| Summary |
Geometrically nonlinear finite element analyses based on shell theory, membrane theory and tension field theory were carried out to discuss directions of major principal stresses in a stretchable circular membrane with a rotation hub. From the simulation results on shell theory, it was presented that the stress field around the hub in the wrinkled region are similar to the plane stress field given by the membrane theory due to the geometrical constraint on wrinkles. According to this stress field including some compressive stresses, it was clarified that the direction of the major principal stresses is drastically changed in the vicinity of the hub, and is unchanged in only wrinkled region with the negligible principal stress ratio (minor principal stress / major principal stress). In tension field theory, since the membrane can carry no compressive stresses, the direction of the major principal stresses is unchanged in any wrinkled region. As a result, tension field theory is unable to predict precisely the directions of the principal stresses within the wrinkled region around the hub as well as the wrinkled region with the negligible principal stress ratio.
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