A Study On The Formation And Construction Of Extremely Shell Of Minimal Surface

Minimal surface is generated by mathematical formula,which has special mathematical beauty and artistic expression.Because of the unique mathematical characteristics of minimal surface and the interesting space modeling features,it has brought many practical application scenes to various subjects.Especially in the field of architecture reflects a huge artistic value and application prospects.However,due to the high complexity and extreme thinness of large and small curved shells,it poses a high challenge to structural mechanics design and surface fabrication technology.Therefore,it is very important to study the form-finding and fabrication methods based on structural properties.In this paper,from the perspective of structural performance,the structural logic behind the highly complex and thin shell and the key problems of the fabrication technology of heterotopic hyperboloid are analyzed.On this basis,the combination of parametric design technology and collaborative raw form method of structure analysis technology,key research based on the structure performance of minimal surface raw form method and process,including unit based on the point of the iteration method,based on the structure optimization to find frame line of iterative optimization method and find find method based on grid the iterative optimization;Through qualitative analysis and quantitative experiments,the feasibility and effectiveness of these three methods are proved.Based on economic considerations,this paper proposes a "differential first and then integral" minimal surface fitting method combining parameterized design and CNC numerical control technology,and demonstrates the convenience and effectiveness of this method and the specific process through experiments.Finally,the reasonable transformation from mathematical model to mechanical model is realized,and the dual goals of economy and efficiency of digital construction of minimal curved surface are realized.The research results on the formation and construction methods of minimal curved shells in this paper can provide theoretical clues for the in-depth development of the field of architecture digital research,and play a positive role in promoting and expanding the interdisciplinary development of architecture and structural engineering.At the same time,it provides practical guidance and empirical reference value for the scientific construction of the design system for nonlinear buildings.