Computational form-finding of tension membrane structures - Non-finite element approaches: Part 2. Triangular mesh discretization and control of mesh distortion in modelling minimal surface membranes

This paper, presented in three parts, discusses a computational methodology for form- nding of tension membrane structures (TMS), or fabric structures, used as roo ng forms. The term ‘form- nding’ describes a process of nding the shape of a TMS under its initial tension. Such a shape is neither known a priori, nor can it be described by a simple mathematical function. The work is motivated by the need to provide an e cient numerical tool, which will allow a better integration of the design/ analysis/manufacture of TMS. A particular category of structural forms is considered, known as minimal surface membranes (such as can be reproduced by soap lms). The numerical method adopted throughout is dynamic relaxation (DR) with kinetic damping. Part 1 gave a background to the problem of TMS design, described the DR method, and presented a new form- nding methodology, based on the Laplace–Young equation and cubic spline tting to give a full, piecewise, analytical description of the surface. Part 2 describes an alternative and novel form- nding method, based on a constant tension eld and faceted (triangular mesh) representation of the minimal surface. Techniques for controlling mesh distortion are presented, and their e ects on the accuracy and computational e ciency of the solution, as well as on the subsequent stages in design, are examined. Part 3 gives a comparison of the performance of the initial method (Part 1) and the faceted approximations (Part 2). Functional relations, which encapsulate the numerical e ciency of each method, are presented