Form-finding Of Membrane Structures Research Articles

Comparison of viscous and kinetic dynamic relaxation methods in form-finding of membrane structures

This study focuses on the efficiency and applicability of dynamic relaxation methods in form-finding of membrane structures. Membrane structures have large deformations that require complex nonlinear analysis. The first step of analysis of these structures is the form-finding process including a geometrically nonlinear analysis. Several numerical methods for form-finding have been introduced such as the dynamic relaxation, force density method, particle spring systems and the updated reference strategy. In the present study, dynamic relaxation method (DRM) is investigated. The dynamic relaxation method is an iterative process that is used for the static equilibrium analysis of geometrically nonlinear problems. Five different examples are used in this paper. To achieve the grading of the different dynamic relaxation methods in form-finding of membrane structures, a performance index is introduced. The results indicate that viscous damping methods show better performance than kinetic damping in finding the shapes of membrane structures.

Form-Finding of Membrane Structures and Necessary Stabilization of this Process

The aim of this contribution is a form-finding process. It is the problem of initial pre-stressed shape generation of membrane constructions. The contribution deals with specific aspects of this process and the necessity of introducing stabilization with regard to its practical application. Individual examples will show the results of methods described in this paper.

The Modified Dynamic Relaxation Method for the Form-Finding of Membrane Structures

The Modified Dynamic Relaxation Method for the Form-Finding of Membrane Structures

Form finding of membrane structures by the updated reference method with minimum mesh distortion

This paper presents a new technique for the solution of the well-known form finding problem in membrane structures. The technique proposed is based on the updated reference configuration method proposed by Bletzinger [Proceedings of the IASS Colloquium on Structural Morphology: Towards the New Millenium, Nottingham, 1997] in which an area functional is minimised within the context of a finite element discretisation. In this paper an additional functional term is introduced with the aim of minimising the mesh distortion during the form finding process. This new term provides in-plane stiffness which prevents the emergence of mechanisms without the need for ad hoc changes of the tangent matrix. As a consequence of this additional strain energy term, the form finding process can be viewed as a standard large strain membrane analysis with a specific choice of hyperelastic strain energy function. This implies that it can be implemented in any standard code as an additional constitutive model. Two well-known simple examples of form finding will be presented to illustrate the method proposed.