Direct area minimization through dynamic relaxation
Ruy Marcelo de Oliveira Pauletti, Daniel M. Guirardi · UPCommons institutional repository (Universitat Politècnica de Catalunya) · 2011
Minimal surfaces, characterized by the property of a minimal area within a fixed boundary, offer an interesting design option for membrane structures, since they are uniquely defined and provide economy of material and more regular fabric patterns. Analytical solution for the non-linear equation governing area minimization may be rather difficult for complex boundaries, leaving numerical solution as the only general way to tackle with the problem. In this paper we show that the dynamic relaxation method offers an interesting alternative to solve the area minimization problem, first interpreted as a nonlinear equilibrium problem, then replaced by a pseudo-dynamic analysis, where fictitious masses and damping matrices are arbitrarily chosen to control the stability of the time integration process.