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中文摘要：
力密度法在张拉膜结构找形过程中不能准确反映膜线单元所代表膜面区域的长度和宽度的非线性变化，找形结果与真实解存在一定的差距。该文提出一种考虑膜面二维变形的改进非线性力密度法，在找形计算过程中同时考虑膜面长度和宽度的变化，并采用Matlab编制了与专业索膜结构软件Easy数据格式兼容的计算程序，通过对比算例证明这种方法可以获得更接近理论解的结果。最后将该方法成功应用于上海2010年世博会世博轴屋盖超大型张拉索膜结构的分析。
英文摘要：
The form finding analysis of tensile membrane structures by the force density method does not reflect the nonlinear deformations in the length or width directions of the membrane areas represented by membrane links, leading to some differences between the numerical result and the real solution. This paper presents an improved nonlinear force density method taking into account for the effect of 2-dimensional deformations of the membrane surface. The membrane deformations in both length and width are considered during the calculation process. The computation program is also designed using Matlab and its data formats are compatible with Easy, a professional program for the analysis of cable and membrane structures. It is proved that the result obtained by the proposed method is closer to the theoretical solution through the comparison example. Finally this method is employed successfully in the analysis of the super-huge tensile cable-membrane roof of the Expo Axis project for Expo Shanghai 2010.
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Shape determination problem of spatial cable-frame type of suspended single-layer reticulated shells
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