Form finding by shape optimization with implicit splines and vertex morphing

The procedure of form finding of mechanically loaded structures is an art. The resulting shape is the goal, the paths to that goal are numerous as well as the tools applied. Everything is possible. The handles which control the process are plenty in number, many are rationally explained, others are heuristic in nature, intuitively chosen or even hidden in the complexity of procedures, tools and their interaction. Even when principally using the same method, the final structural and esthetical result of form finding still tells much about the mind behind. Tools such as computational methods should be designed to support the individual understanding of form finding and the aesthetics, allowing the largest possible design space while being efficient and controlled by a minimum of effort. We present numerical shape optimization with vertex morphing as the solution: Numerical optimization as a rational technique to guide the process and vertex morphing as a most flexible and easiest to be applied method of shape control with arbitrarily large numbers of degrees of freedom. The methodological kernel are so-called implicit splines which don’t need fixed control meshes as standard splines do. Together with so-called filters which again may be defined explicitly or implicitly they are related to variants of subdivision splines allowing for great varieties of solutions to the form finding of structures. The paper gives an illustrative demonstration of the method together with various examples of optimal shell design and some other applications.