中文摘要：

自南曲面结构以其卓越的建筑表现力成为当今空间结构发展的趋势之一，并在越来越多的实际工程中得到应用。与传统的空间结构相比，自由曲面空间结构设计的难点在于如何处理好新颖建筑造型与结构合理受力性能之间的关系。近年来，结构形态学的发展，特别是结构形态创构理论的提出，为解决自由曲面结构的形态设计问题提供了有效途径。借鉴结构形态创构的思想，将非均匀有理B样条（NURBS）曲面造型技术与寻求结构应变能最小的梯度算法相结合，提出一种适合于NURBS自由曲面结构特点的形态创构方法——NURBS—GM法。该方法的特点是，通过调整NURBS曲面的控制点坐标和权因子来获得整体应变能最小的曲面形状，从而改进了以往以直角半标为调整变量的结构形态创构方法的计算效率。最后，通过若干算例证明本文方法的有效性。

英文摘要：

As a new tendency of modern spatial structures, free form surfaces have been widely adopted nowadays because of their predominant architectural representation. However, the main difficulty involving free form architecture design is how to balance the relationship between novel shapes of free form structures and excellent mechanical performance, if compared with traditional space structures. Recently, the development of structural morphology, especially for the production of computational morphogenesis, presents an effective approach. In this paper, a new method of computational structural morphogenesis is put forward, named as NURBS-GM method. Taking tile primary idea of computational morphogenesis as a reference, this numerical method for free form surfaces is based on the N U R BS technique and the gradient method from the principle of optimization with the structure stain energy as the objective function. The key point of this method is that by adjusting the control points and the weights of the numerical funcetion of N URBS surface, the shape of free form structures can be modified to obtain an appropriate mechanical performance. Examples are provided to verify the efficiency of this method.