Predicting actual state of membrane structures based on given planar patterns

Abstract

After planar patterns are assembled, the actual state of the constructed membrane structure including stress and shape, may be quite inconsistent with the designed one due to its undevelopable surface characteristic. However, load analysis is usually conducted based on the ideal form-found state, which results in different bearing capacity and structural behavior from actual situation, and wrinkles and excessive stresses may occur in severe cases. Therefore, load analysis should be performed on the actual state assembled by cutting patterns. The paper presents a technique for predicting the actual state based on given patterns with considering weld seams. The boundary condition of structures and the contour profile of patterns are known, after simply meshing patterns, an initial assumed model is established in accordance with the corresponding topological mesh. Then the method updates the geometry of assumed model iteratively by performing 3D equilibrium analysis until the deformation is within a certain tolerance. The approach ensures convergence to the predicted actual state formed from planar patterns. The feasibility of the technique is validated by several numerical examples.