Optimal gridshell meshing

Description of the research

Elastic gridshells are usually transformed from a flat configuration to their final three dimensional form. In their final form, the stresses in the bars could be very high due to the curvature of the bars. In this research project different strategies were used to optimise the mesh in order to minimise the stresses in the final form of the gridshell. Another problem is to predict if a form can be meshed by a Tchebychev net without singularities.

(Bouhaya 2009) proposed a method by dropping numerically the mesh on a rigid surface and allowing the mesh to slide on the surface.  (Bouhaya 2011) and  (Bouhaya 2014) proposed to minimise the curvature of the bars with the of genetic algorithms on an imposed surface.  (Lafuente Hernández 2013) proposed to start with an irregular mesh to give a final configuration with a lower level of stresses.

It has been demonstrated that a sphere cannot be meshed by a Tchebychev net without singularities. A Tchebychev net can only cover  certain surface, the ongoing research tries to predict which surface can be covered and with which type of singularities.