Form-finding Of Post-formed Gridshell Structures

Post-formed gridshells are a special type of grid structures formed through active bending of a mat of planar grids assembled by two-directional straight members inter-connected by scissors-like joints. Despite the intrinsic advantages of gridshells, including uniform member size, simple form of joints, and the capability of complying with specific free-from surface geometries, only a very small number of gridshells exist worldwide. The limited engineering practice of gridshells is due largely to the complexity of the form-finding issue.Traditional form-finding methods for post-formed gridshells take planar grids with known boundary configuration as input and seek the corresponding surface geometry through either physical or numerical approaches. The major limitation of the traditional methods is that the form-finding process is passive and empirical: tedious adjustment of the boundary configuration of the planar grids via trial-and-error is inevitable for the generation of a final geometry that satisfies the requirements of architects. Obviously, the ideal form-finding method should tackle the form-finding issue reversely. That is, the form-finding method takes the target geometry proposed by architects as input and directly seeks the corresponding configuration of the planar grids which can be accurately deformed into the target geometry.Against the above background, this thesis presents a new form-finding method for gridshells based on vector mechanics, which is able to output the initial planar grid shape from the target surface. In the proposed form-finding method, a sufficiently large mat of planar grids is first placed underneath the target surface geometry. A fictitious pressure field is next applied to force the grids to deform into the shape of the target surface until all nodes enclosed by the target surface are in full contact with the target surface. The redundant grids outside the target surface are then truncated and such generated end nodes are fixed along the boundary,followed by the removal of the fictitious pressure field and the surface constraint. Finally, the internal force in the formed structure is released to obtain the corresponding pattern of the planar grid in pursuit. In order to solve the issue of coupling of nodal degrees of freedom(DOFs) involved in the form-finding process, this thesis deduces an explicit formulation of space beam element with 6 DOFs per node and a set of formulas to simulate the behavior of the scissors-like joints. In addition, this thesis proposes algorithms to tackle the issues of point-surface contact and line-line contact involved in the form-finding process.Finally,numerical verification and examples are given at the end of the thesis to demonstrate the validity and accuracy of the proposed form-finding method.