Nonlinear force density method for the form-finding of minimal surface membrane structures

We develop an alternative approach for the form-finding of the minimal surface membranes (including cable membranes) using discrete models and nonlinear force density method. Two directed weighted graphs with 3 and 4-sided regional cycles, corresponding to triangular and quadrilateral finite element meshes are introduced as computational models for the form-finding problem. The triangular graph model is closely related to the triangular computational models available in the literature whilst the quadrilateral graph uses a novel averaging approach for the form-finding of membrane structures within the context of nonlinear force density method. The viability of the mentioned discrete models for form-finding are studied through two solution methods including a fixed-point iteration method and the Newton-Raphson method with backtracking. We suggest a hybrid version of these methods as an effective solution strategy. Examples of the formation of certain well-known minimal surfaces are presented whilst the results obtained are compared and contrasted with analytical solutions in order to verify the accuracy and viability of the suggested methods. (C) 2013 Elsevier B.V. All rights reserved.