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)-Bézier surface. The control points of the directing Bézier 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.

使用形状优化过程生成的自由形式屋顶制造过程中的各种困难，也称为结构形态，可以使用微分几何的属性和方法来解决。在本文中，提出了一种新的结构形态学方法，用于使用板单元组装自由形式的网格表面。曲面是分段可展曲面的集合，网格框架也由板组件组成。使用 (1- n)-贝塞尔曲面。定向贝塞尔曲线的控制点被选为设计变量。将可展性条件、导向条件和连续性条件作为优化问题中的约束条件，以最小化静载荷作用下网架结构的应变能。在数值例子中研究了所提出方法的有效性和最优结构的力学性能。结果表明，对于由板单元组成的自由形式网格面结构，采用新的形态学方法可以生成集美学、力学和可收缩性于一体的新的合理建筑形态。