THE ALGORITHM OF ZERO-STRESS STATE OF PNEUMATIC STRESSED MEMBRANE STRUCTURE

The whole analysis process of pneumatic membrane structure contains nine states and seven analysis processes. Zero-stress state is the corner-stone of the analysis and design of pneumatic structures, and it combines the numerical analysis state and actual physical state closely. According to the logical model of the whole analysis process of pneumatic structures, a numerical analysis method to solve zero-stress state from the elasticized equilibrium state was firstly proposed, which was called nonlinear compatibility matrix M-P inverse method. Firstly, the pneumatic membrane structure was transferred into grid structure by using membrane link to simulate membrane surface, and the unstressed length and elongation were calculated from tension and material parameters of the elasticized equilibrium state. Secondly, on the basis of equilibrium matrix theory of pin joint structures and small deformation assumption, the compatibility equation of system was established. Using compatibility matrix M-P inverse, the nodal displacement was calculated by solving the compatibility equation, and the configuration of a new state could be obtained through reverse superposition. Finally, the membrane link tension vector and the nodal unbalanced force vector at the new configuration were calculated. The zero-stress state can be solved iteratively. According to the algorithm, the program was coded with MATLAB. The correctness and efficiency of this method were verified by several examples. The work has theoretical significance and practical value for pneumatic membrane structural design.