Abstract Different from large deflection analyses of plates and shells, for analysis of an isotropic membrane structure a form finding procedure is first performed to find the new geometry of membrane. With this new geometry, large deflection analysis is conducted and the membrane works in a pure membrane state. In the conventionally numerical approaches for analysis of membranes, form finding and large deflection analysis are performed separately and quite complexly by different techniques. To overcome this difficulty, this paper proposes a unified adaptive approach (UAA) for analysis of membranes in the framework of isogeometric analysis (IGA). In UAA, both form finding and large deflection analysis are simultaneously and simply performed based on a modified Riks (M-R) nonlinear solver. As another advantage of UAA, it can be applied to various types of structures without any limitation or modification. For membranes, the proposed approach performs both form finding and large deflection analysis naturally. It is convenient that UAA automatically performs large deflection analysis without form finding when plates or shells are considered. Based on the adaptation of UAA, nonlinear responses of plates/shells and membranes are first obtained at the same time in this paper. Especially, a new type of equilibrium path of membranes is first proposed via UAA. The path includes two parts: one is obtained by form finding and another is from large deflection analysis. High accuracy and efficiency of the proposed approach and the present formulation are verified via some benchmark problems. Effects of slenderness ratio, curvature and boundary condition on form finding and nonlinear responses of membranes are rigorously investigated. Some new equilibrium paths of square and cylindrical membranes are first provided.

中文翻译：

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膜结构的统一自适应方法：找形和大挠度等几何分析

摘要 与板壳大挠度分析不同，对于各向同性膜结构的分析，首先要执行找形程序来寻找新的膜几何形状。使用这种新几何结构，可以进行大挠度分析，并且膜在纯膜状态下工作。在用于分析膜的传统数值方法中，找形和大挠度分析是通过不同的技术单独且相当复杂地进行的。为了克服这个困难，本文提出了一种统一自适应方法（UAA），用于在等几何分析（IGA）的框架内分析膜。在 UAA 中，基于改进的 Riks (MR) 非线性求解器同时且简单地执行找形和大变形分析。作为UAA的另一个优势，它可以应用于各种类型的结构而没有任何限制或修改。对于膜，所提出的方法自然地执行找形和大挠度分析。当考虑板或壳时，UAA 自动执行大变形分析而无需找形，这很方便。基于UAA的自适应，本文首次同时获得板/壳和膜的非线性响应。特别是，首次通过UAA提出了一种新型的膜平衡路径。路径包括两部分：一是找形得到，二是大挠度分析。通过一些基准问题验证了所提出的方法和当前公式的高精度和高效率。细长比的影响，曲率和边界条件对找形和膜的非线性响应进行了严格的研究。首先提供了一些新的方形和圆柱形膜的平衡路径。