Computation method of zero-stress state of pneumatic stressed membrane structure

The whole analysis process of pneumatic stressed membrane structure contains nine states and seven analysis processes. The zero-stress state is the corner-stone of analysis and design of pneumatic stressed structure, and has significant impact on the pre-stressed state and load state. According to the logical model of the whole numerical analysis process of pneumatic stressed structure, a numerical analysis method to solve the zero-stress state from the elasticized equilibrium state was firstly proposed, called linear compatibility matrix M-P inverse method. Firstly, the pneumatic membrane stressed structure was transferred into grid structure by using membrane link to simulate membrane surface. Secondly, on the basis of equilibrium matrix theory of pin joint structure and small deformation assumption, compatibility equation of system was established. Thirdly, the unstressed length and elongation of links were calculated from the tension and material parameters of elasticized equilibrium state. Finally, using compatibility matrix M-P inverse, the nodal displacement was calculated by solving compatibility equation, the configuration of zero-stress state could be obtained through reverse superposition, and the stress was released. According to the algorithm, the program was coded with MATLAB. The correctness and efficiency of this method were verified by several numerical examples, and it could be found that one elasticized equilibrium state corresponded to one configuration of the zero-stress state. The work has theoretical significance and practical guidance value for pneumatic membrane structural design.