LAUSR

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.