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工程力学  2012 

充气膜结构零应力态求解

DOI: 10.6052/j.issn.1000-4750.2011.03.0153, PP. 134-140

Keywords: 充气膜结构,分析全过程,零应力态,协调矩阵广义逆,逆解析数值分析

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Abstract:

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。

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