Study On Morphology Of Freeform Surface Structures

As a new tendency of modern spatial structures, freeform surfaces have been widely adopted nowadays because of their predominant architectural representation. Freeform surfaces which cannot be analytically expressed and assembled by simple surfaces are full of amazing curvature. Freeform surfaces, nowadays, are widely used in the area of mechanical manufacture, however, the application in architecture is still in its infancy. This is because freeform surfaces should not only satisfy the demands of architectures but also have excellent mechanical rationality. Therefore, the primary problem in freeform architecture design is how to balance the relationship between novel shapes of freeform structures and excellent mechanical performance. In recent years, the development of structural morphology, especially for the production of computational morphogenesis, presents an effective approach to solve this problem. Structural morphology includes two aspects of contents which are form and performance. Form stands for the structrual shape and performance means the mechanical state of structure. The combination of fabricating freeform surfaces and pursuing rational mechanical performance forms the basic concepts of freeform structural morphogenesis. Structural morphogenesis is becoming one of the most important and hot problems in the area of spatial structures. However, the theoretical system of this research is still not perfect because it is wide enough to accommodate a variety of interests in this field of morphology studies, which starts late not only in China but also all over the wold. Aimed at this research status, study in this paper presents the following parts of work:A new idea of computational structural morphogenesis has been put forward. Based on the concepts of structural optimization, the rationality of performace is treated as optimal objective and form is changed repeatly to get harmonious structures with excellent shapes and rational mechanical performance. Three aspects of contents are included: firstly, the geometric modeling methods of freeform surface. Fitted surfaces and curve-generated surfaces are two common geometric modeling methods, in which the adoption of fitted surfaces is to approximate discrete points using surface fitting techniques, and in the process of establishing curve-generated surface, some curves (generatrix and directrix) are transformed by the operation of traslating, scaling and rotating. The Non-Uniform Rational B-Spline (NURBS) function is adopted to mathematically describe these two freeform surfaces; secondly, the evaluation method of the structural rationality. Static performance of structures is mainly evaluated, in which structural stain energy is taken as the objective function and the single objective optimal method is chosen to achieve rational structures. At the same time, the change of other evaluating items are studied in the process of minimizing stain energy; thirdly, the method of morpholgy optimization. Through comparison, this paper determines to apply gradient method as the optimization method and discusses the problem of accelerating calculation in the process of optimization.Based on the two geometric modeling methods mentioned above, the corresponded computational morphogenesis methods for freeform surfaces are put forward.Firstly, computational morphogenesis method based on the fitted surface. To achieve NURBS freeform surfaces with minimum strain energy, gradient method is used to adjust some control variables separately, which belongs to single-coefficient adjustment strategy. In order to build the NURBS surface, control points and weights or some known points on surface are preliminarily needed, which are treated as the main control variables. Gradient functions between strain energy and these variables are deduced, based on which the characteristics and scopes of these three strategies are compared. Besides, the single-coefficient adjustment strategy is expanded to multi-coefficient adjustment, in which control points and weights are treated as control variables simultaneously. The advantages and disadvantages are summarized concentrating on these optimal strategies. It can be concluded that this method, which have strong applicablility, can be used to optimize arbitrary freeform surfaces.Secondly, computational morphogenesis method based on the curve-generated surface. Since this method is based on NURBS curves, control variables of which can be adjusted to acquire freeform surfaces with minimum strain energy using gradient method. Focusing on the control points and weights of NURBS curves, gradient functions between strain energy and directrix (generatrix) are deduced. Control points and weights of generatrices and directrices can be adjusted simultaneously or separately, which can result in different rational shapes. This method can feature the constant relationship between generatrices and directrices in the process of morphogenesis, and more suitable for the application of grid shells.Both of these computational morphogenesis methods for freeform surfaces can achieve the shapes with minimum strain energy by directly or indirectly adjusting the control points and weights of NURBS curves or surfaces, which can improve the calculation efficiency. Both morphogenesis methods are programmed using FORTRAN language and some examples are carried out to verify the efficiency of these methods.Since the mechanical performance of freeform surfaces under load is complicated, in which tensile stresses, compressive stresses and bending stresses simultaneously exist and the distribution scope of each stresses is also large. The stability of this kind of structure is different from the traditional space structures such as reticulated domes, cylindrical shells and saddle-shape reticulated shells. Aimed at the stability of freeform surfaces, shapes produced in and after the process of morphogenesis are abstracted as the models for analysis. In this paper, studies about the changing regularity of structrual stability are proceeded. It can be conclued that, the buckling load of surfaces can be greatly enhanced in the process of structural morphogenesis, and what's more the post buckling performance can also be changed. For different types of freeform surfaces, rational surfaces acquired after morphogenesis also have different post buckling performance. It can be ascribed to the different proportion of tensile area, compressive area and bending area. If freeform surfaces are almost compressive, extreme buckling will happen. If the proportion of compressive stresses and tensile stresses are large, surfaces can obtain post buckling load capacity. If the proportion of compressive stresses, tensile stresses and bending stresses are appropriate, the decrease of load after buckling can be slowed down.