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Fiber-reinforced plastic (FRP) tubes are used in many different industries, such as electrical engineering and pipeline construction. The tubes are frequently subjected to bending loads, depending on the application. In order that the dimensioning of the tubes can be ensured, analytical bending models are used to calculate the resulting stresses, strains and displacements in the individual layers of the laminate. This enables the making of a statement about the failure of the fiber-reinforced tube by choosing an appropriate failure criterion. For the use of these bending models, it is necessary to understand the respective underlying theory. The theory provides the basis for the mathematical description of the mechanical properties for a single-layered tube and using the relationships between the stresses and strains that occur in the Cylindrical coordinate system for this calculation step. For this reason, a redefinition of the compliance matrix from the transformation about the winding angle to the Cylindrical coordinate system and a modification of the stress and strain vectors is necessary, because the defined Cartesian coordinate system of the model cannot be used for wounded FRP tubes. The transformation causes an exchange of entries in the compliance matrix, which remain in the correct relationship between the particular stress and strains. This step is not specified and may lead to incorrect results due to the incorrect entry of compliances. The present publication refers to sketch on this issue and represent a simplification of the changeover to the level required by the bending models notation of vectors in the form of a permutation. In addition, a new name for the pre-acquisition of the redefined compliances is given to prevent confusion when entering the material law of a bending model. Finally, the permuted and redefined compliances are proved in an example to determine their accuracy.
Review of elasto-static models for three-dimensional analysis of thick-walled anisotropic tubes
(2023)
Most shell or beam models of anisotropic tubes under bending have no validity for thick-walled structures. As a result, the need to develop three-dimensional formulations which allow a change in the stress, strain and displacement distributions across the radial component arises. Basic formulations on three-dimensional anisotropic elasticity were made either stressor displacement-based by Lekhnitskii or Stroh on plates. Lekhnitskii also was the first to expand these analytical formulations to tubes under various loading conditions. This paper presents a review of the stress and strain analysis of tube models using three-dimensional anisotropic elasticity. The focus lies on layered structures, like fiber-reinforced plastics, under various bending loads, although the basic formulations and models regarding axisymmetric loads are briefly discussed. One section is also dedicated to the determination of an equivalent bending stiffness of tubes.