uniformity indicates the deviation from the equilibrium shape for uniformly distributed loads.