Geometry Creating And Topology Morphogenesis For The Space Structures Of Free Surface

In recent years, with Chinese rapid economic development, space structures have developed very fast. Many space-structure buildings have become landmarks for cities and even for a country. Generally, the space structure forms applied in projects are mainly traditional forms including surfaces like sphere, ellipsoid, saddle, cylinder and so on which can be expressed by analytic functions or combination of these surfaces. As people's persistent pursuit of architectural aesthetics, the rapid development of computer technology, gradual improvement in the methods of structure design and construction, more and more space structures with free surface are applied to practical projects. Especially the continuum shells with free curved surface attracted more and more people's attention. However, some problems like lighting affect the application of continuum shells. Opening holes in continuum shells can solve the problems. Based on above-mentioned reasons, this paper studied the methods of geometry creating and topological morphogenesis methods for the space structures with free surface.Firstly, in the process of geometry creating for the space structures of free form surface, this paper created a series of nice free surfaces by the methods of Non-Uniform Rational B-Splines(NURBS) surface fitting and NURBS surface interpolation respectively. At the same time, this paper modified the geometry of free form surfaces through the adjustment of control points and weight respectively. In this part, the implementation of geometry creating provides the architects with powerful tools for the realization of architecture intentions.Secondly, this paper extended the design domain of traditional extended evolutionary structure optimization method into free-form-surface-domain in order to make the traditional Extended-ESO suitable for the topological morphogenesis of various free form surfaces. It makes shell topological morphogenesis possible to be applied in practical projects.In the end, this paper took Mises equivalent stress and strain energy sensitivity as target mechanical values to topologically optimize typical traditional analytic surfaces(parabolic cylinder, hyperbolic paraboloid) as well as free curved shells by the free-form-surface-domain Extended-ESO method, and created many topology forms of shell that are nice in geometry, unexpected and rational in mechanics. In this part, the implementation of topological morphogenesis not only solves some architectural function problems like lighting etc, but also makes the structural materials efficient and economic. It is also significant for the transformation of structural form design from empirical way to scientific way.