Research of the Stress-Strain State of Anisotropic Parts of Interference Fits Based on the Variational RVR-Method

A variational RVR method was proposed for calculating the stress-strain state of statically loaded interference parts that fit in the automated design of critical structural elements. The method is based on Reissner's variational principle, the Vekua method, and the theory of R-functions. The application of Reissner's principle made it possible to increase the accuracy of solving boundary value problems due to independent variation of the displacement vector and stress tensor. The Vekua method allowed for replacing a 3D problem with a regular sequence of solutions to two-dimensional problems. The theory of R-functions at the analytical level considered the geometric information of boundary value problems, which was necessary for constructing solution structures. The RVR-method algorithm was used in the computer program CylShell_RVR, developed by the authors, designed to calculate anisotropic (in particular, isotropic) elastic cylinders of arbitrary thickness. To evaluate the RVR-method's effectiveness, its numerical implementation was performed for a joint part (bandage) made first of an isotropic material (for comparison with solutions to the Lame problem) and then of fiberglass. Depending on the number of approximations and nodes of Gaussian quadrature formulas, as well as the anisotropy of the material, the required displacements and stresses along the thickness of the bandage were presented in tabular and graphical forms.