Edinburgh Napier University

  This thesis aims to provide a set of tools for analysis and design of free-form timber grid-shells. It provides a brief introduction on the relationship between shape and structural behaviour of grid-shells, followed by an introduction to actively-bent structural systems. The design issues are then individuated and three main themes are defined, namely: Form-finding, Structural Analysis and Optimisation. The development and use of a numerical framework, based on a six Degree-of-Freedom (DoF) co-rotational beam-element in conjunction with the Dynamic Relaxation method, has formed the basis, on which a unified procedure for the Form-finding and Structural Analysis tasks are denied.
A two-step analysis procedure allows seeing a target shape for the grid-shell with the aid of a reference surface, whilst taking into account the effect of internal (bending) reactions on the final geometry. Coupling constraints are numerically simulated by development of a single-node cylindrical joint. An algorithm for grid cutting (mesh manipulation) is described, as well as a modified co-rotational beam-element, based on assumption of ‘equivalent’ bending stiffness. The modified formulation allows taking into account the change in stiffness of the double-layer members, when passing from the Form-finding to the analysis of the structure under working loads, by simply seeing a dimensionless parameter. A numerical framework for optimisation of the members’ cross-section is then introduced.
The optimisation problem is decomposed in two main sub-problems, to be separately solved by iterative techniques: the seeking of an ‘allowable’ thickness, for the laths under bending action, is pursued with a procedure based on Newton-Raphson method, whilst: a local-search approach is used to find (for a given load configuration) the optimal variation in thickness of the composite cross-section.
The proposed methods are validated by several numerical and full-size experimental test, as well as comparison with the corresponding analytical solution, where available.