Membrane form finding by means of functional minimization

Abstract

This study deals with the methods of architectural design of structures made of textile membranes. We consider the problem of form finding of membranes strained by rigid skeletons and cables installed along the free edges of the membrane. First, we recall the methods used to solve the simple problem of finding form in the case of constant surface tension. Then we propose a method based on the minimization of the total potential energy. The problem is discretized using membrane triangular finite elements. The potential considered is an energy density per unit area of uniform and constant surface tension. The minimization of this potential leads to the minimal surface solution. However the problem is singular with respect to the in-plane displacement. To handle this problem, the potential is enhanced by an elastic energy in order to regularize the numerical scheme and prevent the mesh degeneration. It is also enhanced by the elastic energy due to the cable tensions. The solution is obtained by minimizing the potential energy using the conjugate gradient method.