Normal and shear stress distributed points on thin walled corrugated tubes by conformal transformation technique

Abstract

The mapping between the two symmetrical unusual complex geometries is used to correlate the parameters by conformal transformation technique. To locate the actual localized stress points (normal and shear) in the thin-walled corrugated tubes (U-shape bellows convolution) geometry, physical correspondence and relationship is compared to orthotropic plate. The transformation of the associated components of membrane stress moment's components between plate and bellows is discussed. The distributed stress-points on the top, center, and bottom parts of the convolution are technically defined and associated nature of the stresses has been confirmed by correlation. The positioning of the stress- points on the convolution geometry surfaces at the top, middle and bottom parts correspondingly in comparison with plate signifies the pressure-based meridional stresses, circumferential membrane stress, and deflection-based meridional stresses respectively. The stress defined theoretical conformation maps are well verified with FEA simulation and confirms the location with type of the stresses by comparing it with the experimental results. The result obtained by both the methodologies found in close match and well verifies the identification and nature of the associated stresses. This study is very useful to compute the stresses for the complex symmetrical shaped metal bodies made up of the thin walled thickness. Complicated shaped bodies could be compared with the analogous simple geometry plates to define the stress-strain locations. The study is more useful in the case of the existence of the plane stress conditions of the bodies.