Static Analysis For Spatial Cable And Membrane Structures By Force Density Method

Tension membrane structures, as a type of tension integrity structure, have been gradually developed since the 60's of the 20th century and increasingly used in China in recent years. As a tension membrane structure, its shape and internal forces are coupled with each other. Therefore, static analysis, including form-finding and loading analysis, is essential to this type of structure. The purpose of analysis is to find the equilibrium shape and corresponding internal forces. And the interaction between the membrane structure and the supporting structure is one of the difficult and key problems in static analysis. Because it is concerned with whether the analysis result is accurate and whether the strength and rigidity of the structure are satisfied with the safety requirement. The Chinese code of 《Technical specification for membrane structures》 suggests that supporting structure and membrane structure should be analyzed integrally if large displacements occur for the supporting nodes. Consequently, it is very necessary to study the problems of interactions between the membrane and the supporting structures during form-finding and loading analysis.In this paper, the static analysis is based on the force density method. According to stress equivalence and rigidity equivalence, a membrane structure is discreted into a cable-net structure in static analysis. The main work of the thesis is summarized as follows:A. Form-finding analysis for membrane structures with rigid point supports:1. The concepts of element's force density matrix and total force density matrix are put forward and the programming for force density method of membrane structures' form-finding is developed. The new way of formulating and programming can greatly raise the computation speed and reduce the computation time. Then relationships between membrane stresses ratio in warp and weft directions or membrane and cable stresses ratio with the initial equilibrium shape or the supports reactions are studied by the program.2. To solve the saw-teeth-shape problem at the boundary between the membrane pieces, T-elements are introduced and force density matrix of the T-elements is derived. Some examples are given. And the proposed approach proves to be feasible. Also, the program proves to be correct.B. Integral form-finding for the membrane structure and the supporting...