Optimization of cross-section of actively bent grid shells with strength and geometric compatibility constraints

• A method for cross-section optimization of actively bent grid shells is introduced.
• A co-rotational formulation allows both Form-finding and Structural analyses.
• The configuration of static equilibrium is sought by Dynamic Relaxation scheme.
• Strength and geometric compatibility constraints are taken into account.

The use of bending as self forming process allows the realization of shape-resistant systems, such as grid shell structures. Here, a numerical method for optimization of the cross-section of actively bent structures is introduced. For a given load distribution, the optimization objective consists of normalizing the bending stresses to a given value on the entire structure. In addition, strength and geometric compatibility constraints are taken into account. The method is demonstrated by numerical examples. Further, in order to handle the large displacements involved, a co-rotational Finite Element formulation is adopted and modified to take into account the changes in stiffness that occur in the forming process of active bending systems. The modified co-rotational formulation is solved for static equilibrium using a Dynamic Relaxation scheme, and is tested against the analytical solutions of some preliminary test cases, as well as experimental results, and shown to be ‘accurate’.