Morphogenesis Of Free-form Surfaces Based On The B-spline Theory

Along with the development of social civilization, continuous improvement and expansion have been occurring in construction space. However, inherent architectural forms are so limited that can hardly satisfy the increasing requirements of the architectural performance. Free-form surface structures have been found to be very effective to solve this problem. The prominent aesthetical styles can lead to strong visual impacts. Besides, a variety of geometries can be modeled to satisfy requirements of architectural design. One of the urgency is to propose a reasonable and efficient method to establish a computational morphogenesis method for free-form structures.According to the B-spline theory, a new method of computational structural morphogenesis has been proposed, combining B-spline surfaces with the sensitivity of strain energy. Thus, the final structural free-form can be obtained by general optimization. The major research contents are listed as follows:1. Initial model of free-form surfaceThe preliminary step of free-form surfaces morphogenesis is to create the initial model. Based on the theory of odd cycle parametric B-spline curve, a series of curves are generated and combined to form the inner and outer bounders of structures in order to obtain rich boundary shapes and reserve openings on the surface.2. Objective function to evaluate structuresIn optimization process, an evaluation of the structural mechanical property is needed for each step. The objective function and the variables should be programmable in order to improve the efficiency of calculation. The strain energy is chosen as evaluating indicator for it can fully reflect the mechanical property of rall structures. After that, the most suitable structure can be obtained by optimization, during which the overall stiffness of the structure increases gradually, ensuring the load would be transferred by membrane effect finally;3. Morphogenesis of free-form structuresA combination of the free-form surface creation and optimization algorithm is carried out in order to obtain the most reasonable geometry. Firstly the strain energy sensitivity formulation of key points on B- spline surface is deducted. According to the product of a fixed step size and the strain energy sensitivity of key points, the adjustment of the key point longitudinal coordinate in the negative gradient direction is conducted to minimize the stain energy of final structure, and during this process the sensitivity convergence in certain conditions stably.A smooth and continuous free-form surface structure can be obtained by the proposedmethod without further adjustment. It is only needed to calculate the strain energy sensitivity of the key point on the surface, which shows a high calculation efficiency. In the meantime, the surface boundary varies a lot. This study has a high value in both theoretical research and practical engineering.