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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 process of aerated membrane structure analysis includes nine states and seven analysis processes. Zero stress state is the basis of structure analysis and design. The numerical analysis state of structure and the actual physical state are organically connected. This paper presents for the first time an inverse analytical numerical analysis method from elastic equilibrium to zero stress, and nonlinear generalized inverse matrix method. Firstly, the membrane surface is modeled by the membrane element, and the membrane structure is transformed into a grid structure. The stress-strain length and elongation of the membrane are calculated from elastic equilibrium prestress and material parameters. Then, based on the theory of equilibrium structure of the rod system and small Deformation assumptions, the establishment of the coordination equation of the system, by the generalized inverse MP matrix solution to solve the node displacement, inverse stack to find the new state configuration. Based on the new configuration, the tension vector and the unbalance force vector are calculated, and the zero stress state is solved iteratively. According to this algorithm, the calculation program is compiled by MATLAB. The example analysis shows that the method is correct and efficient. This article has important theoretical significance and practical guiding value for the design of inflatable membrane structure.