The form and system of the membrane are the unity of architecture and structure. The stable tensile membrane surface is a negative Gaussian curvature surface, with its basic unit being a hyperbolic paraboloid in the shape of a saddle and a conical hyperboloid. The inflatable membrane (either气囊式 or气承式) surface is a positive Gaussian curvature surface, while the tensioned membrane (span generally less than 4-6m) is a zero Gaussian curvature surface. Any complex architectural form is composed of basic shapes, and design is achieved by adjusting specific parameters.
Within the initial equilibrium surface of the membrane structure, the pre-tension is self-balancing. The equilibrium surfaces of the membrane structure can be divided into two categories: isostress surfaces and non-isostress surfaces. An isostress surface refers to the uniform distribution of pre-tension within the membrane surface, at which point the surface area of the membrane is small (i.e., small surface).
Anisotropic stress-free surfaces refer to membrane surfaces with a non-uniform distribution of prestress but self-balanced. For the initial form analysis of membrane structures, it is advisable to first seek out small surfaces with uniform stress, and in the absence of such surfaces, then look for balanced surfaces with non-uniform stress.
The morphological analysis of membrane structures is essentially the process of determining the magnitude and distribution of pre-tension within the structure. The setting of pre-tension values should ensure that the membrane material does not relax due to temperature, creep, and load effects under normal operating conditions, and it should also ensure that the stress in extreme climatic conditions is less than the designed stress. Additionally, consideration should be given to the feasibility of structural tensioning and ease of installation.
The current methods for shape analysis primarily involve computer simulation techniques, such as the density method, dynamic relaxation method, and small modulus geometric nonlinear analysis. Additionally, some special methods are used, including the surface force density method and the constrained small surface method. Physical models serve as a beneficial supplement and tool for shape analysis, using soap bubbles, elastic silk, etc., to determine the natural small surfaces of membrane stress. This approach is accurate, reasonable, and clear, but converting the obtained surfaces into engineering applications is complex and challenging.
Form finding analysis is a process where engineers apply specialized computational software to numerically analyze preliminary architectural forms and conceptual designs proposed by architects, or use physical models to simulate, in order to determine the existence of a rational membrane surface and its specific form.
The relationship between form analysis and architects primarily focuses on achieving a unity of architectural features and technical feasibility. Specific considerations include the physical indicators of membrane structures, fire resistance, lifespan, and the varying economic tension spans and curvatures of different membranes. Key control parameters such as span, column spacing, vault height, membrane curvature, and cable curvature are also taken into account. The fundamental forms and systems, along with the creative intention, are developed. Around the creative theme, continuous adjustments are made to refine and elevate the design.
Pre-stress is a crucial parameter in form-finding analysis, closely related to factors such as membrane materials, structural systems, membrane unit forms, external loads, and installation methods, requiring comprehensive analysis and selection. Different membrane materials have varying ultimate strengths, linear elastic moduli, creep characteristics, and strain compensation values. The structural characteristics of flexible or semi-flexible systems are significantly influenced by pre-stress, whereas rigid systems are less affected. Under any external load, at any point within a membrane structure, neither of the two principal stresses should be simultaneously less than zero (to avoid wrinkling).