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Mathematical models of minimal surfaces

Soap films are common examples of minimal surfaces in nature. Membranes and cable nets are architectural interpretations of the same phenomenon of minimal surfaces. They combine structure and material in a very efficient manner by aligning force and geometric form. This method of form-finding" has been a source of inspiration for designers and architects since the early 1960’s. Recent advances in computer-based modelling have led to a new interest in the field of minimal surfaces.

Mathematically, minimal surfaces can be divided into periodic and non-periodic minimal surfaces. They can be modeled using various minimization strategies such as Spring Energy Minimization, Dirichlet Minimization, Area Minimization or Edge Alignment.

We are specifically interested in how energy minimization strategies such as the aforementioned techniques link to structural energy minimization methods such as the force-density method. Our aim is to advance our understanding of how minimization strategies can be applied for the design of novel structures and envelopes.