Abstract
The paper proposes a method to enable analyzing any large deformation of membrane structures. If the analysis uses even very small rigidity against compression in the structures, the computation becomes multi-bifurcated problem and unstable. The original compression-free model used in the method keeps the structures in tension field and this makes computing the deformation always very stable. The paper uses the advantage of the method and shows a snapping phenomenon during constructing a membrane dome. Though the snapping phenomenon is not so public, the phenomenon occasionally happens in the construction site and it causes the destruction.
Highlights
Since membrane structures are light, expandable and compactly folded, the structures are widely used in various ways
As an example of analyzing the large deformation, the paper shows snapping phenomena of a membrane dome occurring in the inflation
If the tangent stiffness equation shown by Equation (8) derived from differentiating the equilibrium equations of Equation (5) and Equation (6) is used in the iterative methods, the iteration quickly converges to the equilibrium solution
Summary
Since membrane structures are light, expandable and compactly folded, the structures are widely used in various ways. When the structure is constructed or expanded, the characteristic brings unexpected phenomena, such as snapping of a membrane dome shown in the paper. In order to estimate exactly those phenomena, we need a method that can stably compute any state of the membrane structure. If compressive force in the element occurs even very small, computing the equilibrium necessarily becomes a multi-bifurcated problem. Since the compressive force in the membrane is essentially very small, using the compression-free unit is appropriate and besides the use makes the analysis completely free from the multi-bifurcated problem. The method can stably compute equilibrium solutions in any state of membrane structures. As an example of analyzing the large deformation, the paper shows snapping phenomena of a membrane dome occurring in the inflation. If the dome came to just before the snapping, the dome surly ended broken
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