Dynamic relaxation analysis of pretensioned networks supported by compression arches
This thesis is concerned with the application of direct integration methods, particularly Dynamic Relaxation, to the nonlinear formfinding and analysis of pretensioned networks supported by compression arches. The development and application of such methods is reviewed in Chapter 2. The automated control of Dynamic Relaxation is considered in I Chapter 3. and a modified kinetic damping procedure shown to be an efficient and simple alternative to viscous nodal damping that does not require prior determination of a damping constant. It is shown that Dynamic Relaxation may be interpreted as a dynamic implementation of a first order gradient method. A modification of Buchholdt's implementation of the Scaled Conjugate Gradient method to permit arbitrary ýcable strains is presented in Chapter 4. The efficiency of this method and Dynamic Relaxation is compared in Chapter 5 for a generalised test problem having variable design parameters. Dynamic Relaxation is shown to be more efficient in all cases. In Chapter 6 Dynamic Relaxation is applied to the non-linear analysis of plane and space frames. 'The effects of finite displacements, bowing and axial force on the moment-curvature relations are included in the analysis. The method presented is compared successfully with published solutions to planar and spatial problems exhibiting snap-through buckling and subsequent post-buckling response. The development of numerical methods for formfinding isreviewed at the, start of Chapter 7. The suitability of kinetic damping for controlling Dynamic Relaxation formfinding is demonstrated and the generation of moment-free compression arches illustrated. In Chapter 8 the cable and spatial flexural elements are combined for unified Dynamic Relaxation of the -complete structure. This method, with full non-linear idealisation of the boundary structure, has demonstrated convergence at least twice as rapidly as the Scaled Conjugate Gradient method with linear boundary response. Dynamic Relaxation has been shown to be a simple and efficient analysis technique, retaining a clear physical analogy that facilitates the enderstanding, implementation and execution of non-linear response investigations. For the particular problem of pretensioned networks supported by compression arches it is a straightforward procedure to investigate the stabilising effect of the tension network on the boundary structure, thus enabling the use of lighter, more economic, compression members.