Optimization of Free-Form Grid Shells’ Dynamic Performance

Nowadays modern architecture structures commonly utilize non-orthogonal surfaces (e.g. NURBS surfaces, etc.) and up-to-date structural research in this area is related to form-finding and structural optimization. However, in most of the cases these techniques do not take into consideration the structural vibration performance (under wind and seismic conditions) also because grid-shell dynamic behaviour is very complicated to detect. Indeed, these structures usually involve several dynamic problems (e.g. close range of mode shapes, local stiffness variability). Starting from this the main objective of this paper is the characterization of the dynamic properties of a grid shell (e.g. mode shapes, influence of grid shell patterns), as well as to find an optimization tool for enhancing their performance (e.g. in-plane and out-of-plane stiffness and mass distribution). The dynamic optimization of grid-shell structures involved the pursuit of a geometry pattern that allow the vibration property of the system to be regularized, i.e. a structure that requires few fundamental modes that allows to achieve the required level of mass participation defined a priori (e.g. 90%).

The process starts with several parametric studies on simple benchmark surfaces (classified according to their Gaussian curvature) that show how the dynamic behaviour is greatly influenced by the pattern geometry (2D or 3D) and the density of the mesh. Indeed, the geometry influences mainly the stiffness of the system. The extension from a single surface to a full grid structure is achieved through an algorithm that detects the Gaussian curvature for a portion of the system (with a certain variability). Through knowing the curvature in that region of the structure it is possible to assign the optimal pattern and density in 2D and 3D in these regions (as determined from benchmark studies) in such a way that the grid-shell dynamic behaviour is regularized. While this algorithm is still in development the first results show the goodness of the proposed solution.