Form finding for free-curved RC shell using multi-objective optimization considering structural performance and formwork manufacturability

Author

Kimura, Toshiaki and Ogawa, Shuhei and Hayashi, Sei and Muto, Tatsuya and Yamasaki, Kozo and Sakai, Yusuke and Gondo, Tomoyuki

Abstract

This study proposes a form-finding method for free-curved RC shells using multi-objective optimization, considering the structural performance and wooden formwork manufacturability. The shape of the curved surface is represented by using the B-spline function (NURBS) and discretized into triangular elements for the FE Analysis. Additionally, the quad meshes are introduced to represent the plywood form board (PFB) shape in the formwork system. The coordinates of the PFB are described using the NURBS surface. For evaluating the manufacturability of PFB, the curvature of the surface is computed at each corner of the PFB. A design problem is formulated to minimize strain energy and optimize the PFB's curvatures. The z-coordinates of the NURBS control points are adopted as the design variables. The form-finding process is conducted using Rhinoceros+Grasshopper. Numerical examples are represented to demonstrate the effectiveness of the proposed method. Furthermore, a practical formwork design of the optimal solution is conducted to validate the constructability of the whole formwork system.