Regularization of panel shapes for latticed shells


latticed shell; panelization; clustering; constructability


Hayashi Kazuki, Makoto Ohsaki

Project Term

2017.6 –


Grant-in-Aid for JSPS Research Fellow No.18J21456 
JSPS KAKENHI No.16H03014 (Leader: Haruyuki Fujii)
“SPIRITS” program of Kyoto University (Leader: Makoto Ohsaki)


As complex shapes for architectural design have become possible in the framework of computational modeling, there is an increasing interest in obtaining rational shapes considering the cost and constructability of free-form surfaces. Discretization of the latticed shell is one of the solutions for cost reduction, and the uniformity of discretized structural elements is an important factor to reduce the number of types of members and joints. Moreover, regularization of members is expected to prevent buckling of extremely long members and difficulty in constructability due to the existence of short members.

We propose a 2-step regularization method of triangular latticed shell panels on a tensor product Bézier surface, where clustering and optimization are alternately conducted. In the process of clustering, continuous relaxation method is applied to express the degree of participation to each cluster for panel shapes.

Initial Bézier design surface is defined by controlling points.

The continuous design surface is discretized to triangular panels.

The panels are split into several groups using clustering method.

Each dot contains three edge lengths of the triangular panel.

Panel shapes are optimized such that the differences of the triangular shapes within every group are minimized.

Overall process of the regularization method.


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