Mechanical models in computational form finding of bending-active structures

Abstract

This article reviews the different aspects involved in computational form finding of bending-active structures based on the dynamic relaxation technique. Dynamic relaxation has been applied to form-finding problems of bending-active structures in a number of references. Due to the complex nature of large spatial deformations of flexible beams, the implementation of suitable mechanical beam models in the dynamic relaxation algorithm is a non-trivial task. Type of discretization and underlying beam theory have been identified as key aspects for numerical implementations. References can be classified into two groups depending on the selected discretization: finite-difference-like and finite-element-like. The first group includes 3-and 4-degree-of-freedom implementations based on increasingly complex beam models. The second gathers 6-degree-of-freedom discretizations based on co-rotational three-dimensional Kirchhoff-Love beam elements and geometrically exact Reissner-Simo beam elements. After reviewing and comparing implementation details, the advantages and drawbacks of each group have been discussed, and open aspects for future work have been pointed out.

Efficiency-based design of bending-active tied arches

“…Bending-active structures constitute a structural type in which certain flexible structural members are initially bent into curved shapes and then stabilized to form a complete structural system. Because of the geometrical and mechanical properties of the bent (or active) members, they are in general ligthweight structures that achieve the desired stiffness due to the curved shape acquired by active elements and to the action of stabilizing additional members [1]. A pioneering architectural realization using the bending active principle is the Mannheim Multihalle (1976) [2] designed by Frei Otto and conceived as a freeform grid of bent timber members; advantage is taken of the flexibility of the timber lathes during the erection process.…”

Form-driven design of a bending-active tensile façade system

“…Dynamic Relaxation (DR) with 3-degree-of-freedom (DoF) beam models, 12,13 with 4-DoF beam models, 14 with 6-DoF beam models, 15 in combination with the FDM 16 (a more extended review can be found in Lázaro et al). 17…”

Form-finding and Performance of Bending-active Structures. Proposals of Application to Lightweight Braced Arches.

“…The rst examples of bending-active structures are found in vernacular architecture, for instance in the construction of tent-like dwellings by tribal and nomadic societies (Fig. 3), where exible slats are joined to form a lattice and bent to a domeshaped roof [53,56]. In spite of the ancient use of this technique, however, the number of contemporary realisations is limited.…”

“…In addition to the pure form-nding problem, the need to solve the mechanical problem requires four basic features in order to obtain a reliable simulation [56].…”

“…In both cases, a key question is how force-con guration relationships between nodes are established. Those relationships are determined in each case by the underlying beam theory, de ned by the kinematic assumptions of the model, the selected elastic energy terms and the constitutive relations [56]. Three groups of discretisations can be found in the literature in the context of form-nding of bending-active structures: (a) models based in discrete mechanics using 3 or 4 DoFs per node; (b) nite-di erence-like discretisations, that shares the same principles as models based in discrete mechanics and also use 3 or 4 DoFs per node and (c) nite-element-like methods with 4 and 6 DoFs per node.…”