充气膜结构零应力态求解

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

充气膜结构分析全过程包括9个状态和7个分析过程,零应力态是结构分析与设计的基础,将结构数值分析态和实际物理态有机联系起来。该文首次提出了一种从弹性平衡态到零应力态的逆解析数值分析方法,非线性协调矩阵广义逆法。首先,用膜线单元模拟膜面,将膜结构转化成为网格结构,由弹性平衡态预张力和材料参数,计算膜线无应力长度和伸长量;然后,基于杆系结构平衡矩阵理论和小变形假定,建立体系的协调方程,由协调矩阵M-P广义逆求解节点位移,逆向叠加求出新状态位形。根据新位形计算膜线张力向量和节点不平衡力向量,迭代求解零应力态。根据该算法,用MATLAB编制了计算程序。算例分析验证了该方法的正确性和高效性。该文对充气膜结构设计具有重要理论意义和实际指导价值。

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.