Shape optimization of piecewise developable free-form grid surface using plate components

Various difficulties in the manufacturing process of free-form roofs generated using the shape optimization process, which is also called structural morphology, can be resolved using the properties and methods of differential geometry. In this paper, a new structural morphology method is proposed for assembling a free-form grid surface using plate elements. The surface is an assembly of piecewise developable surfaces, and the grid frame also consists of plate components. A new directing condition is introduced as a constraint into the definition of developable surface using the (1-n)-Be ' zier surface. The control points of the directing Be ' zier curves are chosen as design variables. The developability conditions, directing conditions and continuity conditions are taken as the constraints in the optimization problem for minimizing the strain energy of the grid structure subjected to static loads. Effectiveness of the proposed method and the mechanical properties of the optimal structures are investigated in the numerical examples. It is shown that a new rational architectural shape integrating aesthetics, mechanics and constractability can be generated by using the new morphology method for free-form grid surface structure composed of plate elements.

Automated summary

A new structural morphology method is proposed in this paper for assembling a free-form grid surface using plate elements by introducing a new directing condition and choosing control points of directing Be ' zier curves as design variables. The optimization problem aims to minimize the strain energy of the grid structure subjected to static loads under developability conditions, directing conditions, and continuity conditions as constraints. Numerical examples demonstrate the effectiveness of the proposed method in generating a new rational architectural shape integrating aesthetics, mechanics, and constructability for free-form grid surface structures.